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APPENDIX A
INTRODUCTION TO SPREADSHEET1S
Computerized spreadsheets are available nearly everywhere, and they can be easily applied to economic analysis. In fact,
spreadsheets were originally developed to analyze financial data, an d they are often credited with initiating the explosive
growth in demand for desktop computing.
A spreadsheet is a two-dimensional table, whose cells can contain numerical values, labels, or formulas . The software
automatically updates the table when an entry is changed, and there are powerful tools for copying formulas, creating
graphs, and formatting results.

THE ELEMENTS OF A SPREADSHEET

A spreadsheet is a two-dimensional table that labels the columns in alphabetical order A to Z, AA to AZ, BA to BZ, etc.
The rows are numbered from 1 to 65,536 or higher. Thus a cell of the spreadsheet is specified by its column letter and row
number. For example, A3 is the third row in co]umn A and AA6 is the sixth row in the twenty-seventh column. Each cell
can contain a label, a numetical value, or a formula.
A label is any cell where the contents should be treated as text. Arithmetic cannot be performed 011 labels. Labels are
used for va1iable names, row and column headings, and explanatmy notes. In Excel any cell that contains more than a
simple number, such as 3. 14159, is treated as a label, unless it begins with an=, which is the signal for a fonnula . Thus
2"'3 and B1+B2 are labels. Meaningful labels can be wider than a nonnal column. One solution is to allow those cells to
"wrap" text, which is one of the "alignment" options. The table heading row (row 8) in Example A-1 has turned this on
by selecting row 8, right-clicking on the row, and selecting wrap text under the alignment tab.
A numerical value is any number. Acceptable formats for enu·y or display include percentages, currency, accounting,
scientific, fractions, date, and time. In addition the number of decimal digUs, the display of $ symbols, and commas for
"thousands" separators can be adjusted. The format for cells can be changed by selecting a cell, a block of cells, a row, a
column, or the entire spreadsheet. Then tight-click on the selected area, and a menu that includes "fonnat cells" will
appear. Then number formats, aUgnment, borders, fonts, and patterns can be selected.
Formulas must begin vvith an =, such as 3"'4A2 or =B l B2. They can include many functions-financial, statistical,
trigonomenic, etc. (and others can be defined by the user). The formula for the "current" eel] is displayed in the formula
bar at the top of the spreadsheet. The value resulting from the formula is displayed in the cell in the spreadsheet.
Often the printed-out spreadsheet will be pat1 of a report or a homework assignment and the fmmulas must be
explained. Here is an easy way to place a copy of the fom1ula in an adjacent or nearby cell. (1) Convert the ceII with the
fonnula to a label by inserting a space before the= sign. (2) Copy that label to an adjacent cell by using cut and paste. Do
nm drag the cell to copy It, as any formula ending with a number (even an address like B4) will have the numher
automatically incremented. (3) Conve11 the original formula back into a formula by deleting the space.

DEFINING VARIABLES IN A DATA BLOCK

The cell Al, top left corner, is the HOME ce11 for a spreadsheet. Thus, the top left area is where the data block should be
placed. This data block should have every variable in the spreadsheet with an adj acent label for each. This data block
suppmts a basic ptinciple of good spreadsheet modeling, which is to use variables in your models.
The data block in Example A-1 contains entered data-the loan amount (Al ), the number of payments (A2), and the
interest rate (A3), and compured data-rhe payment (A4) . Then instead of using the loan amoum of $5000 in a formula,
the cell reference Al is used. Even if a value is referenced only once, it is better to include it in the data block. By using
one location to define each variable, you can change any value at one place in the spreadsheet and have the entire
spreadsheet instantly recomputed.
Even for simple homework problems you should use a data block.
1. You may be able to use it for another problem.
2. Solutions to simple problems may grow into solutions for complex problems.

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3. Good habits, like using data blocks, are easy to maintain once they are established.
4. It makes the assumptions clear if you've estimated a value or for grading.
In the real world, data blocks are even more impmtant. Most problems are solved more than once, as more and more
accurate values are estimated. Often the spreadsheet is revised to add other vmiables, time periods, locations, etc. Without
data blocks, it is hard to change a spreadsheet and the likeHhood of missing a required change skyrockets.
If you want your formulas to be easier to read, you can name your va1iables. Note : In Excel, the cell's location or name
is displayed at the left of the fotmula bar. Variable names can be entered here. They will then automatical1y be applied if
cell addresses are entered by the point and click method. If cell addresses are entered as A2, then A2 is what is displayed.
To change a displayed A2 to the name of the cell (LoanAmount), the process is to dick on Insert, dick on ame, click on
Apply, and then select the names to be applied.

COPY COMMAND
The copy command and relative/absolute addressing make spreadsheet models easy to build. If the range of ceUs to be
copied contains only labels., numbers, and functions, then the copy command is easy to use and understand. For example,
the formuJa =EXP(l.9) would be copied unchanged to a new location. However, ceH addresses are usually part of the
range being copied, and their absolute and relative addresses are treated differently.
An absolute address is denoted by adding$ signs before the column and/or row. For example In Figure A-la, $A$4 is
the absolute address for the interest rate. When an absolute address is copied, the column and/or mw that is fixed is
copied unchanged. Thus $A$4 is completely fixed, $A4 fixes the column, and A$4 fixes the row. One common use for
absolute addresses is any data block entry, such as the interest rate. When entering or editing a fmmula, changing between
A4, $A$4, A$4, $A4, and A4 is most easily done using the F4 key, which scrolls an address through the choices.
In contrast, a relative address is best interpreted as directions from one cell to another. For example in Figure A- l a, the
balance due in year t equals the balance due in year t - 1 minus the principal payment in Year t. Specifically for the
balance due in Year 1, D10 contains =D9-ClO. Fro m cell D lO, cell D9 is one row up and ClO is one column to the left.
so the fmmula Is really (contents of 1 up) minus (contents of 1 to the left). When a cell containing a relative address is
copied to a new location, it is these directions that are copied to detetmine any new relative addresses . So if cell D10 is
copied to cell Fl4, the formula is =F13-E14.
Thus to calculate a loan repayment schedule, as in Figure A- 1, th e row of formulas js created and then copied for the
remaining years.

EXAMPLE A- 1
Four repayment schedules for a loan of $5000 to be repaid over 5 years at an interest rate of 8% were shown in Table
3- 1. Use a spreadsheet to calculate the amortization schedule for the constant principal payment option.

SOLUTION
The first step is to enter the loan amount, number of periods, and interest rate into a data block in the top left pan of the
spreadsheet. The next step is to calculate the constant plincipal payment amount, which was given as $1252.28 in
Table 3-1. The factor approach to finding this value is given in Chapter 3 and the spreadsheet function is exp1ained in
Chapter 4.
The next step is to identify the columns for the amortization schedule. These are the year, interest owed, principal
payment, and balance due. Because some of these labels are wider than a normal column, the cells are fmmatted so that
the text wraps (row height increases automatically). The initial balance is shown in the Year-o, row.
Next, the formulas for the first year are written, as shown in Figure A- la. The interest owed (cell BlO) equals the
interest rate ($A.$4) times the balance due for Year 0 (D9). The principal payment (celJ ClO) equals the annual payment
($A.$6) minus the interest owed and paid (BlO). Finally, the balance due (cell D10) equals the balance due for the
previous year (D9) minus the principal payment (ClO). The results are shown in Figure A- la.
Now cells Al0 to D lO are selected for Year 1. By dragging down on the right comer of D10, the entire row can be
copied for Years 2 through S. ·ote that If you use cut and paste, then you must complete the year column separately
(dragging increments the year, but cutting and pasting does not). The results are shown in Figure A- lb.

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A B C D E
1 Entered Data.
2 5000 Loan Amount
3 5 Number of Payments
4 8% Interest Rate
5 Computed Data
6 1.252.28 Loan Payment
7
Interest Principa.l Balance
8 Year Owed Payrnent Due
9 0 5000:00
10 1 400.00 852.28 4147.72 =D9-C10
11 / ~
12 ~$A$4*D9 '"=$A$6- B10

(a

A B C D E
Interest Principal Balance
8 Year Owed Payment Due
9 0 5000.00
10 1 400.00 852.28 4147.72
11 2 331.82 920.46 3227.25
12 3 258.18 994.10 2233.15
13 4 178.65 1073 .63 1159.52
14 5 92. 76 1159.52 0.00 =D13- C14
15 / ~
16 ~$A$4*D13 =$A$6-B1 4

( b)
FIGURE A-1 (a) Year 1 amortization schedule. (b) Completed a:mo1tization schedule.

This appendix has introduced the basics of spreadsheets. Chapter 2 uses spreadsheets and simple bar charts to draw
cash flow diagrams. Chapters 4 to 15 each have spreadsheet sections. These are designed to develop spreadsheet
modeling skills and to reinforce your understanding of engineering economy. As spreadsheet packages are built around
using the computer mouse to click on cells and items In chaits, there is usually an intuitive connection between what you
would like to do and how to do it. The best way to learn how to use the spreadsheet package is to simply play around with
it. In additi on, as you look at the menu chokes , you will find new commands that you hadn ' t thought of but will find
useful.

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APPENDIXB
TIME VALUE OF MONEY
CALCULATIONS USING SPREADSHEETS
AND CALCULATORS 1

Spreadsheets and financial calculators are perfect tools for solving economic problems with financial functions that are
very similar to the engineering economy factors-but more powerful. ow there are even smatt phone apps with the same
capabilities. Some types of programmable calculators can be used in the FE exam, making interest tables unnecessary.
This appendix focuses on the use of spreadsheets and cakulators to solve simple time value of money problems.
Inducled are the fo1lowing topics:
• Basics of a 5-Button Spreadsheet Calculator
• Spreadsheets, Calculators, and the FE Exam
• Additional Spreadsheet and Calculator Capabdities
• More Complex Examples
• Possible Errors and Their Solutions

BASICS OF A 5-BUTTON SPREADSHEET CALCULATOR

Figure B-1 shows a variety of cash f1ow diagrams and a five button calculator template that can be used to solve
economic problems quickly and easily.
P = 1500

B-1 F = I J0.25 B-2 B-J tI F = 200

•
i = 5%
t
0- - 1- -2
i = 7%
0- - 1 - - 2- -3
i = 3.5%
0- - 1- - 2- -3

t
P=?
i
P = 5000
l A ="(3000 t
t
A= ?
+ t

B- P = 1000 B-5
i=?
t
0- - 1- -2- -3- -4- -5
F = JOO

•
i = 6.25% A = 450
+
r - - 1- -2 ...
+_j
,i = ?
t t
A = 250
+ t +
P = 2000

For example B-1, the input variables from the cash flow diagram are placed in cells B2 through F2, with the interest
rate in cell B2, the number of petiods in cell C2, etc. Cell H2 calculates the PV using the appropriate cell addresses for the
input variables. The equations used in column Hare shown in column I. Spreadsheets such as Excel and Google docs use
this type of format; others such as Open Office and Quattro Pro use a slightly different fonnat for equivalent functions.
Any of the spreadsheet functions may be copied to a new row and then new data can be inserted to solve similar
problems . Thus, the five annuity functions in Figure B-1 are coJlectively a 5-button financial ca]culator. The same inputs
may be keyed into a financial or programmable calculator to obtain identica] resu]ts. When using a calculator, it is
important to enter all variables if you do not know what value was entered last.. You could have an unknown va]ue
residing in the calculator's memory. Additional examples of using the 5-button spreadsheet calculator can be found in
Chapters 3 and 4.

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EXAMPLE B1-B5
5-BUITON SOLUTION

B C D
t N PIT
s., 2 0
7.0% 3 -3000
3

FIGURE B-1 Cash flow diagrams and the 5-burton spreadsheet calcularor.

EXAMPLE B-1 FACTOR SOLUTIO

The present va]ue of a ca.sh flow of $110.25, two years in the future, at an interest rate of 5% is -$100 .00. ate that
this follows the convention of positive numbers for inflows and negative numbers for outflows. Use of the spreadsheet
or ca]culator avoids looking up factors, which is a primary source of eITors.
Using interest factors,
B-1 P = 110.25(P/F, 5%, 2) = 110.25(0.9070) = $100.00

EXAMPLE B-2 FACTOR SOLUTIO

The FV function can determine the future value of both a P and an A in a :single calculation. Note that negative values
of PV and P T return a positive value for FV of $15,770.
Solving B-2. using factors and the interest tables requires two lookups, two multiplications, and one addition,
because the tabulated factors can on]y convett from one type of cash flow to another.
B-2 F = 3000(F/A, 7%, 3)+5000(F/P, 7%, 3) = 3000(3.215)+5000(1.225) = $15, 770

EXAMPLE B-3 FACTOR SOLUTIO

A unifmm cash flow can be determined using the PMT function, with P and F being entered in a :single calculation.
Using factors requires several steps, as shown here . If the 3.5% table were not avaUable, this wou]d also require
interpolation between the 3% and the 4% tab]es. Due to the round off of the interest factors to 4 significant digjts, the
factor answer is slightly less precise.
B-3 A= 1500(NP, 3.5%, 3) + 200(A/F, 3.5%, 3) = 1500(0.3569) + 200(0.3219)
=$599.73

EXAMPLE B -4 FACTOR SOLUTIO

An unknown interest rare can be solved in a single computation, even though there are three types of cash flows: a P,
an F, and an A. The RATE function requires at least one positive cash fl ow (inflow) and at least one negative cash Oow
(outflow). Using factors and interest tables would :require solving the folJowing equation (or a :similar one):
B-4 0 = 1000 - 250(P/A, i, 5) + lOO(P/F, i, 5)
This requires either an iterative solution or using interpolation.

at 5% 0 = 1000 - 250(4.329) + 100(0.7835) = - 3.90

a 6%, 0 = 1000 - 250(4.212) + 100(0.7473) = 21.7
Interpolating, i = 5.15%
Spreadsheets and calculators are much more efficient than factors when solving for unknowns that require
interpolation, such as the interest rate.

EXAMPLE B-5 FACTOR SOLUTIO

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The PER function will disp lay the answer in fractional periods; in this case, 5.37 peliods. Using factors to solve for
the number of periods again requires the use of interpofation or iterative solutions .
B-5 0 = -2000 + 450(P/A, 6.25%., n)
(PIA. 6.25%, n) = 2000/450 = 4.444
This will require interpolation to find two variables, one interpolation to find a set of values for n at 6.25% (because
there is no 6.25% table available), and another for determining the answer. These will not be performed here, but yield
an answer of 5.37 periods.

There are many advantages to using spreadsheets and financial calculators instead of, or in addition to, using the
interest tables . These include:
• Time is saved because problems are entered directly without having to look up factors in tables, then copying those
factors. Problems are solved with the use of a few key strokes.
• There is less chance for error because there are fewer steps. Many errors are made in looking up factors due to
looking down the wrong column or row. Transcribing errors, or finding a factor but writing it down wrong, are
minimized.
• There is no need to interpoJate when detennining an interest rate or number of pe1iods. This greatly speeds this
type of calculation.
• Students who use a spreadsheet will leave an elecu-onic, srudent accessible paper trail. Once a spreadsheet is
successfully built, such as the one in Figure B-1, students can access these saved files for studying, performing
homework. and perhaps during a test. This can aid in students' learning and comprehension by focusing time and
attention on setting up problems rather than spending time doing financial arithmetic.

SPREADSHEET S, CALCULAT ORS, A ND T HE FE EXAM

The naming of variables is slightly different between engi neering economy, spreadsheets, and calculators. Table B-1
shows the typical naming conventions.
Spreadsheets use Equation B-1 to solve for the unknown variable. Equation B-2 rewrites this in standard factor
notation.

1 + o-nl (B-1)
PMT 11 - i, + FV(l + i)- 11 +PV =0
A(P/ A i,n) + F(P/ F i,n) +P =0 (B-2)

Financial calculators use Equation B-3 to solve for the unknown vaiiable . Note that Equation B-3 is written so that i is
entered as a percentage, so 8 is entered for 8%, which is how the interest rate is entered for financial calculators. How the
interest rate is entered is the single difference between how spreadsheets and calculators solve time value of money
problems .

1 (1 i/ 100)-nl
PMT [ - i;lOO I+ +FV(l i/ ]00)-n + PV =0
(B-3)

Since the factors are all positive, one of PMT, FV, or PV (or A, F, and P) must be different in sign from the other two.
If tv.ro positive cash flows are entered to solve for the third cash flow, then that third value must be negative to solve the
equation. These equations are the foundation for the sign conventfon that is used in financial calculators and the
spreadsheet annuity functions PV, FY, PMT, RATE, and ' PER.
There are three classes of calculators that are of interest. First, there are many financial or business calculators that
have buttons labeled i, N, PMT, PV, and FV or equivalents. The button for the uniform series cash flow, A, is labeled
PMT, because one of the most important uses of these calculators is for calculating loan payments (PM'I). Examples
include the Texas Instrument BAH Plus and BAH Pius Professional, the Sharp EL-738C, and the Hewlett Packard lObH.
We no longer recommend the HP 12C for new purchases since when solving for n, the 12C rounds fractional values of n
up to an integer value (see Example B-8). These calculators also typically have the capability to find the PY of complex
cash flow patterns, but we suggest using spreadsheets for more complex patterns.

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TABLE B-1 Naming Conventions in Engineering Economy, Spl"eadsheets, and Calculators

Variable Engin.ee.ring Ernnomy Spreadshe-ets 'Typical Cakulator Button

Present value p PV PV
Puture va]ue F FV FV

Uniform series A p T p T

Interest rate i RATE IN

umber of pe1iods n PER

There are also graphing cakulators that have the time va]ue of money cakulations in a menu. There are menu entries
for i, N, PMT, PV, and FVor equivalents. Example calculators include the Texas Instrument 83 and 84 Plus.
Finally, there are programmable scientific calculators where Equation B-3 can be entered to create the menu that is
built into the graphing caku]ators. For example, Chapter 17 of the manuals for the Hewlett Packard 33s and 35s details
tMs. These chapters use a non-standard notation of B or balance for PY and P or payment for PMT. We suggest using
standard notation and substituting P for Band A for P. 'ote that on the HP 35s this changes the checksum from 382E to
8DD6. The HP 33s and HP 35s calculators are currently allowed for use on the Fundamentals of Engineering (FE) exam.
while the financial and graphing calculators are not.
There are too many variations of labeling and physical layout of the keys and too many financial calculators for a text
to provide details. However, the website www.TVMCaks.mm provides good tutorials on financial calculators, and
calculator manuals are available for download from the manufacturers.
Some calculators are shipped from the factory with a setting of 12 months per year, so that n will be entered as years
for loans with monthly payments. We recommend that this be changed to 1 payment per "year or period" and left on this
setting. Then you know to enter n as the number of petiods or payments, and there is no confusion for prob]ems with
different length periods.
Phone apps are now widely available that perform as financia] cakulators, making it possible to cany the capability
anywhere.

AD·D ITIONAL SPREADSHEET AND CALCULATOR CAPABILITIES

When initia1ly building a spreadsheet. equations must be entered into a cell to solve the problem. In Figure B-1, the
following equation is entered into cell H2 to solve for the present value:

= PV(rate nper, pmt, [fv], [type])

The [ ] denotes that these are optional values where the default is zero. If nothing Is entered for the future value, it will
be assumed to have a zero value. If no value is entered for the type, pe1iodic cash flows (A) wiJl be assumed to occur at
the end of the time periods.

[ ype] = 0 (d fault) End of period cash flow

[type]> 0 Beginning period cash flow
Most financia] calcu]ators can be set to either end of period (default) or beginning of peliod cash flows.
The RATE function requires a combination of positJve and negative inputs in order to calculate an interest rate.

= RATE nper, pmt pv [fv], [type [gue s])

Note that the RATE function contains an optional input guess, where you can guess what the rate will be. If you do not
enter a value, the default is 10%. Uthe RATE function does not provide an answer, change the guess. An entry is usually
nae required. For more see the last section of this Appendix.

MORE COMPLEX EXAMPLES

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The following examples demonstrate problems that are more complex, but still make use of the basic spreadsheet annuity
functions .
• Example B-6 requires conversion of annual rates and periods to monthly.
• Example B- 7 is a PV problem including an initial payment and a salvage value.
• Example B-8 solves a discounted payback problem.
• Example B- 9 includes cash flows at the beginning of the period.
• Example B- 10 is an EAC problem with multiple cash flows.
• Example B- 11 involves the doubling, nipling, and quadrupling of money.

EXAMPLEB-6
Kris is buying a used car and needs to find the monthly payment. The loan is for $14,000, and the dealer is willing to
offer financing for 5 years at 6.5% interest. What is the monthly payment?

SOLUTION
First, we need to convert the period and interest rate to months. There are 60 (= 5 x 12) monthly payments at a monthly
interest rate of 6.5%/12 = 0.5417%. The required monthly payment is $273.93.

A B C D E p G H I
1 Problem i n PMT PV FV Solve for Answer Ponnul.a
2 B-6 0.5417% 60 -14000 0 p T $273.93 =P T(B2,C2,E2,F2)
3 PMT(rate, 11pe1~ pv, [fv], [type])

This problem can also be solved using a financial or programmable calculator. The keys on most calculators are the
same as the spreadsheet variables, so Plv!T(i, n, P, F) = PMT(0.5417%, 60, - 14000, 0) = $273.93. ote that the
calculator requires the same sign convention as spreadsheets.

EXAMPLEB-7
Automating a process will cost $8000 now, but it will save $2200 annually for 5 years. The machinery will have a
salvage value of $1500. What is the present wm1h of the machinery if the interest rate is 10%?

SOLUTION

1500

t t too t t
0- -1- -2- -3- -4- -5

j
8000

Let us first solve this with the tabulated factors .

PW = - 8000 + 2200(P/A • 09{ 5) + 1500(P/F, 10% 5)

= - 8000 + 2200(3.791) + 1500(0.6209
= - 8000 + 8340 + 931 = $1271
The spreadsheet can find the combined present value of the $2200 annual savings and the salvage value of $1500
hAr:mc;:i, thP intP1"Pc;:t r.::it P :mrl n11mho:>l' ,-,f ni>rinik .::irP tho:> <:.::1mo:>
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because the interest rate and number of periods are the same.
A B C D I!: p G H I
1 Problem i 11 PMT PV FV Solve for Answer Pormula
2 B-7 10.0% 5 2200 1500 PV -9271.11 =PV(B2,C2,D2,F2)
3 -8000 PV 1271.11 =-H2+E3

Notice that the present value of the future cash flows is negative when the A and F values are entered as positive
numbers. This comes from so]ving Equation B-1. Since in this case we want the positive PV of the returns to the
project, we can change the sign of the answer in step 2, subtracting the $8000 initial cash flow to find the PV of $1271.
Using a calculator, PV (i, n, A, F) = PV (10, 5, 2200, 1500) = -9271.11. The calculator finds the combined present
worth of the $2200 annual savings and the salvage value of $1500. The initial cash flow of $8000 is subtracted to find
the PV of $1271. 11. Like the spreadsheet, positive values for A and F produce a negative value for P.

EXAMPLEB-8
A firm might purchase a compute1ized quality contro] system. The proposed system wil1 cost $76,000, but is expected
to save $22,000 each year in reduced ove1time. The firm requires that all cost reduction projects have a discounted
payback of no more than 4 years with a 10% interest rate. Should the film invest in the new system?

SOLUTION

A B C D E F G H
1 Problem i 11 PMT PV FV SoJve for Answer
2 B-8 10.0% 22000 -76000 0 PER 4.45

The time for the system to pay for itself can be found using the PER function; the discounted payback period is 4.45
years. Because a proposed project can have a discounted payback of no more than 4 years, the project would not be
approved.
The problem can also be solved with a calculator using N(i, A, P, F) = N(10%, 22000, - 76000, 0) = 4.45 years.
Note that th e HP 12C calculator wil1 report 5 years. ln fact, the HP 12C will repmt N = 5 years when the payback
period .is as small as 4.005 periods.

EXAMPLEB-9
Some equipment is needed for a 4-year project. It can be leased for $15,000 annually, or it can be purchased for
$60,000 at the beginning and sold for $35,000 at the end. What Is the rate of return for owning the equipment rather
than ]easing it?

SOLUTION
Because the lease payments occur at the beginning of each period, [type] is set to any number above O (such as 1) to
automatically shift the cash flows into beginning rather than end of petfod. This affects only the A and not the F.

A B C D E p G H
1 Problem i n PMT PV FV Solve for Answer
2 B-9 4 15000 -60000 35000 RATE 23.49%

A financial calculator must also be shifted into begin rather than end mode, then enter i(n, A, P, F) = i( 4, 15000,
-60000, 35000) = 23.49%.
Without knowledge that the rate is nearly 25%, using the tabulated factors would require multiple trial solutions to
solve the following 3-factor equation.

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0 =- 60 000 + 15 000(F/ P,i, l )(P/A, i 4 + 35 000 P / F , i,4)

EXAMPLE B -10
What is the EAC to keep a piece of new equipment operating? The warranty covers repair costs for the first 2 years,
but expected repair costs are $1500 per year for the rest of the 7-year life. ormal maintenance is expected to cost
$1800 annually. There is an overhaul costing $8500 at the end of year 4. The firm 's interest rate is 8% .

SOLUTION
Whether solved with tables, spreadsheets, or a financial calculator, the first step is to draw the cash flow diagram.
0- -1- -2- -3- -4- -5- -6,____-7

1800
} } 1500 1
8500
iii
Let us first solve this with the tabulated factors.

EAC = 1800 + 1500(F/A 8%, 5)(A/ F, 8%, 7) + 8500 P/ F , 8%,4)(A/ P, 8%, 7

= 1800 + 1500(5 .867)(0.1121) + 8500(0.7350) 0. 1921
= 1800 + 986.5 + 1200 = 3986.5
With a spreadsheet, it is easiest to separately calculate the EUAC values for the repair costs and the overhaul.

A B C D E p G H
1 Problem i n PMT PV FV Solve for Answer
2 Repair 8% 5 1500 0 FV -8799.9
3 8% 7 0 -8799.9 I? T 986.,23
4
5 Overhaul 8% 4 0 8500 PV -6247.75
6 8% 7 -6247.75 0 PMT 1200.02
7
8 aim. 1800 EAC $3,986.25

This is very similar with a financial calculator. For the repair costs, FV(i, n, A, P) = FV (8, 5., 1500, 0) = -8, 799.90.
Since the i and P values are unchanged, they do not need to be re-entered. The only entry needed is N = 7, since the F
was just calculated. PMT(i, n, P, F) = PMT(8%, 7, 0, -8799.90) = $986 .23.
For the overhaul costs the i value need not be re-entered, PV(i, n, A, F) = PV(8%, 4, 0, 8500) = -6, 247.75. Now N
is changed w 7 and F to 0, then solving for PMT(i, n, P, F) = PMT(8%, 7, -6247.75, 0) = $1200.02.
Maintenance is $1800 per year..
Adding the three values is the same as before, and the EAC is $3986.25.

EXAMPLE B -11
How long does it take for your money to doub]e if you can eam 7% on your investment? Trip]e? Quadruple?

SOLUTION

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A B C D E F G H
1 Problem i n PMT PV FV Solve for Answer
2 B-11 7.0% 0 -1 2 PER 10.24
3 7.0% 0 -1 3 PER 16.24
4 7.0% 0 -1 4 PER 20.49

Using a financial calculator, the setup is similar~ for doubling, 11(i, A, P, F) = n(7, 0, -1, 2) = 10.24.
The problem can also be solved using functions, but requires interpolation, or can be solved mathematically.

F = P(l +in
2 = 1(1.0?t
ln (2) = n In (1.07)
n = n (2)/ In (1.07) = 0.6931 / 0.06766 = 10.24

POSSIBLE ERRORS AND THEIR SOLUTIONS

RATE and IRR

When using RATE or IRR, the #NUM! error may occur. Both of these functions are iterative~ they home in on an answer
using multiple attempts or iterations. The default staning point (guess) is 10%, and if a specific answer cannot be found
within 20 iterations, the e1rnr value appears. This usually happens for interest rates that are very high or very negative, but
even moderate answers can cause difficulty. The problem Is usually solved by trying values for [guess] that approximate
the answer.

EXAMPLE B -12
An account having $800,000 will be used to make a series of 20 annual payments of $150,000 each. What interest rate
is needed to fund the payments?

SOLUTION
A simple rate problem can unexpectedly result in an error message, but are usually corrected by inse rting a [guess].
Notice that the guess does not need to be very accurate.

A B C D E F G H I
1 Problem i n PMT PV FV Solve for Answer Formula
2 B-12 20 150,000 -800,000 0 RATE # M ! =RATE(C2,D2,E2,F2)
3 20 150,000 -800,000 0 RATE 18.10% =RATE(C3,D3,E3, F3,0,30%)

NPER
The function NPER is also iterative- like RATE and IRR. Unf0111.1nately, PER does not have a [guess] option to help .
NPER sometimes returns an etTor if the value is very large. The answer can sometimes be found by using GOAL SEEK,
as shown in Example B- 13.

EXAMPLE B -13
An account having $600,000 wiH be used to make a series of annual payments of $45,000 each. The account returns
7.5% per vear. How manv years will oavments be made?
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1.;:i,o per j'~dr. nuw IIIdUJ year.; wm !Jd)'meu~ ue llldU~ r

SOLUTION
Using PER returns an error showing that U could not solve the problem. NPER is increasing very rapidly as the
interest increases by a very small amount. This can be solved by finding a value of n where the PV or FV = 0. GOAL
SEEK returns a value of 617 plus years. SOLVER can also be used to provide the same answer.

A B C D E F G H I
1 Problem i n PMT PV FV Solve fo r Answer Fonnul.a
2 B-13 8% 45,000 -600,000 0 PER # M ! = PER(B2,D2,E2)
3 8% 617.3 45,000 -600,000 0 fV 0.00% =fV(B5,C5,D5,E5)

IGoal S@e:k ? X

s~ cell: H3

Toyalue : 0

By £Nnglng cell: CJ

L___!: 01(
J Cancel

STUDENT STUDY GUIDE

These questions are intended for self-study. Click the [solution] box to revea] a detailed solution.
B- InstaJJing a heat exchanger in an office buHd ing wm cost $750,000. It will save $65,000 annually for 20 years, when it will have a
1 saJvage value of $40,000. What is the PW of the heat exchanger at an interest rate of 5%?
Wi.,•Gi@i
B- Suppose that a computer costs you $150 0 to buy and you sell it 3 years later fo r $300. If your interest rate for the time value of
2. money is 8%, wha t is your annual cost of own ership?
Wi•ll',U•ki
B- How many months to pay off a credit card balance of $8000 with payments of $200? The card's monthly interest rate is 1.5%.
3 Assume th ere are no new charges.

Wi■j•GU-Ri

PROBLEMS
Key to icons: D = click to reveal answer; (9 = Green, which may include environmental ethics; G= Ethics other than
green; = autograded problems that are available online in Dashboard; = The icon indicates that a spreadsheet is
recommended.

Present Worth
B- A p rocess redes1gn wiIJ cost $70,000 now, but it wiIJ save $18,000 annua11y for 6 years . The new machinery will have a saJvage
1 value of $12,500. What is the present worth o f the machinery, if the in terest rate is 12%?

B- oving to a new faciUty will save 400,000 annually for 20 yea.rs. The cost of building the facility and moving is $2.5 millfon

•
2. now. The facility wi11 have a salvage value of $100,000. What is the facili ty's PW, if the interest rate is 12%?

B- A lottery pays the win ner $1 mjllion in 20 equal annual payments of $50,000. The firs t payment wiH be made at the end of the
3 second year. What is the p resent worth if the win ner 's annual interest rate is 5.25%?

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Equivalent Annual Worth

B- Yo u need to save $20,000 to buy a car in 3 years. At a 2% nomfoal annual interest rate, how much do you need to save each
4 month?
I
B- You can receive lottery winnings of either $800,000 now or $100,000 per year for the next 10 years. If your interest rate is 5% per
5 yea1~ which do you prefer?

B- A new road wiU cost $45 milli.on to build, and $2 mi.lHon annuaUy to maintain and operate over its 50-year li£e. The roadbed and
6 right-of-way are estimated to have a salvage value of $15 million. If the state highway department uses an interest rate of 5%, what
I is the EUAC for the road?
B- A new car will cost $24,000 to buy and $5500 annually to operate. If it is sold for $9300 after 6 years, what is the EUAC? Assume
7 that the owner's interest rate is 3% for the time value of money.

Price of a Bond
B- A $1000 bond has 15 more years to maturity, an interest rate of 6%, and it pays interest semj-annually. If the current market
B interest rate is 5%, what is the price of the bond?
I
B- A $1000 bond has 12 more years to maturity, an interest rate of 6%, and it pays interest semi-annually. If the current market
9' interest rate is 8%, what is the price of the bond?

B- An investor purchased a 10-yea.r, $20,000 corporate bond just over 12 months ago. The bond pays 6.5% interest, due semi-
10 annually. The current market interest rate for simifar bonds has increased to 7.25%. What price wil.l this bond sell for today?
I
Loan Payment
B- What is the month]y payment for a 5-year car loan al a nominal interest rate of 8.5%? The 1.oan's initial balanC'e is $16,885.
11

B- A couple is buying a house, but they need a mortgage for $150,000. A 15-year loan can be obtained for 3.25% annual interest.
12 What is the monthJy payment?
I
Number of Periods
B- A student owing $17,565 on a credit card has decided to use only a debit card jn the future. The nomina.l annual rate on the credit
13 card is 13.8%. If the student makes monthly payments of $250, how long is it until the credit card is paid off?

B- A homeowner may .install solar paneJs on the roof of .her house. The total installed cost is $15,000 after federal and state credits.
14 This solar system will meet the monthly electricity need, which costs $120 per month. The homeowner's interest rate is 3%
I annually.
(9 (a) If electricity prices remain constant, how long will it be until tlh.e system pays fo r itself?
{b) If electricity prices increase in the future, how will this affect the installation paying for itself?

Internal Rate of Return

B- An automated storage and renieval system will cost $135,000, but it will save $33,000 annualJy in labor costs. The system's
15 salvage value is expected to be $20,000 when it is renovated in 10 years. What is the rate of ~etum on the project? Do people need
G to be laid off to j ustify the instaJJation of the new system?
B- oving to a new faciUty will save $400,000 annu.ally for 20 yea.rs. The cost of buUding the facility and moving is $2.5 mi.lHon
16 now. The facility wm have a salvage value of $100,000. What is the rate of 11eturn on this project?

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. ,....., r, • ..,_ ,.. ,.,_ .__.._,..,.._....,.} , ., .., ..... . . . . .. , .._...., ._.....,.. r ..,.t:J.'' - , ....,,..'-"..._ ...,.._ ...,.,....,...'J,,...,OJOJ• , r ... . _....,.., .,._. .., •• ..._ • ._...,..._ ...,. ,._ • .._ ,.. .......... ._. • .• .._. ,..,...., I."",.....,.,, .._..._.., ,,

0
B- A new road wm cost $45 million to build, and $2 million annuaUy to maintain and operate over its 50-year life. The roadbed and
17 right-of-way are ,estimated to have a salvage va.lue of $15 million. If user benefits are ,estimated at $5.5 mi.Ilion annually, what is
the rate of return on this road?
B- Some equi pment is needed for a construction project. It can be leased for $150,000 annually, or it can be pu11chased for $900,000 at
18 the beginning and sold for $225,.000 at the end of 3 years. What is the rate of return for owning the equipment rather than leasing
o it?

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APPENDIXC
COMPOUND INTEREST TABLES
Values of Int.erest Factors When n Equals Infinity
Single Paym ent: Uniform Payment Series:
(F/P, i,oo) =oo (AIF, i,oo) = 0
(P/F, i,oo) = 0 (AIP, i,oo) = i
Ari thmetic Gradient Series: {FIA, /,oo) = oo
(NG, i, oo) = l/i {PIA, i, oo) = 1/i
(PIG, i, oo) = 1//2

-. - ., -. - .,
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1/4% Compound Interest Factors 1/4%

Sin.gle Payme;nt U,nifonn IPa,ymeRt Seriies Arit!l:imetic Gradient
Compoun d Pre~nt Sinking Capital Compound Present Gradient Gradient
Amount Worth Fund Recovery Amount Worth Un iform Present
Factor Factor Factor Factor Factor Factor Series Worth
find f Find P Find A Find A Find F find P Find A Find P
Given P Given F Giive n, f Given P Given A Given A Given G Given G
t) FIP PIF AIF AIP FIA PIA AIG PIG ,,
1 1.003 .9975 1.0000 1.0025 1:000 0.998 0.000 0.000 1
2 LOOS .9950 .49()4 ..-019 2.000 1.993 0.499 0.995 2
3 LOO& .9925 .3325 .3350 3:008 2.985 0.998 2.980 3
4 L0IO .9901 .2491 .2516 4.015 3.975 1.497 5.950 4
5 L0!3 .9876 . 1. 990 .2015 5:025 4.963 1.995 9.90 1 5
6 LOIS .9851 .1656 . 1. 681 6.038 5.948 2.493 14.&26 6
7 1.01& .9827 . 1418 .144-3 7:053 6.931 2.990 W.722 7
8 1.020 .9802 .1239 . 1264 &.070 7.9 1.l 3.4&7 27.584 8
9 L023 .9778 . 1100 . l 125 9:091 8.&89 3.9 3 35.406 9
10 L0?....5 .9753 .0989 . 1014 10. 113 9.&64 4.479 44.184 10
11 1.02& ..9729 .0898 :0923 11.139 I0.&37 4.975 53.913 u
12 L030 .9705 .0822 .0847 12. 167 11.&07 5.470 64.5 89 ]2
13 J.033 .9681 .0758 :0783 13.1 97 12.7T 5.965 76.-05 ]3
14 1.036 .9656 .0703 .0728 14.230 13.74 1 6.459 88.759 ]4
15 L03& .9632 .0655 .0680 15.266 14.704 6.953 102 .244 ]5
16 l.04!1 .9608 .0613 .0638 16.304 15.665 7.447 l 16.657 16
17 1.043 .9584 .0577 .0602 17.344 16.624 7.944 131.992 17
18 L046 .9561 .0544 :0569 I &.388 17.580 8.433 148. 245 ]8
19 L049 .9537 .0-15 .0540 19.434 18.5 33 8.1/25 1.65.4 11 ]9
2-0 J.051 .9513 .0488 .0513 20.482. 19.485 9.417 183.485 20
21 1.054 _()489 .0464 :0489 21.534 20.434 9.908 202.463 21
22 l.056 _()465 .0443 .0468 22.587 21.380 10.400 222.341 22
23 1.059 .9442 .0423 .0448 23.644 22.324 10.&90 243 .113 23
24 L062 .94 18 _040- .0430 24.703 23 .266 11.3 0 264.775 24
25 L064 .9395 .0388 .0413 25.765 24 .206 11.&70 287.323 25
26 l.067 .9371 .0373 .0398 26.829 25 .143 1. 2.360 3 I0.752 26
27 1.070 .9348 .0358 .0383 .:7.896 26.078 12.&49 335.057 27
28 J.072 .9325 _034 - .0370 2&.966 27.0lO 13.337 36L33 28
29 1.075 .9301 .0333 .0358 30.038 27.940 13.&25 386.278 29
JO L07& .9278 .032 1 :0346 31. 114 28.&68 14.313 4 13.185 30
36 1.094 .9 1.40 .0266 .0291 37.621 34.387 17.23 1 592.499 36
46 1.105 .9049 .0238 .0263 42:014 38.020 1. 9.167 728.740 40
48 1.127 .8871 .0196 .0221 50.932. 45. 179 23.02 1 1040.055 411
50 l.133 .8826 .01.88 .0213 53.189 46.947 23.9&0 l 125.777 so
52 l.139 .8782 .0180 .0205 5,5.458 48.705 24.938 1214.588 52
60 1. 162 .8609 .01 55 .0 180 64.647 55 .653 28.751 1600.085 60
70 1.191 .8396 .0131 .0 156 76.395 64.1 44 33.4& 1 2 147.6 11 70
72 l.197 .8355 .0127 :0 152 7&.780 65 .&17 34.422 2 265.557 72
81} 1.221 .8189 .Oll3 .0138 &&.440 72.427 38.169 2764.457 80
84 1.233 .8 1. 08 .0107 .0132 93..343 75 .682 40.033 3029.759 84
90 L25_ .7987 .00992 .0 1.24 100..789 80.504 42.&16 3446.&70 90
96 1.271 .7869 .00923 .0117 I0&.349 85 .255 45 .5&4 3886.283 96
100 1.2&4 .7790 .00 81 .0 113 113.451 88.383 47.422 41 91. 242 ]00
104 l.297 .7713 .00843 :0 1. 09 I l&.605 91.480 49.252 4505.557 104
12-0 l.349 .74 11 .00716 .00966 139.743 103 .563 56.508 5 852 .112 120
246 l.821 .5492 .00305 .00555 32!U06 180.3 12 107.5&6 19398.985 240
360 2.457 .4070 .00 172 .00422 5&2.745 237 .19 1 1-2.&90 36263.930 360
480 3.315 .3016 .00108 .00358 1/26:074 279.343 192.670 53820.752 4110

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1/2%, Compound Interest Factors 1/2%

Single Paymemt Unifo:rm Payme:nt S,e,ries Arithmetic Grad ient
Com poun d Pre.sent Sin ki ng Capital Compoun d Pre.sent Gradient Gradient
Amou nt Worth Fund Recovery Amount Worth Un iform Present
Factor Factor factor Factor Factor Factor Series Worth
Find f Find P Find A Find A Find f Fiind P Find A Find P
Given P Give.n f Given F Given P Given A Given A Given G Given G
IJ FIP PIF AIF AIP FIA PIA AJG PIG n
1 1.005 _99 -0 1.0000 l.0050 l.000 0.995 0 0 J
2 I.OIO .9901 .49&& .503& 2.005 1..985 0.499 0.99 1 2
3 l.015 .985 1 .3317 .3367 3.015 .970 0.996 2.959 3
4 I.OW .9802 .24&1 .253 1 4.030 3_9 - 1 1.494 5.903 4
5 1.02.5 .9754 .19&0 .2030 5.050 4.926 1.990 9.&03 5
6 1.030 .9705 .1646 .1696 6.076 5.896 2.486 14.660 6
7 1.036 .9657 .1407 .1457 7.106 6.862 2.980 2.0.448 7
8 l.O:fl .9609 L2& .L78 8.141 7.823 3.474 27.178 8
9 1.04!6 .956 1 .10&9 .1139 9.1&2 &.779 3.967 34.&25 I)
10 l.051 .9513 .0978 .I028 10.22& 9.730 4.459 43.389 10
n 1.056 .9466 .0&&7 .0937 11.279 10.677 4.950 52 .&55 11
]2 1.062 .941. 9 .0&11 .0&61 12.336 11.6 19 5.441 63.-18 12
13 1.067 .9372 .0746 .0796 13.397 12 ..556 5.93 1 74.465 13
14 1.072 .9326 .069 1 .074 1 14.464 13.489 6.41 9 86.590 14
15 1.07& .9279 .0644 .0694 15.537 14.4 17 6.907 99.574 15
16 1.083 .9233 .0602 .0652 1. 6.614 15.340 7.394 113.4_7 16
17 1.08& .9 187 .0565 .0615 17.697 16.259 7.&80 128 .125 17
18 1.094 .9141 .053_ .05&2 18.7&6 17. 173 8.366 143.668 18
19 1.099 .9096 .0503 .0553 19.&&0 l&.082 8.850 160.037 ll)
20 1.105 .9051 .0477 .0527 20 .979 l&.987 9.334 177.237 20
21 I.I IO .9006 .0453 .0503 22.0&4 19.888 9.&17 195.245 21
22 1.116 .&961 .0431 .04&1 23.194 20.784 I0.300 214.070 12
23 1.122 .89 1. 6 .0411 .046 1 24 .310 1.676 I0.781 233 .680 23
24 1.127 .8872 .0393 .0443 25 .432 22.563 11 .261 254.088 24
25 1.133 .8828 .0377 _04_7 26.559 23 .446 11.741 275.-73 25
26 1.138 .&784 .0361 .0411 27.692 24.324 12 .220 297.233 26
27 l.144 .&740 .0347 .0397 28.&30 25.1 98 12.698 319.955 27
28 1.150 .8697 .0334 .03&4 29 .975 26.068 13 .175 343.439 28
29 1.156 . 653 .032 1 .0371 31. 124 26.9 3 13 .65 1 367.672 21)
30 l.161 .8610 .03!0 .0360 3L&O 27.794 14.1 27 392.640 30
36 1.197 .&3 -6 .0254 .0304 39.336 3-.871 16.962 557.564 36
40 1.221 .& 191 .0226 .0276 44.159 36. 172 18.&36 681.34 1 40
48 l.270 .787 1 .01&5 .023 - 54.09& 4 ..580 22.544 959 .928 48
50 1.283 .7793 .0177 _02_7 -6.645 44.143 23 .463 I 035.70 50
52 1.296 .7716 .0169 .0219 59.21& 45.690 24.378 I 113.&2 52
60 1.349 .7414 .0143 .0193 69.770 51.726 28.007 1448.65 60
70 1.4 1& _70-3 .0120 .0170 83.566 5&.939 32.468 I 913.65 70
72 1.432 .6983 .Qll6 .0166 86 .409 60.340 33.35 1 2012.35 72
80 l.490 .67.IO .0102 .0152 98 .06& 65.802 36.848 2424.65 80
84 1.520 .6577 .0096 1 .0146 1.04.074 6&.453 38.576 2640.67 84
1)0 1.567 .6383 .00&&3 .013& 11 3.311 7 __331 41.1 45 2976.0& 90
1)6 1.614 .6 19- .00&1 4 .0131 1. 22.&29 76.095 43.685 3324.19 96
100 1.647 .6073 .00773 .01-1 129.334 7&.543 45.361 3 -62 .&0 mo
]04 1.680 .5953 .00735 .0124 1. 35.970 &0.942 47.025 3806.29 104
120 1.819 .5496 .006!0 .OIi I 1. 63 .&&0 90:074 53 .551 4 823.52 120
240 3.3IO .302 1 .00216 .00716 462.041 139.-81 96.113 13 4[ 5.56 240
360 6.023 .1660 .00100 .00600 I 004.5 166.792 128.324 21403.J _ 360
480 10.957 .09 13 .00050 .00550 1991.5 181.748 151.795 27588.37 480

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3/4% Com pound Interest Factors 3/4%

Sin.gle Payment Unifonn IPaymen,t Series Arit!hmetic Gradient
Compoun d Present Sinking Capital Compound Present Gradient Gradient
Amount Worth Fund Recovery Amount Worth Un iform Pre-sent
Factor Factor Factor Factor Factor Factor Series Worth
fin d f Find P :Find A Fin d A Find F Find P Find A Find P
Given P Given F Givenf Given P Given A Given A Given G Given G
t~ f/P PIF AIF AiP FIA PIA AIG PIG n
1 J.00& .9926 1.0000 1.0075 1:000 0.993 0 0 1
2 J.015 .9852 .498 1 .-056 __ 008 1.978 0.499 0.987 2
3 l.023 .9778 .3308 .3383 3:023 2.956 0.996 2.943 3
4 1.030 .9706 .2472 .2547 4.045 3.926 1.492 5.&57 4
5 l.03& .9633 .1970 .2045 5:076 4. &89 1.9&6 9.7.12 5
6 l.046 .9562 .1 636 .]711 6. 114 5.846 2.479 14.494 6
7 1.054 .9490 . 1.397 . 1472 7. 160 6.795 2.97 1 2.0.187 7
8 1.062 .942.0 .1218 ..1293 &.213 7.737 3.462 26.785 8
9 l.070 .9350 .1078 . 1.153 9.275 8.672 3.951 34.-65 !I
10 l.07& .9280 ..0967 . 1042 10.344 9.600 4.440 42.6 19 10
11 l.086 .9211 .0876 :0951 11 .422 I0.5 2] 4.927 51.831 11
12 l.094 .9 142 .0800 .0875 1__508 11 .435 5.412 61.&89 l2
13 1.102 .9074 .0735 :0810 13.602 12.342 5.&97 72.779 B
14 LI IO .9007 .0680 .0755 14.704 13.243 6.3&0 84.49 1 ]4
15 LI 19 .8940 .0632 .0707 15.814 14. 137 6.&62 97.005 15
16 J.127 .8873 .0591 .0666 16.932 15 .024 7.343 I I0.3 18 16
17 l.135 .8807 .0554 :0629 l&:059 15 .905 7.822 124.4 10 ]7
18 1.144 .8742 .0521 .0596 19. 195 16.779 8.300 139.273 ]8
19 l.153 .8676 .0492 .0567 20.339 17.647 8.777 154.89 1 l!I
28 1.161 .8612 .0465 .0540 21.491 18.508 9.25 3 171.254 20
21 J.170 .8548 .0441 :0 - 16 22.653 19.363 9.727 I 8.352 21
22 1.179 .8484 .0420 .0495 23.823 20.211 10.20 1 206.170 22
23 I.I&& .8421 .0400 .0475 lS.001 2 1.053 10.673 224.69 - 23
24 1.196 .8358 .0382 .0457 26. 189 21.&89 11.143 243.924 24
25 1.205 .8296 .0365 .0440 .:7..385 22.719 11.613 263.&34 25
26 1.214 .8234 .0350 .0425 ~&.591 23.542 12.0&1 284.42 1 26
27 l.224 . 173 .0336 .04 11 29.805 24.360 12.548 305.672 27
28 1.233 .8112 .0322 .0397 31:029 25 .171 13.01 4 327.576 28
29 1.24- . 052 .03 10 .0385 3-.261 25.976 13.479 350.122 2!1
30 1.251 .7992 .0298 :0373 33.503 26.775 13.942 373.302 30
36 l.309 .7641 .0243 .0318 41.153 31.447 16.696 525.038 36
46 1.34& .7416 .0215 .0290 46.447 34.447 18.507 637.5 19 40
48 l.431 .6986 .0 174 .0249 57.521 40.185 22.070 886.&99 48
50 l.453 .6882 .0166 .0241 60.395 41.367 22.949 953.9 11 50
52 1.4175 .6780 .0158 .0233 63.31 2 42.928 23.822 1022.64 52
60 1.566 .6387 .0 133 .0208 75.425 48.174 27.2.68 I 313.59 60
70 l.6&7 .5927 .0109 .0 184 91.621 54.305 31 .465 I 708 .68 70
72 1.713 .5839 .010- :0 180 95:008 55.477 32.289 I 791.33 n
80 1.81& .5500 .00917 .0 167 109:074 59.995 35.540 2 132.-3 80
84 l.873 .5338 .00859 .0161 116.42.8 62 .154 37 .137 2308 .22 84
90 l.959 .5104 .00782 .0153 127.881 65.2T 39.496 2 578.09 !10
96 2.049 .4881 .00715 .0 147 139.858 68.-59 4 1.&12 2854.04 !16
100 2.111 .4737 .00675 .0 143 14&. 147 70.175 43.332 3040.&5 ]00
104 2.175 .4597 .00638 :0139 156.687 n.or 44.&34 3229.60 104
uo 2.451 .4079 :00517 .Ol27 193.517 78.942 50.653 3 998.68 120
240 6.009 .1664 .00150 :00900 667.901 111.1 4- 85 .4_2 9494.-6 240
360 14.731 .0679 .oocn .00805 I &30.8 124.282 107 .115 13312.50 360
481} 36. 111 .0277 .00021 .00771 4 6&1.5 129.641 11 9.662 15513.16 480

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1% Compound Interest Factors 1%

Single Pay,nent Unifonn ,P·a.ymemt Seriies Arithmetic Gradie111t
Compound Present Sinkin g, Capital Compound Present Gradient Gradi ent
Amou nt Worth Fund Recove ry Amou nt Worth Un iform Pre.s.e nt
Factor Factor Factor Factor Factor Factor Series Worth
Find F Find P Find A Find A f ind F Find P Find A Find P
Given P Given f Given F Given P Given A Given A Given G Give n G
t) FIP PIF AIF AIP FIA PIA AIG PIG II

1 1.0 1.0 .9901 1.0000 I.OIOO 1.000 0.990 0 0 1

2 1:020 .9803 .4975 .5075 2.0IO 1.970 0.498 0.980 2
3 1:030 .9706 .3300 .3400 3.030 2.94.1 0.993 __921 3
4 L04 I .96!0 .2463 .2563 4.060 3.902 1.488 5.80i 4
5 1.05 1 .9515 .1960 .2060 5.IOI 4.853 1.980 9.6!0 5
6 1.062 .9420 .1625 .1725 6.152 5.795 2.47 1 14.320 6
7 1.072 .9327 .1386 .1486 7.214 6.72& 2.960 19.917 7
8 1:083 .9235 .1 207 .1307 8.286 7.652 3.448 2.6.381 8
9 1.094 .9143 .1067 .11 67 9.369 8.566 3.934 33.695 9
10 1. 105 .9053 .0956 . 1056 10.462 9.471 4.4 18 41.843 10
11 I. 11 6 .8963 .0865 .0965 11.567 I0.36S 4.900 50.806 11
12 1. 127 .8874 .0788 .0888 12.682 11.255 5.3S I 60.568 12
13 1.1.38 .8787 .0724 .0824 13.809 12.134 5.S6 l 71.112 13
14 1. 149 .8700 .0669 .0769 14.9 .7 13.004 6.338 g_.422 14
15 1. 1.6 1 .8613 .0621 .072 1 16.097 13.865 6.S l4 94.481 ]5
16 1.1.73 .8528 .0579 .0679 17.258 14.71& 7.289 107.273 16
17 1. 184 .8444 .0543 .0643 18.430 15.562 7.761 120.783 1'7
18 1. 196 .8360 .0510 .06 10 19.61 5 16.39& 8.232 134.995 18
19 1.208 .8277 .0481 .058 1 20.811 11.226 8.702 149.895 19
2-0 1.220 .8 195 .0454 .0554 22.019 18.046 9.169 165.465 20
21 1.232 .8114 .04-30 .0530 23 .239 18.857 9.635 I Sl.694 21
22 1.245 .8034 .04-09 .0509 24.472 19.660 10.100 198.565 22
23 1.257 .7954 .0389 .0489 -5.716 20.456 10.563 216.065 23
24 1.270 .7876 .037 1 .0471 26.973 2 1.243 11.0?...4 234.179 24
25 1.282 .7798 .0354 .0454 28.243 22.023 11 .483 252.892 25
26 1.295 .7720 .0339 .0439 29.526 22.795 1.1.94 1 272.1 95 26
27 1.308 .7644 .0324 .0424 30.821 -3.560 12.397 -92.069 27
28 1.32 1 T68 .0311 .04 11 32.129 24.316 l2.S52 31 .504 28
29 1.335 .7493 .0299 .0399 33. 50 25.066 13.304 333.486 29
30 1.348 .74 19 .02.87 .0387 34.785 25.80& 13.756 355.001 30
36 1.43 1 .69 9 .0232 .0332 43.077 30.107 16.4_8 494.620 36
40 1.489 .67 17 .02.05 .0305 48.886 32.835 18.178 596.854 40
48 1.6 12 .6203 .0163 .0263 6 1.223 37.974 21.598 820.1414 48
50 1.645 .6080 .0155 .0255 64.463 39.196 22.436 879.417 50
52 1.678 .5961 .01 4S .0248 67.769 40.394 23 .269 939.916 52
60 1.8 17 S04 .0122. .0222 Sl.670 44.955 26.533 1192.80 60
70 2.007 .4983 .00993 .0 199 100.676 50.16& 30.470 I 52.8.64 70
72 2.047 .4885 .00955 .0 196 104.710 -1. 150 31.239 I 597.86 72
80 2.2 17 .45 11 .00822 .0 182 1-1 .671 54.88& 34.249 I &79.87 80
84 _.307 .4335 .00765 .0 177 130.672 56.64& 35.7 17 2023.31 84
90 2.449 .4084 .00690 .0169 144.863 59.161 37.872 2240.56 90
96 2 ..599 .3847 .00625 .0 163 159.927 6 L52S 39.973 2459.42 96
100 2.10 - .3697 .005&7 .0 159 170.481 63.029 41.343 260S .77 100
104 2.8 15 .3553 .0055 1 .0 155 18 1.464 64.471 42.688 2752.17 104
12-0 3.300 .3030 Jl0435 .0143 _30.039 69.701 47 .S35 3334.11 120
240 I0.893 .09 18 .OOIOI .OI 10 9&9.254 90.819 75.739 687&.59 240
360 35.950 .0278 .00029 .0 103 349 -_o 97.21& 89.699 8720.43 360
480 118.648 .00843 .00008. .010 1 11764.8 99.157 95.920 9511.15 480

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1 1/4% Compound Interest Fact ors 1 1/4%

S1n.gle IPaymemt Uniform Payment Sei ies Arithmetic Gradieint
1

Compound Present 5inking 1 Capita l Compound Present Gradient Gradient

Amount Worth Fund Recovery Amount Worth Uniform Present
Factor Factor Factor Factor Factor Factor Serie~ Worth
Find F IFind P Find A Find A Find F Find P Find A Find P
GivenP Given F Given F Give nP Given A Given .A Gnven G Given G
n FIP P/F AIF AJP FIA PIA AIG PIG I)

1 1.013 .9877 1.0000 1.0125 1.000 0.988 0 0 1

2 1.025 .9755 .4969 .5094! __ 013 1.963 0.497 0.976 2
3 J.038 .%34 .3292 .34!l7 3:038 2.927 0.992 2.904 3
4 J.05 1 .95 15 .2454 .2579 4.076 3.878 1.485 5.759 4
5 1.064 .9398 .1951 .2f.fl6 5..1 27 4. 818 1.976 9..518 5
6 1.077 .9282 .1615 .1740 6. 191 5.746 2.464 14. 160 6
7 1.091 .9167 .1376 .1501 7.268 6.663 2.951 19.660 7
8 1.104 .9054 .11% .1321 8.359 7.568 3.435 25 .998 8
9 LI 18 .8942 .1057 .1182 9.463 _46_ 3.918 33. 152 9
10 1.132 .8832 .0945 .1070 10.582 9.346 4.398 41. 101 10
1 U46 .8723 .0854 .0979 11.7 14 10.218 4.876 49.825 u
12 1.161 .86 1. 5 .0778 .0903 12. 60 1 l.079 5.352 59.302 l2
13 1.175 .8509 .0713 .0838 14.021 l l.930 5.827 69..513 13
14 1.190 .8404 .0658 .0783 15. 196 12.771 6.299 80.438 ]4
15 1.2.05 .8300 .0610 .0735 16.386 13.601 6.769 92.058 ]5
16 l.22.0 .8197 .0568 .0693 IF91 ]4.420 7.237 104.355 6
17 1.235 .8096 .053 .0657 18.811 1.-_230 7.702 117.309 17
18 1.25 1 .7996 .0499 .0624 20.046 16.030 8. 166 130.903 18
19 1.266 .7898 .0470 .0595 _1.297 [6.849 8.628 145.1 19 19
20 J.2.IL .7800 .0443 .0568 -2.563 1. 7.599 9.088 159.940 20
21 l.298 .7704 .0419 .0544 23 .845 1.8.370 9.545 175.348 21
22 1.314. .7609 .0398 .0523 25. 143 19. 131 10.001 191.327 22
23 1.331 .75 15 .0378 .0503 26.458 1. 9.882 10.455 207.859 23
24 1.34.7 .7422 .0360 .005 27.788 20 .624 10.906 2.24.930 24
25 1.364 .7330 .0343 .0468 29.136 21.357 11.355 242..523 25
26 l.381 .7240 .0328 .04.53 30500 22.081 11.803 260.623 26
27 1.399 .7150 .0314 .04.39 31.881 22.796 12.248 279.2 15 27
28 1.416 .7062 .0300 .04.25 32.280 23.503 L .691 298.284 28
29 1.434 .6975 .0288 .04.13 34.696 24.200 13.133 317.8 14 29
30 1.452 .6889 .0277 .0402 36. 129 24. 889 13.572 337.792 30
36 1.564. .6394 .0222 ..0347 45 .11 6 28.847 16. l64 4!66.297 36
40 l.64.4 .6084 .0194 .0319 51.490 31.327 17.852 559.24 7 40
48 1.845 .5509 .0153 .0278 65.2 9 35.932 _1.130 759.248 48
50 1.861 .5373 .0145 .02.70 68.882 37.013 _t.930 811.692 50
52 1.908 .5242 .0138 .0263 72.628 38 .068 22.722. 864.960 52
60 __107 .4746 .0113 .0238 88. -75 42.035 lS.809 I 084.86 60
70 2.386 .419 1 .00902 .0215 110.873 46.470 29.492 1370.47 70
72 2.446 .4088 .00864 .0211 11 5.675 47.293 30.2.05 1428.48 72
80 2.701 .3702 .00735 .0198 136. 12.0 50.387 3-.983 1661.89 80
84 2.839 .3522 .00680 .0193 147.130 51.822 34.32.li 1778.86 84
90 3.059 .3 69 .00607 .0186 164..706 53.846 36.286 1953 ..85 90
96 3.296 .3034 .00545 .0179 183.643 55.725 3&.180 2127..55 96
100 3.463 .~887 .00507 .0176 197:074 56.901 39. 406 2242.26 100
104 3.640 .2747 .00474 .0172 211.190 58.021 40.604 2355.90 104
120 4.440 __ 252 .00363 .0161 •.75.22.0 6 1..983 45.119 2 796.59 120
240 19.7 16 .0507 .00067 .0132 1497.3 75.942 67.177 5 IOl.55 240
360 87.543 .01 14 .00014 .012ii 6923 .4 79.086 75 .840 5 997.9 .1 360
480 388.713 .00257 .00003 .0125 31017. 1 79.794 78.762 6284.74 480

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Compound Interest Factors

Singl'e Payment Uniform IPa,yment Series Arithmetic Grad1i.e nt
Compou nd Pres;ent Sin king Capital Compound Present Gradient Gradient
Amount Worth Fund Recovery Amount Worth Un iform Present
Factor Factor Factor Factor factor Factor Series Worth
Find F Find P Find A Find A Find F FindP Fin d A Find P
Given P Given F Given F GivenP Given A Given A Given G Given G
n FIil PIF AIF A/fl FIA PIA AIG PIG II

1 .0 15 .9852 1.0000 1.0150 1.000 0.985 0 0 1

2 .030 .97fJ7 .4963 .5113 2..0 15 1.956 0.496 0.970 2
3 .046 .9563 .3284 .3434 3_04 - .912 0.990 .883 3
4 .061 .9422 .2444 .2594 4.09 1 3.854 l.4!U 5.709 4
5 .077 .9283 .194 1 .2091 5.1 52 4 ..783 1.970 9.422 5
6 .093 .9145 .1605 .1755 6.230 5.697 2.456 13.994 6
7 ..11 0 .9010 .1366 .1 516 7.323 6.598 2.940 19.400 7
8 . 126 .8877 .1186 .1336 8.433 7.486 3.422 LS.614 8
9, .143 .8746 .1046 .1196 9.559 8.360 3.901 32.610 9
to, . 161 .8617 .0934 .1084 I0.703 9.222 4.317 40.365 10
11 . 178 .8489 .0843 .0993 11.863 I0:071 4.85 1 48.855 11
12, ..196 .8364 .0767 .0917 13.041 I0.907 5.322 58:054 12
13 .2 14 .8240 .0702 .0852 14.2 7 11.731 5.791 67.943 13
14 .232 .8118 .0647 .0797 15 .450 12543 6.25 8 78.496 14
15 .250 .7999 .0599 .fJ749 16.682 13.343 6.7'12 89.694 15
16 .269 .7880 .0558 .0708 17.932 14.131 7.184 101.5 14 16
17 .288 .7764 .05_1 .0671 19.20 1 14.908 7.643 113.937 17
18 .307 .7649 .0488 .0638 20.489 15.673 8.100 126.940 18
19, .327 .7536 .0459 .0609 21.797 16.426 8.554 140.505 19
w 1.347 .7425 .0432 .0582 2.3. 124 17.J 69 9.005 154.611 20
21 1.367 .7315 .0409 ..OS59 24.470 17.900 9.455 169.24 1 21
22 1.388 .nm .0387 .0537 25 .837 18.621 9.902 184.375 22
23 1.408 .7100 .0367 .0517 2.7.2r 19.331 I0.346 199.996 23
24 1.430 .6995 .0349 .0499 28.633 20.030 10.788 216.085 24
25 1.451 .6892. .0333 .0483 30.063 20.720 11.227 232.626 25
26 1.473 .6790 .0317 .0467 31.5 14 21 .399 11.664 249.601 26
27 1.495 .6690 .0303 .0453 32.987 22:068 12.()99 2.(i(i.995 27
28 1.-.17 .6591 .0290 .0440 34.48 1 22.7 7 12.531 284.790 28
29' 1.540 .6494 .0278 .0428 35 .999 2.3 .376 12.961 302.972 29
30 1.563 .6398 .0266 .Ml6 37.539 24.0 16 13.388 321.525 30
36 1.709 .-85 1 .021 .0362 4L76 27.661 15.90! 439.823 36
4(1, 1.814 _-513 .0184 .0334 54.268 29.916 17.52& 524.349 40
48 2.043 .4894 .0144 .0294 69.T 34:042 20.666 703.537 48
50 2. 105 .4750 .0136 .0286 73.682 35 ..000 21.428 749.955 50
52 2. 169 .4611 .Ol28 .0278 77.925 35.929 22.179 796.868 52
60 .443 .4093 .OI 04 .0254 96. 14 39.380 25.093 988. 157 60
70 2 ..835 .352.7 .00817 .0232 122.363 43. 155 28.529 1231. 15 70
72 2.921 .3423 .0078 1 .0228 128 .076 43.845 29.1&9 1279.78 72
80 3.291 .3039 .00655 .021 5 152.710 46.407 31.742 1473.06 80
84 3.493 .2863 .00602 .02.IO 166.172 47.579 32.967 1568.50 84
90 3 ..8 19 .2619 .00532 .0203 187.929 49.210 34.740 1709.53 90
96 4.1 76 .2395 .00472 .0197 211.7 19 50.702 36.438 1847.46 96
100 4.432 .22.56 .0043 7 .01 94 2.28.802 51.625 37.529 1937.43 100
1(}4 4.704 .2126 .00405 .0190 246.932 5 .494 38.5&9 2025 .69 104
1.W 5.969 .1675 .00302 .0180 331.286 55.498 42.518 2359.69 120
240 35.632 .0281 .00043 .0154 2308.8 64 ..796 59.737 3870.68 240
360 212.700 .00470 .00007 .0151 14 113.3 66.353 64.966 4 310.7 1 360
480 1269.7 .00079 .0000 1 .01 50 84577.8 66.614 66.288 4 415.74 480

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Compound Interest Fact ors 13/ 4%

Single Pa,ymen,t Uniform Payme111t Se'ries Arhllimetic GHdie1nt
Compound Present Sinking Capital Compound Present Gradient Gradient
Am ount Worth Fund Recove;ry Amount Worth Un iform Present
Factor Factor Factor IFactor Factor Factor Series Worth
Find F Find P Find A Find A Find F Find P Find A Find P
Give;n P Give;n F Give;n F Given P Given A Given A Given G Given G
n FIP PIF AIF AIP FIA PIA AIG PIG n
l 1.018 .9828 1.0000 1.0175 I.ODO 0.983 0 0 l
2 1.035 .9659 .4957 .5132 2.018 1.949 0.496 0.966 2
3 1.053 .9493 .3276 .3451 3.0-3 2.898 0.989 2.865 3
4 1.072 .9330 .2435 .2610 4. 106 3.831 1.478 5.664 4
5 1.09 1 .9169 .1931 .2I06 5.178 4.748 1 965 9.332 5
6
7
I.I 10
I.I 9
.90! I
.8856
.1595
.1355
.1770
.1530
6._69
7.378
5.649
6.535
2.450
2.931
13.837
19.152 .,6
8 1.149 .8704 .1175 .1350 8.508 7.405 3.409 25 .245 8
9 1.169 .8554 .1036 .U I 9.656 .261 3.885 32.088 9
1.0 1.189 .8407 .0924 .1099 I0.825 9.10! 4.357 39.655 ]0
u 1.210 .8263 .083 _ .1007 12.015 9.928 4.827 47.918 n
12 1.23 1 .8121 .0756 .093 1 13. 25 10.740 5.294 56.85 1 l2
13 1.253 .7981 .0692 .0867 14_4-7 11.538 -.758 66.428 ]3
14 i. _r .7844 .0637 .0812 15.710 12.322 6. 19 76.6_5 ]4
15 1.297 .7709 .0589 .0764 16.985 13.093 6.677 87 .417 15
16 1.3_0 .7576 .0547 .0722 18.282 13.851 7.132 98 .782 ]6
17 1.343 .7446 .0510 .0685 19.602 14.595 7.584 110.695 ]7
18 1.367 .7318 .0477 .0651 20.945 15.327 8.034 123.136 ]8
19 1.390 .7192 .0448 .0623 22.3 1.l 16.046 8.481 136.08 1 ]9
20 1.415 .7068 .0422 .0597 23.702 16.753 8.924 149.51 1 20
21 1.440 .6947 .0398 .0573 25. 116 17.448 9.365 163 .405 21
22 1.465 .6827 .0377 .055 2 26.5 56 18.130 9.804 177.742 22
23 1.490 .6710 .0357 .0532 28 .021 18.801 10.239 192 .503 23
24 1.516 .6594 .0339 .051 4 29 .5 l l 19.461 10.671 207 .67 1 24
25 1.543 .6481 .0322 .0497 31.028 20 .109 11..101 223._25 25
26 1.570 .6369 .0307 .0482 32.57 1 20.746 11.5 8 239 .149 26
27 1.597 .6260 .0293 .0468 34.141 21.372 11.952 255 .4 5 27
28 1.625 .61 52 .0280 .0455 35.738 21.987 12.373 272.036 28
29 1.654 .6046 .02.68 .0443 37.363 22.592 12.791 288 .967 29
30 1.683 .5942 .0256 .043 1 39.0 17 23 .186 13.206 306.200 30
36 1.867 .5355 .0202 .0377 49.5 66 26.543 15.640 41 5.130 36
40 2.002 .4996 .0175 .0350 57.234 28.594 17.207 492.017 40
48 2-.300 .4349 .0135 .03!0 74.263 32.294 20.209 6-2.612 48
50 2.38 1 .4200 .01 _7 .0302 78.903 33.141 20.932 693 .708 50
52 2.465 .4057 .0119 .0294 83 .706 33 .960 21.644 735 .039 52
- 10¢ .676
60 2. 832 .3531 .00955 .0271 36.964 24.389 901 .503 60
70 3.368 .2969 .()0739 .0249 135.331 40.178 27.586 I .!08.34 70
n 3.487 .2868 .00704 .0245 142 .127 40.757 28 .195 I 149 .12 n
80 4.006 .2496 .00582 .0233 171.795 42.880 30.533 I. 309.25 80
84 4.~94 .2329 .00531 .0228 188.246 43.836 3 1..644 l 387.16 84
90 4.765 .2098 .00465 .02- 1 215 .166 45.1 52 33.241 1500.88 90
96 5. 88 .1891 .00408 .0216 245.039 46.337 34.756 1610.48 96
100 5.668 .1764 .00375 .0212 266.753 47.062 35.721 I. 681 .09 ]00
104 6.075 .1646 .00345 .0209 290.028 47.737 36.652 1749.68 ]04
120 8.019 .1247 .00249 .0200 401.099 50.017 40.047 2003 .03 ]20
240 64.308 .01 56 _0002,8 .0178 3 617 .6 56.254 53.352 3001.27 240
360 5 15.702 .00194 .00003 .OIT 29 4 11.5 -7_032 56.443 32 19.08 360
480 41 35.5 .00024 .0175 236259 .0 57.129 57.027 3257.88 480

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2% Com pound Inte rest Factors 2%

Sing .e Pa,y ment Uniform Payment SeriM Aridimetic G1adient
Compound Present Sinkin g Capital Compound ~resent Gradient Gradient
Amount Worth Fund Recovery Amount Worth Un iform Present
Factor Factor Factor Factor Factor Factor Ser1ies Worth
Find F Find P Find A Find A Find F Find P Find A Find P
Given P GiYeill F Given F GivenP Given A Given A Given G Given G
I) FIP P/F AIF AIP FIA PIA A/G PIG n
1 1.020 .9&04 1.0000 1.0200 1.000 0.980 0 0 1
2 1.040 .9612 .4951 .5 151 2.0'20 1. 942 0.495 0.961 2
3 1.061 .9423 .3268 .3468 3.060 2.884 0.987 .S46 3
4 1.082 .9238 .2426 .2626 4.122 3.808 1.475 5.617 4
5 1.104 .9057 .1922 .2 122 5.204 4.7[3 1.960 9.240 5
6
7
1.126
1.149
.88SO
.8706
.1 585
.1345
.1785
.1545
6.308
7.434
5.60 1
6.472
2.442
2.92 1
13 .679
l8.903 .,
6
8 1. 172 .8535 .1165 .1365 8.583 7325 3.396 24-877 8
9 1.195 .8368 .1025 .1225 9.755 8. l62 H68 31.57.1 9
10 1.2 19 .8203 .0913 .1113 10.950 8.983 4.337 38.954 10
11 1.24 3 .8043 .0822 .1022 12.169 9.787 4.S02 46.996 11
12 1.268 .7885 .0746 .0946 13.41 2 10.575 5.264 55.669 12
13 1.294 .7730 .0681 .088 1 14.680 11.34 5.723 64.946 13
14 1.3 19 .7579 .0626 .0826 15.974 12. l06 6.178 74.798 14
15 1.346 .7430 .0578 .0778 17.293 12.849 6.63 1 85.200 15
16 1.373 .72S4 .0537 .0737 18.639 13. -73 7.080 96. L7 16
17 1.400 .7142 .0500 .0700 20.012 14. 292 7.526 l07.S53 17
18 1.428 .7002 .0467 .0667 2 1.412 14.992 7.968 [1 9.456 18
19 1.4 -7 .6864 .0!!38 .0638 22.840 15.678 8.407 131.8n 19
20 1.486 .6730 .04L .0612 24.297 16.35] 8.S43 144.598 20
21 L5 l 6 .6598 .0388 .0588 5783 17.011 9 ...:76 157.793 21
22 1.546 .6468 .0366 .0566 -7.299 17.658 9.705 171.377 22
23 1.577 .634_ .0347 .0547 28.845 18.292 l.0.132 [85.328 23
24 1.608 .6 17 .0329 .0529 30.422 18.914 10.555 l99 .6_8 24
25 1.64 1 .6095 .031 - .051_ 32.030 19.523 10.974 214.2.56 25
26 1.673 .5976 .0297 .0497 33.671 20.121 11.39 1 229 .196 26
27 1.707 .5S59 .0283 .O!l83 35.344 20.707 l l.804 244.428 27
28 1.741 .5744 .0270 .O!l70 37.05 1 21.28[ 12.21 4 259.936 28
29 1.776 .5631 .0258 .O!l58 38.792 21.844 12.62 1 275 .703 29
30 1.8 1l .5521 .0247 .04147 40.568 22.396 13.025 29l.7U 30
36 2.040 .4902 .0192 _039 _ 51.994 25.489 15.38 1 392.036 36
40 2.20 .45 9 .0166 .0366 60.402 27T5 16.888 461.989 40
48 .587 .3865 .om; .0326 79.353 30.673 19.75 - 605 .% 1 48
50 2 . 692 .371 5 .0118 .0318 84.579 31 .424 20.442 642.355 50
52 __ 800 .3571 .0111 .0311 90.016 32. 145 21.116 678 .779 52
60 3.281 .3048 .00877 .0288 11 4.051 34. 76 [ 23 .696 823 .692 60
70 4.000 .2500 .00667 .02£,7 149.977 37.499 26.663 999 .8'29 70
72 4.161 .2403 .00633 .0263 158.056 37.984 27.223 I 034.050 72
80 4.875 .2051 .00516 .0252 193.771 39.744 29.357 1166.781 80
84 5.277 .1895 .00468 .0247 -13.865 40.525 30.36 1 1 230.413 84
90 5.943 .1683 .00405 .0240 247.155 41.587 31.793 l 322.164 90
96 6.693 .1494 .00351 .0235 84.645 42 .529 33.137 1409 .291 96
100 7.24 5 .13SO .00320 .0232 312.230 43.098 33.986 1464.747 100
1D4 7.842 .L75 .00292 .0229 342.090 43.624 34.799 15 18.082 104
120 10.76 - .0929 .00205 .0220 488.255 45.355 37.71 1 I 710.41 l 120
240 11 5.887 .00863 .00017 .0202 5744.4 49 .569 47.91 1 2374. 878 240
360 1247.5 .000&0 .00002 .0200 6_326.8 49.960 49.71 1 2483.567 360
480 13429.8 .00007 .0200 671442.0 49.996 49.964 2498.027 480

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Compound Interest Factors

Singfo Payment Uniform Pa,y ment Series A11ithmetic Gradii ent
Compound Present Sinking Capital Compound Pre~nt Gradient Gradient
Amount Worth Fund rlecovei-y Amount Worth Un iform Present
Factor Factor Factor Factor Factor Factor Series Worth
Find F f ind P Find A Find A Find F Find P Find A Find P
GivenP Given F Given f Given P Given A Given A Given G Given G
n F/P Pl f AJF AIP FIA PIA AIG PIG n
1 1.025 .9756 1.0000 1.0250 1.000 0.976 0 0 1
2 1.051 .951& .4938 .51&& __025 1.927 0.49-4 0.952. 2
3 1.077 .928.6 .325 1 .3501 3.076 2.856 0.9&4 2.809 3
4 1.104' .9060 ,_408 .265& 4. 153 3.762 1.469 5.527 4
5 1.131 .8&39 .1902 .2152 5.256 4.646 1.95 .1 9.062 5
6 1.160 .8623 .1566 .1816 6.388 5.508 2.42& 13.374 6
7 1.189 .8413 .1325 .1 575 7.547 6.349 2.90 1 l&.421 7
8 1.218 .8207 .1145 .1395 &.736 7.1 70 3.370 _4_166 8
9 l.249 .8007 .1005 .1255 9.955 7.971 3.&35 30.572 9
10 1.280 .781 2 .0893 .1143 11.203 8.752 4.296 37.603 ]0
11 1.312 .7621 .0&0 1 .I05 1 1__ 483 9.514 4.753 45.224 u
12 1.345 .7436 .0725 .0975 13 .796 10.258 5.206 53.403 12
13 l.379 .7254 .0660 .0910 15. .140 10.983 5.65- 62. 108 l3
14 1.413 .7077 .0605 .0&55 16.519 11.691 6.IOO 7 1.309 ]4
15 l.448 .6905 .0558 .O&O& 17.932 12.381 6.540 &0.975 ]5
16 1.485 .6736 .05 16 .0766 19.380 13.055 6.977 91.080 16
17 1.522 .6572 .0479 .00 9 20.865 13.712 7.409 101.595 7
18 1.560 .6412 .0447 .0697 22.386 14.353 7.&38 112.495 ]8
19 1.599 .6255 .04 18 .066& 23.(}46 14.979 8.262 I 3.754 19
2-0 1.639 .6103 .0391 .0641 L.5.545 15.589 8.6&2 135.349 20
21 1.680 .5954 .0368 .061& 27. 183 16..185 9.099 147.257 21
22 1.722 .5809 .0346 .0596 2&.863 16.765 9.51 I 159.455 22
23 1.765 .5661 .0327 .0577 30.584 17.332 9.919 171.922 23
24 1.809 _55_9 .0309 .0559 32.349 17.885 l0.324 1&4.638 24
25 l.854 .5394 .0293 .0543 34.158 l&.424 10.724 197.584 25
26 1.900 .5262 .027!! .052.8 36.012 l&.951 11.120 210.740 26
27 1.948 .5134 .0264 .05 14 37.912 19.464 11.513 224.088 27
2S 1.996 .5009 .025 1 .0501 39.860 19.965 11.901 237.612 28
29 __ 046 .48&7 .0239 .04&9 41.856 20.454 IL&6 L.51.2.94 29
30 2.098 .4767 .0228 .047& 43.903 20.930 12.667 2.65.120 30
31 .150 .4651 .02 17 .0467 46.000 1.395 13.044 _79_073 31
32 .204 .453& .0208 .045& 4&.150 24.849 13 .417 293.140 32
33 2.259 .4427 .Ol99 .0449 50.354 22.292 l3.7&6 307.306 33
34 2.315 .4319 .0 190 .0440 52.613 22.724 14. 15 .1 321..559 34
35 2.373 .4214 .0182 .0432 54.928 23.145 14.512 335.886 35
40 2.685 .3724 .01 48 .039& 67.402 25 .103 16.2.6..; 40&.221 40
45 3.038 .3292 .0123 .0373 &1.5 16 2.6.833 17.91& 4&0.806 45
50 3.437 .2909 .OI03 .0353 97.484 2&.362 19.4&4 552.600 50
55 3.889 .2572 .0086- .0337 115.551 _9_714 20.961 622.827 55
60 4.400 .2273 .00735 .0324 135.991 30.909 22.352 690.865 60
65 4.978 .2009 .00628 .0313 159. 11 8 31.965 23.660 756.280 65
70 5.632 .1776 .OIY 0 .0304 1&5.284 32.898 24.&&& &I &.763 70
75 6.372 .1569 .00465 .0297 214.888 33.723 26.039 &7&.114 75
so 7.2!0 .13&7 .00403 .0290 24&.382 34.452 27.117 934.217 80
S5 8.157 .12:?...6 .00349 .02&5 2-8.6.278 35.096 28 .123 9&7.026 85
90 9.229 .I0&4 .00304 .02&0 329. 154 35.666 29 .063 I 036.54 90
95 10.442 .095& .00265 .0276 377.663 36.169 29 .93& I 0&2.83 95
100 11.814 .0846 .0023 1 .0273 432.548 36.614 30.752 1125.97 ]00

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3% Compound Interest Factors 3%

Single Payment Uniform ,P·a.ymertt Serii:es Arithmetic Gradiei.t
Compound Present Sinking, Ca pital Compound Pres;ent Gradient Gradi ent
Amou nt Worth Fund Recovery Amou nt Worth Un iform Present
Factor Factor Factor factor Factor Factor Series Worth
Find F Find P Find A Find A f ind F Find P Find A FindP
Given P Givenf Given F Given P Given A Given A Given G Give n G
t) FIP PIF AIF AIP FIA PIA AIG PIG II

1 1.030 .9709 1.0000 1,0300 1.000 0.971 0 0 1

2 1:06 1 .9426 .4926 .5226 2.030 1.913 0.493 0.943 2
3 1.093 .9151 .3235 _3-35 3.091 2.829 0.9&0 __773 3
4 1. 126 .8885 .2390 .-690 4.184 3.717 1.463 5.438 4
5 1. 159 .8626 .1884 .2184 5.309 4.5&0 1.941 8.889 5
6 1.1.94 .8375 .1546 .1&46 6.468 5.417 2.41 4 13.076 6
7 1.230 .8131 .1305 .1605 7.662 6.230 2.882 17.955 7
8 1.267 .7894 .1125 .1425 8.89 _ 7.020 3.34 - 23.481 8
9 1.30 - .7664 .()984 . 1284 10.159 7.7&6 3.803 29.612 9
10 1.344 .7441 .0872 . 11 72 II. AM 8.530 4.256 36.309 ]0
11 1.384 .7224 .0781 .108 1 12.808 9.253 4.70 - 43_-33 11
12 1.426 .7014 .0705 .1005 14.192 9.954 5.148 51.248 12
13 1.469 .6810 .0640 .0940 15.618 10.635 5.587 59.419 13
14 1.5 13 .6611 .0585 .0885 17.()86 11 .296 6.02 1 68.014 14
15 1.558 .6419 .0538 .0838 18.599 11.938 6.450 77.000 ]5
16 1.605 .6232 .0496 .0796 20.157 12.561 6. 874 &6.348 16
17 1.653 .6050 .0460 .0760 2 1.762 13. 166 L94 96.028 1'7
18 1..702 5874 .0427 .0727 23.414 13.754 7.708 106.014 18
19 1.754 5703 .0398 .0698 _-_117 14.324 8.118 116.279 19
2-0 1.806 5537 .0372 .0672 26.870 l4.877 8.523 12.6.799 20
21 1.860 5375 .0349 .0649 Z&.676 15.415 8.923 137549 2]
22 1.9 16 .5219 .0327 .0627 30.537 1-_937 9.319 148.509 22
23 1.974 .5067 .0308 .0608 32. 53 [6.444 9.709 159.656 23
24 2.033 .4919 .0290 .0590 34. 26 l6.936 I0.095 170.971 24
25 2.094 .4776 .0274 .0574 36.459 17.413 I0.477 182.433 25
26 2. 157 .4637 .0259 .0559 38.553 17.877 1.0.853 194.026 26
27 2.22 1 .4 -02 .0246 .0546 40.7IO 18.327 11.-'26 205.731 27
28 2.288 .4371 .0233 .0533 42.931 18.764 11.593 -17.532 28
29 2.357 .424 3 .0'221 .052 [ 45.219 l9.I 8 11.956 __9.413 29
30 _.427 .4 120 .0210 .05 10 47.575 19.600 12.3 14 241.361 30
31 2.500 .4000 .0200 .0500 50.003 _o_ooo 12.668 253.361 31
32 2.575 .3883 .0190 .0490 52.503 20.389 13.017 265.399 32
33 2.652 .3770 .0182 .0482 55.078 20.766 13.362 277.464 33
34 2.732 .3660 .0173 .0473 57.730 21.132 13.702 89.544 34
35 2.8 14 .3554 .0165 .0465 60.462 21.487 14.037 301.627 35
40 3.262 .3066 .0133 .0433 75.401 23. 115 [5.650 361.750 40
45 3.782 .2644 .0108 .0408 92.720 24.519 17.156 420.632 45
5(1 4.384 .2281 .00887 .0389 112.797 r.730 18.558 477.480 50
55 5:082 .1968 .00735 .0373 136.07_ 26.774 19.&60 531.7411 55
60 5.892 .]697 .00613 .036 1 163.053 27.676 21.067 583.052 60
65 6.830 .1464 .00515 .035 1 194.333 28.453 22.1&4 631.201 65
70 7.9 l8 .1263 .00434 .0343 230.594 _9_123 2Ll5 676.087 70
75 9 ..179 . 1089 .00367 .0337 272.631 29.702 241.163 717.698 75
80 I0.64 1 .0940 .00311 .033 1 321.363 30.201 25.or 756.086 80
85 12.336 .0811 .00265 .0326 377.857 30.631 25 .835 791.353 85
90 141.300 .0699 .0022-6 .0323 443 .349 3 1.002 26.567 8?.3 .630 90
95 16.578 .0603 .00193 .03 19 519.272 3 l.323 ni:r 853.074 95
100 19.2 1.9 .0520 .00165 .03 [6 607.287 31.599 27.844 879.854 100

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may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

Compound Interest Facto1

rs
Singlle Pa,y ment Uniform Pa,y ment Series Ariithmetic G:radi:ent
Compound Present Sinking Capital Compound Present Gradient Gradient
Amount Worth Fund Recove,ry Amount Worth Un iform Present
Factor Factor Factor Factor Factor Factor Series Worth
IFind F f ind P Find A FiindA Find F Find P Find A Find P
GivenP Given F Given F Given P Given A Given A Given G Given G
n f/P Pl f .M AIP FIA PIA AIG PIG n
1 1.035 .966_ 1.0000 1.0350 1.000 0.966 0 0 l
2 l.071 .9335 .49 1.4 .5264 __035 1.900 0.491 0.933 2
3 1.109 .9019 .32 19 .3569 3.1 06 2.802 0.977 2.737 3
4 1.1 48 .8714 .2373 .27TI 4.215 3.673 1.457 -.352 4
___ 15
5 l.188 .8420 .1865 5.362 4.5 15 1.931 8.719 5
6 1.229 .8135 .1527 .1877 6.550 5.329 2.400 12.787 6
7 1.272 .7860 .1285 .1635 7.779 6.11 5 2.&62 17.503 7
8 1.317 .7594 .11.05 .1455 9.052 6.874 3.320 22.819 8
9 1.363 .7337 .0964 .1314 10.368 7.608 3.771 -8.688 9
10 1.4 11 .7089 .0852 .12.02 11.731 8.317 4.217 35.()69 ]0
11 1.460 .6849 .076 1 .1111 13. 142 9.002. 4.657 41.918 11
12 1.511 .6618 .0685 .1035 14.602 9.663 5.oin 49.198 l2
13 1.564 .6394 .062 1 .0971 16.113 l0.303 5.520 56.87 1 l3
14 1.619 .6178 .0566 .0916 17.677 l0.921 5.943 64.900 14
15 1.675 .5969 .05 18 .0&68 19.296 11.517 6.36 ] 73.258 ]5
16 1.734 .5767 .0477 .08 ..:7 20.971 I .094 6.773 81.909 6
17 1.795 .5572 .0440 .0790 22.705 L.651 7.179 90.824 17
18 1.857 .5384 .0408 .0758 2COO 13.190 7.SSO 99. 76 18
19 1.922 .52.02 .0379 .0729 26.357 13.7!0 7.975 !09.339 19
2-0 1..990 .5026 .0354 .0704 28.280 14.212 8.365 118.888 20
21 .059 .4856 .0330 .06SO 30.269 14.698 8.749 128.599 21
22 2. 132 .4692 .0309 .0659 32.329 15.167 9.128 138.451 22
23 2.206 . 533 .0290 .0640 34.460 15.62.0 9.502 148.423 23
24 2.2.83 . 380 .0273 .0623 36.666 16.058 9.870 158.496 24
25 2.363 .4231 .0257 .0607 38.950 16.482 l0.233 168.652 25
26 - .446 .4088 .0242 .0592 4 1.3 13 16.890 10.590 178.873 26
27 2.532 .3950 .0229 .0579 43.759 17.285 10.942 189.14'3 27
28 - .62.0 .3817 .02 16 .0566 46.291 17.667 11.2.&9 199.448 28
29 __712. .3687 .0204 .0554 48.911 18.036 11.63 1 209.773 29
30 2.807 .3563 .0 1.94 .0544 5 1.623 18.392 11.967 220. !05 30
31 2.905 .3442 .0184 .0534 54.429 18.736 12.299 230.432 31
32 3.007 .3326 .Ol74 .0524 57.334 19.069 12.625 240.74'2 32
33 3.112. .3213 .0166 .0516 60.341 19.390 12.946 251.005 33
34 3.221 .3105 .0 1.58 .0508 63 .453 19.701 13.262 261.271 34
35 3.334 .3000 .0150 .0500 66.674 2.0.001 13..573 27 1..470 35
40 3.959 .2.526 .01 18 .M-68 84.550 _1.355 15.055 321.490 40
45 4.702 .2127 .00945 .0¢45 105.781 22.495 16.417 369.307 4.5
50 5.585 .1791 .00763 .0426 130.998 23.456 17.666 414.369 50
55 6.633 .1508 .0062 1 .0412 160.1}46 24.264 18.S08 456.352 55
60 7.878 .1269 .00509 .0401 196.516 24.945 19.848 495.104 60
65 9.357 .1069 .004 19 .0392 238.762 25 .5 18 20 .793 530.598 65
7G 11.113 .0900 .00 6 .03&5 288.937 26.000 21 .650 56-.895 70
75 13.199 .0758 .00287 .0379 348.529 26.407 22.423 592. 121 75
80 15.676 .0638 .00238 .0374 419.305 26.749 23.1 _0 618.438 80
85 18.618 .0537 .00 199 .0370 503 .365 _7_037 23.747 642.036 85
90 22.112 .04l52 .00 166 .0367 603 .202 27.279 24.308 663.118 90
9-5 26.262 .0381 .00 139 .0364 7 _1.778 _7.4g3 24 .81 I 681.890 95
100 31.191 .0321 .00 11 6 .0362 862.608 27.655 25.251} 698.554 ]00

26 of 52 1/25/2020, 11:37 AM
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4% Compound Interest Factors 4%

Single Payment Unifonn P·a1ymen.t Seri.es Arithmetic Gra.dierrit
Compound Present Sinkin g, Capital Compound Present Gradient Gradient
Amount Worth Fund Recovery Amou nt Worth Un iform Pres,ent
Factor Factor Factor Factor Factor Factor Series Worth
Find F Find P Find A Find A find F Find P Find A FindP
Given P Given f Given F Given P Given A Given .A Given G Give n G
tJ FIP PIF Alf AIP FIA PIA AIG PIG II

1 1.040 .96 15 1.0000 1.0400 1.000 0.96 0 0 l

2 1:082 .924 6 .4902 .5302 2.040 1.886 0.490 0.925 2
3 ur .8890 .3203 .3603 3.12 .. 2.775 0.974 ...702 3
4 1. 170 K48 .2355 . 155 4.246 3.630 1.45 1 5.2b7 4
5 1.2 17 .8219 .1846 .2246 5.416 4.45.. 1.922 8.555 5
6 1.26:'i .7903 .1508 .1908 6.633 5.242 2.386 1...506 6
7 1.3 16 .7599 .12£,6 .1666 7.898 6.002 2.843 17.066 7
8 1.369 .7307 .1085 .1485 9.214 6.733 3.294 22.180 !I
9 1.423 .702£, .1)945 . 1345 10.583 7.435 3.739 ..7 .801 I)
10 1.480 .6756 .0833 . 1233 12.006 8.111 4. 177 33.881 10
11 1.539 .6496 .0741 .11 4 1 13.486 8.760 4.609 40.377 11
12 1.601 .624 6 .0666 .1066 15.02£, 9.385 5.034 47.248 12
13 1.665 .6006 .0601 .100 1 16.627 9.986 5.453 54.454 13
14 1.732 .5775 .0547 .0947 18.292 I0.563 5.866 61.962 14
15 1.80 1 .5553 .°'1-99 .0899 20.024 JLI IS 6.272 69.735 ]5
16 1.873 .5339 .°'1-58 .0858 .. 1.825 11.65.. 6.672 77.744 16
17 1..948 5 134 .°'1-22 .0822 3.697 12.166 7.066 S.5.9-58 17
18 2.026 .4936 .0390 .0790 25.645 12.659 7.453 94.350 l!I
19 2. 107 .4746 .0361 .076 1 .. 7.671 13.134 7.S.34 !02.893 19
20 ... 191 .4564 .0336 .0736 29.77& 13.590 8...09 111.564 20
21 2.279 .4388 .0313 .0713 31.969 14.029 8.578 120.341 21
22 2.370 .4220 .0292 .0692 34.248 14.45 1 8.94 1 129.202 12
23 2.46:'i .4057 .0273 .0673 36.61& 14.857 9.297 138..128 23
24 2.-63 .390 1 .0256 .0656 39.083 1-_247 9.64 147.IOI 24
25 2.666 .3751 .0240 .0640 4 I.6'Ui 15.622 9.993 156.IM 25
26 2.772 .3607 .022£, .0626 44.31 2 15.983 10.33 1 165. 121 26
27 2.883 .3468 .0212 .06 12 47.084 16.330 10.664 174.138 27
28 2.999 .3335 .0200 .0600 49.968 16.663 10.99 1 183.142 28
29 3. 11 9 .3207 .0189 .0589 52.966 16.9 4 11.312 192.120 29
30 3.24 3 .3083 .0178 .0578 56.085 17.292 11 .627 201.062 30
31 3.373 .2965 .0169 .0569 59.328 17.588 l 1.937 209.955 31
32 3.50 .2851 .01 59 .0559 62.701 17.874 12.24 1 .. 18.792 32
33 3.648 .274 1 .0151 .055 1 66.209 18.148 12.540 227.563 33
34 3.794 .2636 .01 43 .0543 69.858 18.41 I 12.832 236.2£,0 34
35 3.946 .2534 .0136 .0536 73.652 18.665 13.120 244.876 35
40 4.80 1 .2083 .OI05 .0505 95.025 19.793 14.476 286.530 40
45 5.84 .1 .1712 .00826 .0483 121.029 20.720 1. 5.705 325.402 45
50 7. 107 .1407 .00655 .0466 152.667 2 1.482 16.812 361.163 50
55 8.646 .1157 .00523 .0452 191.159 22.109 17.8.07 393.689 55
60 10.520 .0951 .{)0420 .0442 237.990 22.623 18.697 422.996 60
65 12,,799 .078 1 .00339 .0434 ..94.968 23.047 1. 9.49 .1 449.201 65
70 15.572 .0642 .00275 .0427 364.290 ..3.395 20.196 472.479 70
75 18.945 .0528 .00223 .0422 448.630 23.680 20.S.2 ] 493.041 75
80 23,0 -0 .0434 .001&1 .04 1. 8 551.244 23.915 21.372 5 11.116 80
85 28.044 .0357 .001 48 .04 15 676.089 24.109 21.857 526.938 !15
90 34.11 9 .0293 .00121 .04 12 &27.981 24.2b7 22.283 540.737 90
95 41.51.1 .024 1 .00099 .04 1. 0 I 012.8 24.398 22.65- 552 ..730 95
100 50.505 .0 198 .00081 .0408 1237.6 24.505 22.980 563.125 mo

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Compound Interest Factors

Singte Payment Uniform Pa,yment Series Ariithmetic G:radi:ent
Compound Present Sin king Capital Compound Present Gradient Gradient
Amount Worth Fund Recovecy Amount Worth Un iform Pres;ent
Factor Factor Factor Factor Factor Factor Series Worth
IFi nd f find P Find A Find A Find F Find P Find A Find P
Given P Given F Given F Given P Given A Give,nA Given G GivenG
ll F/P Pl f AIF AIP FIA PIA AIG PIG f1

1 1.045 .9569 1.0000 1.0450 1.000 0.957 0 0 1

2 1.092 .9157 .4&90 .5340 2.045 1.873 0.4&9 0.916 2
3 1.1 41 .8763 .3 l88 .363& 3. 137 2.749 0.971 2.668 3
4 1.193 .83&6 __337 .27&7 4.278 3.588 1.445 -.184 4
5 1.246 .8025 .1828 .227& 5.471 4.390 1.9 [2 8.394 5
6
7
1.302
1.361
.7679
.734&
.1489
.1247
.1939
.1697
6.7 17
&.0 19
5.158
5.893
2..372
2.&·24
1__233
16.642 .,6
8 1.422 _703 _ .1066 .1 516 9.380 6.596 3.269 _l.564 8
9 1.486 .67_9 .0926 .1376 10.802 7.269 3.707 _6_94& 9
10 1.553 .6439 .08 14 .1264 12.288 7.913 4.138 32.743 lD
l1 1.623 .616_ .0722 .1172 13 .841 &.529 4.562 3&.905 l1
12 1.696 .5897 .0647 .1097 15 .464 9.119 4.97& 45.391 l2
13 1.772 .5643 .0583 .1033 17. 160 9.683 5.3&7 52.163 l3
14 1.852 .5400 .0528 .097& l&.932 I0.223 5.7&9 59.182 ]4
15 1.935 .5167 .048 1 .0931 20.784 I0.740 6.1&4 66.416 15
16 __022 .4945 .0440 .0890 22.719 11.234 6.572 73.833 16
17 .113 .4732 .0404 .0854 24.742 11.707 6.953 &1.40¢ ]7
18 __208 .45~& .0372 .0&22 26.855 l-.160 7.327 &9.102 18
19 2.308 .4333 .0344 .0794 29.064 12.593 7.695 96.901 19
2-0 2.412 .4146 .03 19 .0769 31.371 13.1)08 8.055 104.779 20
21 .520 .396& .0296 .0746 33.783 13.405 8.409 112.715 21
22 __ 634 .3797 .02T .0725 36.303 13.784 8.755 120.689 22
23 2.752 .3634 .0257 .0707 3&.937 14.148 9.096 12&.682 23
24 __ 876 .3477 .0240 .0690 41.689 14.495 9_4_9 136.680 24
25 3.005 .3327 .0224 .0674 44.565 14.828 9.756 144.665 25
26 3.1 41 .31&4 .02 10 .0660 47.571 15.1 47 10.077 152.625 26
27 3.282 .3047 .Ol97 .0647 50.711 15.451 J0.391 160.547 27
28 3.430 .29 16 .Ol85 .0635 53.993 15.743 l0.698 168.42.0 28
29 3.584 .2790 .0 1.74 .0624 57.423 16.022 10.999 176.232 29
30 3.745 .2670 .0 164 .0614 61.007 16.289 l 1.295 1&3.975 30
31 3.91 4 .2555 .0154 .0604 64.752 16.544 l I .S &3 191.64{1 31
32 4.1)90 .2445 .Ol 46 .05% 6&.666 16.789 11.&66 199.220 32
33 4.274 .2340 .0137 .05&7 72.T6 17.023 12.143 206.707 33
34 4.466 .2239 .0 130 .05&0 77.030 17.247 [2.41 4 _14_095 34
35 4.667 .2143 .0 123 .0573 &1.497 17.461 12.679 221.380 35
-
4D 5.816 .1719 .00934 .0543 I07.030 18.402 13.917 256.098 40
45 7.248 .13&0 .00720 .05_2 138.850 19.156 l5.0?...0 287.732 45
5D 9.033 .1107 .O!i-60 .0506 l7&.503 19.762 15 .998 316.145 50
55 11.256 .08&& .00439 .0494 227.918 20.248 16.&60 341.375 55
60 14.027 .0713 .00345 .04&5 2&9.497 2.0.638 17.617 363.571 60
65 17.481 .0572 .00273 .OH7 366.237 20.951 18.27& 3&2.946 65
7(1t 21.784 .O:l-59 .002 l 7 .0472 461.869 _1.2m 18.&54 399.750 70
75 27.147 .036& .00172 .0467 5&1.043 1.40:l- 19.354 414.242 75
80 33.830 .0196 .00137 .0464 729.556 _(.565 19.7&5 4- 6.680 80
85 42.158 .0237 .00 109 .0461 914.630 _1_695 20.157 437.309 85
90 5 .537 .0190 .00087 .0459 1145.3 _1_799 20 .476 446.359· 90
95 65.471 .0153 .00070 .0¢57 143-.7 _1_883 20.749 454.039 95
100 &1.588 .0123 .00056 .04l5-6 1790.9 21.950 20.9& 1 460.537 ]00

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5% Com pound Inte rest Factors 5%

Single Payment Unifonn P·a1ymen.t Seri es Arithmetic Gra.dierrit
Compound Present Sinkin g, Capital Compound Present Gradient Gradient
Amou nt Wo rth Fund Recove ry Amount Worth Un iform Present
Factor Factor Factor Factor Factor Factor Series Worth
Find F Fiind P Find A Find A f ind F Find P Find A Find P
Given P Given f Given F Given P Given A Given A Given G Give n G
J1 FIP PIF AIF AIP FIA PIA AIG PIG n
1 1.0 -0 .9524 1.0000 1.0500 1.000 0.952 0 0 1
2 1. 102 .9070 .4878 .5378 2.050 l.859 0.488 0.907 2
3 1.1.58 .8638 .3172 .3672 3.152 2.723 0.%7 2.635 3
4 1.2 16 .8227 .2320 . 820 4.310 3.546 1.439 5.103 4
5 1.276 .7835 .1810 .23 10 5.526 4.329 1.902 8.237 5
6
7
1.340
1.407
.7462
.7!07
.1 470
.1228
.1970
.1728
6.802
8.142
-.076
5.786
2.358
2.805
11.968
16.232 .,
6

8 1.477 .6768 .1047 .1547 9.549 6.463 3.244 20.970 8

9 1.55 1 .6446 .0907 . 1407 11 .027 7.108 3.676 2.6.127 9
10 1.629 .6139 .0795 .1. 295 12.578 7.722 4.099 3 1.652 10
11 1.7 10 .5847 .07M .L04 14.207 8.306 4.51 4 37.499 11
12 1.796 .5568 .0628 .1 128 15.917 8.863 4.922 43 .624 12
13 1.886 .5303 .0565 .1065 17.713 9.394 5.3 I 49.988 13
14 1.980 .50- 1 .0510 .10 10 19.599 9.899 5.713 56.553 14
15 2.079 .48IO .0463 .0963 21.579 l0.380 6.097 63.288 ]5
16 2. 183 .4581 .0423 .0923 23.657 10.838 6..474 70. 159 16
17 2..292 .4363 .0387 .0887 5.840 I 1.274 6.842 77.140 1'7
18 2.407 .41 55 .0355 .0855 - 8.1 32 l l.690 7.203 84.2.M 18
19 2.527 .3957 .0327 .0827 30.539 12.085 7.557 91.327 19
20 2.653 .3769 .0302 .0802 33.066 12.462 7.903 98.488 20
21 2.786 .3589 .0280 .0780 35.719 12.821 8.242 105.667 21
22 2_9r .3419 .02.60 .0760 38.505 13.163 8.573 II .846 22
2'3 3:072 .3Y6 .0241 .0741 4 1.430 13.489 8.897 120.008 23
24 3.225 .3 101 .0225 .0725 44.502 13.799 9.-1 4 1.:7.140 24
25 3.386 .2953 .0210 .071 0 47.727 14.094 9.524 134.227 25
26 3.556 .2812 .0196 .0696 51.113 14_:m 9.827 141.258 26
27 3.733 .2678 .0183 .0683 54.669 14.643 10.U 148.222 27
28 3.920 .255 1 .0171 .067 1 58.402 14.898 10.41 1 155.1 IO 28
29 4. 11 6 .2429 .0160 .0660 62.323 L141 I0.694 161.912 29
3(1 4.322 .231 4 .0151 .065 [ 66.439 15.372 I0.969 168.622. 30
31 4.538 .2204 .0141 .064 1 70.761 15.593 11.238 175.233 3]
32 4.765 . 099 .0133 .0633 75.299 1-_803 11.501 I 81.739 32
33 5,003 .1 999 .0125 .o6r 80.063 16.003 11.757 188.135 33
34 5.253 .1 904 .011 8 .06 [8 85.067 [6.1 93 12..006 194.4116 34
35 5.5 16 .1813 .0111 .06 1l 90.320 l6.374 12...'.50 200.580 35
40 7.040 .1420 .00828 .0583 120.799 17.159 l3.377 229.545 40
45 8.98 - .J l l3 .0062.6 .0563 159.699 17.774 l4.364 L55.314 45
5(1 11 .467 .0872 .00478 .0548 209.347 18.256 15._23 277.91 4 50
55 14.636 .0683 .00367 .0537 _72.711 18.633 15.966 _97_510 55
60 18.679 .0535 .00283 .0528 353.58 _ l8.929 16.606 314.343 60
65 23.840 .0419 .00219 .0522 456.795 19.161 17.154 328.691 65
70 30.426 .0329 .00170 .0 - 1.1 588.525 19.343 17.62 1 340.841 70
75 38.832 .0258 .0013 _ .05 [3 756.649 l9.485 18.018 351.072. 75
80 49 .-6 1 .0202 .001 03 .05 [0 97 1.2.2 _ [9.596 18.353 359.646 80
85 63.254 .0158 .00080 .0508 1245.1 19.684 18.635 366.800 !15
90 80.730 .0124 .()0063 .0506 1594.6 19.75_ 18.87 1 37-.749 90
95 103.034 .00971 .00049 .0 -05 _040.7 19.806 19.069 377.677 95
100 131.500 .00760 .00038 .0504 26!0.0 l9.848 19.234 381.749 100

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6% Com pound Interest Factors 6%

Sii:igle Payment Uniform Payment S"llries Arithmetic Gra.dieBt
Compou nd Present Sinking; Capital Compoun d Present Gradient Gradient
Amount Worth Fund !Recovery Amount Worth Uniform Present
Factor Factor Factor Factor Facto r Factor Se,ries Wo rth
Find F Find P Find A Find A fi nd F Find P Find A Find P
Given P Given F Given F Given P Given A Given A Given G Given G
n FIP PIF Alf AIP f /A PIA AIG PIG I)

1 1.060 .9434 UJOOO 1,0600 I.OOJ 0.943 0 0 1

2 1. 124 .8900 .4854 ..5454 2.00) um 0.485 0.890 2
3 1. 191 .8396 .3141 .374 1 3.184 2.673 0.96 1 2.569 3
4 1.262 .7921 .22&6 .2886 4 .375 3.465 1.427 4.945 4
5 1.338 .7473 .1774 .2374 5.637 4-.212 1.884 7.934 5
6 1.419 .7050 .1434 .2034 6.975 4.917 2.330 11.459 6
7 1.504 .6651 .1191 . 1791 8.394 5.582 2.768 15.450 7
8 1.594 .6274 .IOIO .1610 9.897 6.210 3.1 95 19.841 8
!I 1.689 .5919 .0870 . 1470 11 .491 6.802 3.613 24.577 !I
]0 1.791 .5584 .0759 .1359 13.181 7.3-60 4.022 29.602 ]D
11 1.898 --2.68 .066& .1268 14.972 7.&&7 4.421 34.870 u
12 _,012 .4970 .0593 .1.1 93 16.870 8.384 4.8 ll 40.337 ]2
l3 __133 .4688 .0530 . 11 30 18.& 2 8.&53 5. 192 45.963 l3
1.4 2.261 .4423 .0476 . 1.076 21.015 9. 95 5.564 51.713 14
15 __397 .4173 .0430 . 1030 23 ..:76 9.712 5.926 57.554 15
16 2.540 .3936 .0390 .0990 r .672 10.106 6.279 63.4159 16
17 2.693 .371 4 .0354 .0954 28.213 10.477 6.624 69.401 ]7
]8 2.854 .3503 .0324 ,0924- 30 .906 10.&2& 6.960 75.357 ]8
]!I 3,026 .3305 .0296 ,0896 33.760 1. 1.15& 7.287 81.306 l !I
20 3.207 .3118 .0272 ,0872 36.7&6 11.470 7.605 87.230 2D
21 3.400 .2942 .11250 .0850 39.993 11.764 7.915 93.113 21
22 3.604 .2775 .0230 .0830 43.392 12.04_ 8.2 17 98.941 22
23 3.82.0 .2618 .0213 :0 13 46.996 12.303 8.510 104.700 23
24 4.04-9 .2470 .0197 ,0797 -0.&15 12.550 &.795 110.381 24
25 4.292 .2330 .01&2 ,0782 54.&64 12.783 9.072 11 5.973 25
26 4.549 .2198 .0169 :0769 59.156 13.003 9.34 1 12 1.46& 26
27 4.822 .2074 .0157 ,0757 63.706 13.211 9.603 I 6.860 27
28 5. 112 .1 956 .0146 :0746 68.52.& 13.406 9.857 132.14- 28
29 5.4 18 .I :6 .0136 .0736 73 .640 13.591 I0..103 137.309 29
30 5.743 .1741 .0126 ,072.6 79 .05& 13.765 l0.342 142.359 3D
31 6,088 .1643 .OIi& .07 18 84.801 13.929 10.574 147.286 31
32 6.453 .1550 .01 IO ,07 10 90.890 14.084 I0.799 152.090 32
33 6.841 .1462 .0103 .0703 97.343 14.230 11 ..017 1-6.76& 33
34 7.251 .1379 .00960 :0696 !04. 184 14.36& 11.228 161.319 34
35 7.686 .1301 .00897 .0690 111.435 14.498 11 .432 165.743 35
40 10.286 ..0972 .00646 :0665 154.76_ 15.046 12.359 1&5.957 40
45 13.765 .0727 .00470 .0647 212.743 15.456 13 .141 W3.l09 4.5
50 18.42.0 ..0543 .00344 ,0634 190.335 15.762 13 .796 _1 7.4-57 50
55 _4_650 .0406 .00254 ,0625 394 .171 15.991 14..341 229.322 55
60 32.988 .0303 .00188 .0619 533 .126 16.16.1 14.791 239.043 6D
65 44. 145 .0227 .00139 ,06 1. 4 7 19.080 16. 89 15. 160 246.945 65
70 59,076 .0169 .00103 ,06 10 967.92& 16.3&5 15.46 1 253.327 70
75 79.057 .0126 .00077 ,0608 1300 .9 16.456 15 .706 258.4-53 75
80 105.796 .00945 .00057 .0606 1746.6 16.509 15 .903 262.549 8D
85 141.578 .00706 .00043 .0604 2343.0 16.549 16.062 265.&IO 85
90 1&9.464 .00528 .1)0032 ,0603 31 4 1.1 16.579 16. 189 268.395 !10
95 253.545 .00394 .00024 ,0602 4-09.1 16.601 16..290 270.437 !15
100 339.300 .00295 .0001& .0602 5 638.3 16.61& 16.37 1 272.047 100

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7% Compound Interest Factors 7%

Single Payment Uniform ,fl•aymerit Series Arithmetic Gra.die111t
Compound :Pre.s.e nt Sinking, Ci pital Compound Pre~nt Gradient Gradi ent
Amou nt Worth Fund Recovery Amou nt Worth Un iform PreS-ent
Factor Factor Factor Factor Factor Factor Series Worth
Find F Find P Find A Find A f ind F Find P Find A FindP
Given P Givenf Given F Given P Given A Given A Given G Give n G
t~ FIP PIF Alf AIP FIA PIA. AIG PIG II

1 1.070 .9346 1.0000 1.0700 1.000 0.935 0 0 J

2 1. 145 .8734 .4831 .553 1 2.070 1.808. 0.48.3 0.873 2
3 1.225 .8163 .3111 .38 11 3.215 2.624 0.955 __506 3
4 1.3 11 .7629 .225 _ __952 4.440 3.38.7 1.416 4.795 4
5 1.403 .7130 .1739 .2439 5.751 4.100 I.S.65 7.647 5
6 1.50 I .6663 .1398 .2098 7.153 4.767 2.303 10.978 6
7 1.606 .6227 .1156 .1856 8.654 5.389 2.730 14.715 7
8 1.7 18 .5820 .0975 .1675 10.2.60 -.971 3.147 18..789 8
9 1.838 .5439 .0835 . 1.535 ll.978. 6.515 3.552 23.140 9
10 1.967 .5083 .0724 . 1424 13.816 7.024 3.946 27.716 ]0
11 2. 105 .4751 .0634 .1334 15.784 7.499 4.330 3_.467 11
12 2.252 .4440 .0559 .1259 17.888 7.943 4.703 37.351 12
13 2.4 10 .4150 .0497 .I 197 -0.141 8.358. 5.065 42.330 13
14 2.579 .3878 .0443 .11.43 22.551 8.745 5.417 47.372 14
15 2.759 .3624 .0398. .1098 25.129 9.IOS. 5.758 52.446 15
16 2.952 .3387 .0359 .l059 _7_ 88 9.447 6.090 57.527 16
17 3. 159 .3 166 .0324 .1024 30.840 9.763 6.41 1 62.592 1'7
18 3.380 .2959 .0294 .0994 33.999 10.059 6.722 67.622 18
19 3.6 17 .2765 .02.68. .0968 37.379 10.336 7.024 72.599 19
2-0 3.870 .2584 .0244 .0944 40.996 10.594 7.3 16 77.509 20
21 4. 141 .24 .1 5 .0223 .0923 44.865 10.836 7.599 S.2.339 21
22 4.430 .2257 .0204 .0904 49.006 11.061 7.S.72 87.079 22
23 4.74 1 .2J09 .0187 .0 87 53. 36 1. 1.272 8.137 91.720 23
24 5:072 .1 971 .0172 .0872 58.177 11.469 8.392 96.255 24
25 5.421 .1842 .0158. .0858 63.249 11.654 8.639 100.677 25
26 5.807 .1722 .0146 .0846 68..677 11.826 8.8.77 104.981 26
27 6.214 .1609 .0134 .0834 74.484 11.987 9.107 109. 166 27
28 6.649 ..i-D4 .0124 .0824 80.698 12.137 9.329 113.227 28
29 7. 114 .1406 .0114 .08 14 87.347 12.278. 9.543 117. 162 29
30 7.6 12 . 131 4 .0106 .0806 94.461 12.409 9.749 120.972 30
31 8.145 .1228 .00980 .0798 102.073 12.532 9.947 124.655 31
32 8.7 1. 5 .1 147 .00907 .079 1 110.218 12.647 10.138 128.212 32
33 9.3r .J072 .00841 .0784 118.934 12.754 10.322 131.644 33
34 9.978 .1002 .0078.0 .0778 12 .259 12.854 I0.499 134.951 34
35 10.677 .0937 .00723 .0772 138.237 12.948. I0.669 138..135 35
40 14.974 .0668 .00501 .0750 199.636 13.332 11.4 3 15- .293 40
45 21.002 .0476 .00350 .0735 285.750 13.606 12.036 163.756 45
50 29 .457 .0339 .00246 .0725 406.530 13.801 1. 2.529 172.905 50
55 41.3 15 .024 2 .00174 .07 17 575.930 13.940 12.92 1 18.0. 124 55
60 57.947 .0!73 .00123 .07 12 8 13.523 14.039 IL32 185.768 60
65 81.273 .0123 .00087 .0709 1146.8 14.110 13.476 190. 145 65
70 113.990 .00877 .0006 .0706 161 4.1 l4.160 13.666 193.519 70
75 159.877 .00625 .00044 .0704 2269.7 14.196 13.S.1 4 196.IM 75
80 224.235 .00446 .00031 .0703 3 189.1 14.222 13.927 198..075 80
85 314.502 .00318 .00022 .0702 4478.6 14.240 14.0 15 199.572 85
90 441. 105 .00227 .00016 .0702 6287.2 14.253 14.0S. I 200.704 90
95 618 .673 .00 .1 62 .00011 .070 1 8823.9 14.263 14.132 201.558 95
100 867 .720 .00115 .00008. ,070 1 1238.1.7 14.269 14.170 202.200 100

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8% Com pound Interest Factors 8%

Sii:igle Payment Uniform Pa,yment Series Arithmetic Gradie111t
Compound Present Sin king; Capital Compoun d Prese nt Gradient Gradient
Amount Worth Fu nd !Recovery Amount Worth Uniform Pre s;ent
Factor Factor Factor Factor Factor Factor Series Worth
Find F Find P Find A Find A f ind F Find P Find A Find P
Given P Given F Given F Given P Given A Given A Given G Given G
n FIP PIF AIF AJP FIA PIA AJG PIG n
1 1.080 .9259 l.0000 1,0800 1.00) 0.926 0 0 1
2 1. 166 .8573 .480& .5608 2.0&0 l.7&3 0.481 0.857 2
3 1.260 .7938 .30&0 .3880 3.246 2577 0.949 2.445 3
4 1.360 .7350 .2-19 .3019 4 .506 3.31 _ 1.404 4.650 4
5 1.469 .6806 . 1705 .2505 5.&67 3.993 1.846 7.372 5
6 1.587 .6302 .1363 .2163 7.336 4.623 2.276 10.523 6
7 1.714 .-835 .IU .1 921 8.9'J-3 5.206 2.694 14.024 7
8 1.851 .5403 .0940 . 1740 10.637 5.747 3:099 17.806 8
I) 1.999 .5002 .0&01 .1 601 12.4&& 6.247 3.491 21.80& I)
10 2.159 .4632 .0690 .l490 14 .487 6.71 0 3.871 25.977 lD
11 _.332 .42~9 .0601 . 1401 16.645 7.139 4.240 30.266 u
12 - .518 .397 1 .0527 . 1327 18.977 7.536 4.596 34.634 12
13 2.720 .3677 .0465 .1.265 21.495 7.904 4.940 39.046 13
14 __937 .3405 .0413 . 1213 24. 21 5 8.244 5.273 43.472 14
15 3.172 .3152 .036& . 11 68 27 .15- 8.559 5.594 47.8&6 ]5
16 3.426 .29 19 .0330 . 1130 30.324 8.&51 5.905 52.264 ]6
17 3.700 .2703 .0296 .1 096 33.750 9.L2 6.204 56.58& ]7
18 3.996 .2502 .fJJ-67 . 1067 37 .450 9.372 6.492 60.843 ]8
]I) 4.316 .2317 .0241 . 1041 41.446 9.604 6.770 65.0!3 llJ
20 4.661 .21 45 .0219 .1 019 45.762 9.&18 7.037 69.090 2D
21 5,034 .1 987 .019& ,0998 -o. 23 10.017 7.294 73.063 21
22 5.437 . 1839 .01&0 .0980 -5_457 10.201 7541 76.926 22
23 5.871 .1 703 .0164 ,0964 60 .&93 10.371 7.779 80.673 23
24 6.341 .1577 .01 50 ,0950 66 .765 10.529 !t007 84.300 24
25 6.848 .1460 .0137 ,0937 73 .106 10.675 &.225 87.804 25
26 7.396 .1352 .0125 ,0925 79.954 10.&IO 8.435 91.184 26
27 7.988 .1 252 .0114 ,09 14 87.351 10.935 8.636 94.439 27
28 &.627 . 1159 .0l05 ,0905 95.339 l I.OSI 8.829 97.569 28
21) 9.317 .1073 .00962 .0896 103 .966 l I.IS& 9.013 1·00.574 21)
30 10.063 .0994 .00&&3 ,0888 113.2&3 11.258 9.1 90 103.4156 JD
31 I0.868 .0920 .00&11 .0881 123.346 11.350 9.358 106.216 31
32 I 1.737 .0852 .00745 ,0875 134.214 l l.435 9.520 108.85& 32
33 12.676 .0789 .006&5 ,0869 145.951 11.514 9.674 11l.3&2 33
34 13.690 .0730 .00630 ,0863 15 .6TI 11.5&7 9.82 1 113.792 34
35 14.785 .0676 .005&0 ,0858 172..317 l 1.655 9.961 116.092 35
40 1.725 .0460 .003&6 ,0839 59.057 11.925 I0.570 126.042 40
45 31.92.0 .0313 .00259 .0826 386.506 12.10& 11.045 133.733 45
50 46.902 .0213 .00174 ,0817 573.771 12.233 11 .411 139.593 50
55 6&.914 .01 45 .0011& ,0812 848.925 12.319 11 .690 144.006 55
60 l01.257 .009&& .000&0 .0808 125L 12s377 11 .902 147.300 6D
65 l4&.780 .00672 .()0054 ,o 05 I &47.3 12.416 12.060 149.739 65
70 218..607 .00457 .00037 ,0804 2720.1 12.443 12 .178 15 1.533 70
75 3_1_205 .00311 .00025 ,0802. 4002.6 12.461 12..266 152.845 75
80 471.956 .002 ' - .00017 .0802 5887 .0 12.474 12.330 153.&00 8D
85 693 .458 .00144 .00012 .0801 8655.7 12.4&2 12.377 154 .492 85
90 I 01&.9 .00098 .0000& ,0801 12724.0 12.4&& 12.41 2 154.993 90
95 1497. 1 .00067 .00005 ,0801 I& 70 1.6 12.492 12.437 155.352 1)5
100 2199.8 .00045 .00004 .0800 2:7 484.6 12.494 12.455 155.611 ]00

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9% Compound Interest Factors 9%

Singl'e Payment Unifonn :P·a1ymen.t Series Arithmetic Gra.die111t
Compound :Pre.sent Sinking, Capital Compound Present Gradient Gradient
Amount Wo rth Fun d Recovery Amount Worth Un iform Pre.s,ent
Factor Factor Factor factor Factor Factor Series Worth
Find F Find P Find A Find A f ind f Find P Find A Find P
Given P Givenf Given F Given P Given A Given .A Given G Give n G
D FIP PIF Alf AIP FIA PI/J.. AIG PIG n
1 1.090 .9174 1.0000 1.0900 1.000 0.917 0 0 1
2 1. 188 .84 17 .4785 .5 685 2.090 1.759 0.478 0.842 2
3 1.29 - .7722 .3051 .395 1 3.27& 2.531 0.943 __386 3
4 1.41.2 .7084 .2187 .3087 4.573 3.240 1.393 4.511 4
5 1.539 .6499 .1671 .257 1 5.985 3.890 l.&28 7.111 5
6 1.677 .5963 .1329 .-229 7.523 4.486 2.l.50 10.092 6
7 1.828 .5470 .1087 .1987 9.200 5.033 2.657 13.375 7
8 1.993 _-019 .0907 .1807 11.0'.2& 5.535 3.05 1 16.888 8
__172
9 .4604 .076& .1 668 13.0'.2I 5.995 3.43 1 20.571 9
10 2.367 .4224 .065& . 1558 15.193 6.4 1& 3.798 24.373 10
11 2.580 .3875 .0569 .1469 17.560 6.805 4. 15 .1 2&.248 11
12 2.8 13 .3555 .0497 .1397 - 0.141 7.161 4.49 1 32. 159 12
13 3.066 .3262 .0436 .1336 22.953 7.487 4.&18 36.073 13
14 3.342 .2992 .0384 .1284 6.019 7.786 5.133 39.963 14
15 3.642 .2745 .0341 .124 1 29.361 8.061 5.435 43 .807 ]5
16 3.970 T l9 .0303 .1203 33.003 8.313 5.724 47.585 16
17 4.328 .2311 .0270 .1170 36.974 8.544 6.002 51.282 17
18 4.7 17 .2120 .0242 .1142 41.301 8.756 6.269 54.886 18
19 5. 142 .]945 .0217 .111 7 46.019 8.950 6.524 5&.387 19
20 5.604 .1784 .0195 .1095 5 1.160 9.129 6.767 61.777 20
21 6. 109 .1637 .0176 .1076 56.765 9.292 7.001 65.051 21
22 6.659 .1502 .01 59 .1059 62.873 9.442 7.223 68.205 12
13 7.258 .1378 .01 44 .1044 69.532 9.580 7.436 71.236 23
24 7.9 1.1 .1264 .0130 .1030 76.790 9.707 7.63 74.143 24
15 8.623 . 11 60 .Oil & .10 18 &4.701 9.823 7.&32 76.927 25
16 9.399 . 1064 .0107 .!007 93.324 9.929 8.0l6 79.586 26
27 I0.24- .0976 .00973 .0997 102.723 10.0'.27 8.19 .1 &2 ..124 27
28 11. 167 .0895 .008 5 .0989 112.96& 10.116 8.357 &4.542 28
19 12. 172 .0 22 .00806 .098 1 124.136 10.19& 8.51 - &6.842 29
30 13.268 .0754 .00734 .0973 136.30& W.274 8.666 &9.0'.2.8 30
31 14.462 .0691 .00669 .0967 149.575 l0.343 8.&08 91.102 31
32 15.763 .0634 .006!0 .096 1 164.037 10.406 8.944 93.069 32
33 17. 182 .0 -82 .00556 .0956 179.801 10.464 9.072 94.931 33
34 18.728 .0534 .0050& .095 1 196.983 10.51& 9.193 96.693 34
35 20.414 .0490 .00464 .0946 215.711 10.567 9.308 9&.359 35
40 31 .409 .03 18 .00296 .0930 337.883 10.757 9.796 105.376 40
45 48.327 .0207 .00190 .09 19 5r.860 10.881 10.160 110.556 45
50 74.358 .0134 .001 23 .09 12 &15.085 10.962 I0.430 114.325 50
55 11 4.409 .00874 .00079 .0908 1260.1 ll.014 I0.626 117.036 55
60 176:032 .00568 .00051 .0905 1944.8 ll.04& I0.768 I l&.968 60
65 270.847 .00369 .00033 .0903 _99g_3 11.070 10.&70 120.334 65
70 416.73 1 .00240 .00022 .0902 4619.2 J 1.084 10.943 U .294 70
75 641.193 .00156 .00014 .090 1 7113.3 11.094 I0.9()4 U.965 75
80 986S5 .00 IOI .00009 .090 1 109 -0.6 I l.100 11.030 12•..4-31 80
85 1517.9 .00066 .00006 .090 1 16&54.9 11.104 11.055 L2.753 85
90 2 335.5 .00043 .00004 .0900 25939.3 11.106 11.073 122.976 90
95 3 593.5 .0002.8 .00003 .0900 39916.8 11. IO& 11.os - 123.129 95
100 5 529. 1 .00018 .00002 .0900 61422.9 I l.109 11.093 123.233 100

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10% Compound Interest Factors 10%

Single Payme;nt Uniform Payme;nt Series Arithmetic Gradient
Compound Present Sin king Capita l Compound Present Gradient Gradient
Amou nt Worth fond Recovery Amount Worth Un iform Present
Factor Factor factor Factor Factor Factor Series Worth
Find f Find P Find A Find A Fiind F Find P Find A Find P
Given P Given F Given f Given P Given A Given A Given G Given G
n FIP PIF AIF AIP FIA PIA AIG PIG D

1 l. lOO .9091 l .0000 I. 11)00 1.000 0.909 0 0 1

2 l.210 .8264 .4762 .5762 2.1-00 1.736 0.476 0.826 2
3 1.331 .7513 .302 1 .4021 3.3!0 2.487 0.937 2.329 3
4 1.464 .6830 __155 .3155 4.641 3.170 1.38. l 4.378 4
5 1.611 .6209 .1638 .2638. 6.1 05 3.791 I.SID 6.862 5
6 1.772 .5645 .1-96 .2296 7.716 4.355 L24 9.684 6
7 1.949 .5132 .1054 .2054 9.487 4.868 2.622 L.763 7
8 .1 44 .4665 .OS.74 .1874 11 .436 5.3.35 3.004 16.029 8
9' __358 .424 1 .0736 .1736 13.579 5.759 3.372 19.421 !I
10 _.594 .3855 .0627 .1627 15.937 6.145 3.725 - 2.891 10
11 2.853 .3505 .0540 .1540 IS..53 1 6.495 4.064 26.396 11
12 3.138 .3186 .0468 .1468. 21.384 6.814 4.38.S. 29.901 12
13 3.452 .2897 .0408 .1 408 24.523 7.10.3 4.699 33.377 ]3
14 3.797 .2633 .0357 .1357 27..975 7.367 4.996 36.801 14
15 4.1 77 .2394 .03 15 .1315 31.772 7.606 5.279 40.152 15
16 4.595 .2176 .0278 .1278. 35.950 7.824 5.549 43.416 16
17 5.054 .1978. .0247 .1247 40.545 S..022 5.8.07 46.582 17
18 5.560 .1799 .02 19 .1219 45.599 S..2.01 6.053 49.640 18
19' 6.1 16 .1635 .Ol9 - .1195 51.159 S..365 LS.6 52.583 l!I
2() 6 ..728 .1 486 .Ol75 .1175 57.275 S..514 6..508 55.407 20
21 7.400 .1351 .0156 .1156 64JXl3 S..649 6.719 58..1 IO 21
22 S..140 .1228. .0140 .1140 71 .403 S..772 6.919 60.689 22
23 8.954 .1117 .0126 .1126 79.543 S..883 7.IOS. 63.146 23
24 9.850 .IOl5 .01 13 .1113 88..497 S..985 7. S.8 65.481 24
25 I0.835 .0923 .0102 .1102 98..347 9.077 7.458 67.696 25
26 11.9 18 .0839 .009 [6 .1092 109.1 82 9. l61 7.619 69.794 26
27 13. 1IO .0763 .OOS.26 .IOS.3 121 .1 00 9.237 7.770 71.777 27
28 14.421 .0693 .0074 .1075 134.210 9.307 7.914 73.650 28
29' 15.863 .0630 .00673 .1067 148..631 9.370 8.049 75.415 2!1
30 17.449 .0573 .00608 .1061 164.494 9.427 8.176 77.077 30
31 19.1 94 .0521 .00550 .I055 181.944 9.479 8.2% 78..640 31
32 _1.114 .0474 .00497 .I050 201.138 9.526 8.409 S.0.108 32
33 23.225 .0431 .00450 .1045 222.252 9.569 8.515 S.1.486 33
34 25.-48 .0391 .00407 .1041 245..477 9.600 8.61 - S.2.777 34
35 _S,J 02 .0356 .00369 .1037 271.025 9.644 8.709 S.3.987 35
40 45.259 .0221 .00226 .1023 442.593 9.779 9.096 S.S..953 40
45 72.891 .Ol37 .00139 .IOl4 7 18..905 9.863 9.374 92.454 45
50 117.391 .00852 .00086 .1009 1163.9 9.915 9.570 94.889 50
55 IS.9.059 _005 _9 .00053 .1005 188.0.6 9.947 9.708 96.562 55
60 304.482 .00328. .00033 .1003 3034 ..8 9.967 9.S.02 97.701 6D
65 490.371 .00204 .00020 .1002 4893.7 9.980 9.8.67 98..471 65
70 78.9.748 .001 _7 .000 13 .1001 7887.5 9.987 9.911 98..987 70
75 I _71..9 .00079 .00008 .1001 12709.0 9.992 9.94 1 99.332 75
80 2048..4 .00049 .0000 - .IOOO 20474.0 9.995 9.% J 99.561 80
85 3 _99_0 .00030 .00003 .1000 32979.7 9.997 9.974 99.71- 85
90 5313:0 .00019 .00002 .IOOO 53 120.3 9.998 9.98.3 99.812 90
95 8556 ..7 .OOOL .0000 1 .IOOO 85556 ..9 9.999 9.98.9 99.877 !15
100 13 78.0.6 .00007 .OOOO J .IOOO 137796.3 9.999 9.993 99.920 100

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may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

12% Compound Interest Factors 12%

Single Payment ti 111 iform Payment Series Aritihmetic Grad iei;it
Compound Present Sinki ng Capita! Compound Pre.sent Gradient Gradient
Amount WoTtn Fund Recove ry Amount Worth Unifom1 Pre.sent
Factor Factor facto r Factor factor Fa.:tor ~ries Worth
Find F Find P Find A Find A Find f Find P Find A Fin d P
Given P Given F Given F Gnve nP Given A Given A Given G Given G
n FIP PIF AIF AIP FIA PIA AIG PIG II

l 1.120 .8929 1.0000 l.l200 1.000 0.893 0 0 1

2 1.254 .7972 .4717 .5917 2.120 1.690 0.472 0.797 2
3 1.405 .7118 .2963 .4 163 3.374 2.402 0.925 2.221 3
4 1.574 .6355 .2092 .3292 4.779 3:037 1.359 4.1 27 4
5 1..762 5674 . 1574 .2774 6.353 3.605 l.775 6.397 5
6 1.974 .-066 .1232 .2432 8.1 15 4. 111 2.172 S..930 6
'7 2.21J .4523 .1)991 .2191 I0.089 4. -64 2.551 11 .644 7
8 2.476 .4039 .OS.13 .2013 12.300 4.968 2.913 14.471 8
~ 2.773 .3606 .0677 .1877 14.776 5.328 3.257 17.356 9
10 3.106 .3220 .0570 .1770 17 .549 5.650 3.5&5 20.254 10
l.t 3.479 .2875 .04&4 . 1684 20.65 - 5.938 3.895 23 .129 11
12 3 ..896 .Z-67 .0414 . 161 4 24.133 6. 194 4.190 25 .952 12
B 4.363 .2292 .0357 .1557 28.029 6.424 4.46& 2&.702 13
14 4.887 .2046 .0309 .1509 32.393 6.628 4.732 31.362 14
15 5.474 . 1827 .026& .1468 37.280 6.8 11 4.9&0 33.920 15
16 6.130 .1631 .0234 ..1434 42.753 6.974 5.215 36.367 16
17 6.866 .1456 .0?...05 .1405 48.S.84 7.120 5.435 3&.697 l7
18 7 ..690 . 1300 .0179 ..1379 55.750 7.250 -.643 40.908 18
J~ S..613 ..1 161 .Ol5S. .1358 63 .440 7.366 5.83& 4 .998 19
w 9.646 . 1037 .0139 .1339 72.052 7.469 6.0?...0 44.968 20
21 I0.804 :0926 .01_2 . l322 81.699 7562 6.191 46.819 21
22 12.lOO .0826 .OIO& ..1308 92.503 7.645 6.351 4&.554 22
23 13 ..552 .0738 .()0956 . 1296 104.603 7.718 6.501 50.178 23
24 15. 179 .0659 .00846 .1 2ll5 118 .1 55 7.784 6.641 51.693 24
25 17:000 .0588 .00750 . 1275 133.334 7.843 6.771 53.105 25
26 19.040 .0525 .00665 .1267 150.334 7.896 6.892 54.418 26
27 21.325 .0469 .00590 .1 259 169.374 7.943 7.005 55.637 27
28 23 ..884 :0419 .00524 .1252 190.699 7.984 7.110 56.767 28
2~ 2.6.750 :0374 .00466 .1247 214.583 &:022 7.207 57.814 29
30 29.960 :0334 .0041 4 .1241 241.333 &:055 7.297 5&.782 30
31 33555 .0298 .00369 .1237 271._93 8:085 7.381 59.676 31
32 37.5 2 .0266 .0032& .1233 304.848 8. 11 2 7.459 60.-01 32
33 42.092 .0238 .00292 ..1229 342.429 8.135 7.530 61 .261 33
34 47. 143 .0212 .00?-60 .1226 384.52 1 8. 157 7.596 61.961 34
35 5-.800 .0189 .00232 .1223 431.663 8. 1.76 7.658 62.605 35
40 93:051 :0107 .00130 .1213 767 .09 1 8.244 7.899 65.1 16 40
5 163.988 :006IO .00074 . 1207 1358.- 8.283 8.057 66 ..734 45
50 2ll9.002 :00346 .00042 .1204 2400 ..0 8.304 8.160 67.762 50
55 509.321 .00196 .000?-4 .1202 4236 ..0 8.317 LlS 68.408 55
60 897.597 .00111 .000 13 .1201 7 471.6 8.324 8.266 68.8IO 60
65 1581.9 .00063 .00008 . 1201 13 173.9 8.328 8.292 69.058 65
'70 2787 .8 :00036 .00004 .1 200 23223.3 8.330 8.308 69.210 70
'75 4913 . 1 :00020 .00002 .1200 40933.8 8.332 8.318 69.303 75
80 8658.5 .00012 .0000 1 .1200 72 145 ..7 8.332 8.324 69.359 80
85 15 259.2 .00007 .0000 1 .1200 127 151.7 8.333 8.32& 69.393 85
90 26 891.9 :00004 .1200 224 091.1 8.333 8.330 69.414 90
95 47392.8 .00002 . 1200 394931.4 8.333 8.331 69.426 95
100 83 522.3 :00001 .1 200 6960!0.5 8.333 8.332 69.434 100

35 of 52 1/25/2020, 11:37 AM
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may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

15% Compound Interest Fact ors 15%

Single Payment Unifo ,m Payme111t Series Arithmetic Gradient
Compound Present Sinking Capital Compou nd Present Gradient Gradient
Amount Worth IFund Recovery Amount Worth Un iform Pre.sent
Factor Factor Factor Factor Factor Factor Series Worth
Find F Find P Find A Find A Ftind F Find P Find A Find P
Given P Given F Given F Given P Given A Given A Given G Given G
n FIP PIF AIF AIP FIA PIA AIG PIG I)

l 1.150 .8696 l.0000 1.1500 1.000 0.870 -0 0 l

2 1.322 .7561 .46.5 1 .6151 2. 150 1.626 0.465 0.756 2
3 1.521 .6575 .~880 .4380 3 ..472 __283 0.907 __ 071 3
4 1.749 .5718 .2003 .3503 4.993 2.855 1.326 3.786 4
5 2.011 .4972 .1483 .2983 6.742 3.352 1.723 5.775 5
6 _.313 .4323 .1142 .264 _ 8.754 3.784 2.09'7 7.937 6
7 2.660 .3759 .0904 .2404 11.067 4.160 2.450 10.192 7
8 3.059 .3269 .0729 .2229 13.727 4.487 2.781 12.481 8
9 3.518 .2M3 .0596 .2096 16.786 4.772 3.092 14.755 9
10 4.046 .2472 .0493 .1993 20.304 5.019 3.383 16.979 10
u 4.652 .21 49 .041 1 .1911 24.349 5.234 3.655 19.129 u
12 5.350 .1869 .034 - .1845 29JX)2 5.42 1 3.908 _1.185 12
13 6. 153 .1625 .029 1 .1791 34.352 5.583 4.144 23.135 ]3
14 7:076 .1 413 .0247 .1747 40.505 5.724 4.362 24.972 ]4
15 lU37 .1229 .02 l0 .1710 47.580 5.847 4.565 -6.693 15
16 9.358 .1069 .0179 .1679 55.7 17 5.954 4.752 28.296 16
17 10.761 .0929 .0154 .1654 65 ..075 6.047 4.925 29.783 17
18 12.375 .0808 .0132 .1632 75. 36 6.m: 5.084 31.156 18
19 14.232 .0703 .01 l3 .1613 88.212 6.198 5.23 1 32.421 19
2.0 16.367 .061 I .00976 .1598 102.444 6.259 5.365 33.582 20
21 18.822 .0531 .00842 .1584 118.810 6.312 5.488 3 .645 21
22 _(.645 .046_ JXJ727 .1573 137.632 6.359 5.601 35.615 22
23 24.891 .0402 .00628 .1563 159.276 6.399 5.704 36.499 23
24 ~8 ..625 .0349 .00543 .1554 184.168 6.434 5.798 37.302 24
25 3-.919 .0304 .00470 .1547 2L.793 6.464 5.883 38.031 25
26 37_3 -7 .02.64 .00407 .1541 245.7 12 6.491 -.961 38.692 26
27 43.535 .0230 .00353 .1535 283.569 6.514 6.032 39.289 27
28 50:066 .0200 .00306 .1531 327. 1-04 6.534 6.096 39.828 28
29 57.-75 .0174 .00265 .1527 377. 170 6.551 6.154 40.315 29
30 66.212 .0151 .00230 .1523 434.745 6.566 6.207 40.753 30
31 76.144 .0131 .00200 .1520 500.957 6.579 6.254 41.147 31
32 87.565 .0114 .00173 .1517 577. 100 6.591 6.-97 41.501 32
33 100.700 .00993 .00 1. 50 .1515 664.666 6.600 6.336 4 1.818 33
34 115 ..805 .00864 .OO l3 I .1513 765.365 6.609 6.37 ] 42.!03 34
35 133. 176 .00751 .001 13 .1511 881.170 6.617 6.402 42.359 35
40 267.864 .00073 .00056 .1506 1779.1 6.642 6.517 43.283 40
45 538.769 .00186 .00028 .1503 3 585.J 6.654 6.5&3 43.805 4.5
50 I 083.7 .00092 .000 14 .150I 7217.7 6.661 6.620 44.096 50
55 2179.6 .00046 .00007 .150! 14524. l 6.664 6.641 44.256 55
60 4384.0 .00023 .00003 .1500 29220:0 6.665 6.653 44.343 6D
65 8817.8 .00011 .00002 .1500 58 778.6 6.666 6.659 44.390 65
70 17735.7 .00006 .0000 1 .1500 II 8 231.5 6.666 6.663 44.416 70
75 35672.9 .00003 .1500 237812..5 6.666 6.665 44.429 75
8-0 71750.9 .00001 .1 500 47833 .6 6.667 6.666 44.436 80
85 144316.7 .00001 .1500 962104.4 6.667 6.666 44.440 85
-

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18%, Compound Interest Factors 18%

Single Payment \lnifoim Payment Series Aritih metic G'rad ieillt
Compound Pre5ent Sin ki ng Capiui! Compound Present Gradient Gradient
Amount Worth Fund Recove ry Amou nt Worth Uniform Pre.sent
Factor Factor factor Facto:r factor Factor Series Worth
Find F Find P Find A Find A Findf Find P Find A Find P
Given P Given F Give n F GnvenP Given A Given A Given G Given G
n FIP PIF AIF AIP FIA PIA AIG PIG n
1 Ll80 .&475 l.0000 IJ800 1.000 0.&47 0 0 l
2 1.392 .7 182 .4587 .6387 2.180 1.566 0.459 0.7 18 2
3 1.643 .6086 .2799 .4599 3.572 - . 174 0.890 1.935 3
4 1.939 .5158 .1917 .37 17 5.215 __690 1.295 3.483 4
5 2.288 .4371 .1398 .3198 7.154 3. 1. 27 l.673 5.231 5
6 2.700 .3704 .I059 .2859 9.442 3.498 2.025 7.083 6
7 3. 185 .3 139 .0824 .2624 12.142 3.8 12 2.353 8.967 7
8 3.759 .2660 .065- .2452 15.327 4:078 2.656 I0.829 !I
9' 4.435 .2255 .0524 .2324 19.086 4.303 2.936 1-.633 9
10 5.234 . 1911 .0425 .2225 23.52 1 4.494 3.194 14.352 ]0
11 6.1 76 . 1. 619 .0348 .2148 28.755 4.656 3.430 15.972 11
12 7.288 .1372 .0286 .2086 34.93 1 4.793 3.647 17.481 12
13 8.599 .l 163 .0237 .2037 42.219 4.9 10 3.845 18.877 13
14 IO. l47 .0985 .0197 .1997 50.8 18 5:008 4.0?...5 20.158 ]4
15 11.974 .0835 .0164 .1964 60.965 5.092 4. 189 21.327 15
16 14.129 .0708 .0137 . 1937 72.939 S. 162 4.337 -2.389 16
17 16.672 .0600 .01 IS .19 15 87.068 5.222 4.471 23.348 l7
18 19.673 .0508 .00964 .1896 103.740 5.273 4.592 24.212 18
19' 23.2 l4 .043 1 .00810 .1881 123.4 13 5.3 16 4.700 2.4.988 19
20 27.393 .0365 .00682 .1868 146.628 S.353 4.798 15.681 20
21 32.324 .0309 .00575 . 1857 174.02 1 5.3&4 4.885 26.300 21
22 38.142 .0262 .00485 .1 848 206.345 5.41 0 4.963 26.851 22
23 45 .008 .0222 .00409 . 1841 244.487 5.432 5.033 27.339 23
24 53. 109 .0188 .00345 .1 835 289 .494 5.451 5.095 27.772 24
25 62.669 .0160 .00292 .1829 342.603 5.467 5.150 28.155 25
26 73.949 .0135 .00247 J 825 405.-72 5.480 5.199 28.494 26
27 87.260 .0115 .00209 . 1821 479 __ 21 5.492 5.243 28.791 27
28 102.966 .00971 .00177 ..1818 566.480 5.502 5.281 29:054 28
29' 121.500 .00823 .00149 .1815 669.447 5.5 10 5.315 -9.284 29
30 143.370 .IJ0697 .00126 .1813 790.947 5.517 5.345 29.486 30
31 169 ..177 .0059 1 .00107 .1 811 934.3 17 5_ -23 5.371 9.664 31
32 199.629 .00501 .0009 1 .1809 1 103.5 5.528 5.394 29.819 32
33 235.562 .OM25 .00077 .1808 l 303. 1 5.532 5.415 29.955 33
34 277.963 :00360 .00065 .1806 1538.7 5.536 5.433 30.074 34
35 327.997 .00305 .00055 .1806 1816.6 5.539 5.449 30.177 35
0 750.377 .00133 .00024 J 802 4 16L 5.548 5.502 30.527 40
5 1716.7 .00058 .00010 .J80I 9 53 1.6 5.552 5.529 30.701 45
50 3 927.3 .00025 .00005 .1800 21813.0 S.554 -_543 30.786 50
55 8984.8 .000 11 .00002 .1800 499IO. I S.555 5.549 30.827 55
60 20555 .J .00005 .0000 1 .1800 1l4189.4 S.555 5.553 30.846 60
65 47025. l .00002 .1 00 261244.7 S.555 5.554 30.8-6 65
70 l07 581.9 .00001 . 1800 597671.7 S.556 5.5SS 30.860 70

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20% Compound Interest Fact ors 20%

Si ngle Paymeint Uniform Paymea:it Se ries Arithmetic Gra dient
Compound Present Sinking Capita l Compound Pre.s-e nt Gradient Gradient
Amount Worth IFund Recovery Amount Worth Un iform Present
Factor Factor Factor Factor Factor Factor Series Worth
Find F Find P Find A Find A Find F Find P Find A Find P
Given P Given F Given F Given P Given A Given A Given G Given G
n fl P PIF Alf AIP FIA PIA AIG PIG I)

1 1.200 .8333 1.0000 1.2000 1.000 0.833 0 0 1

2 1.440 .6944 .4545 .6545 2..200 1.528 0 .455 0.694 2
3 1.72.8 .5787 .2747 .4747 3.640 .106 0.879 1.852 3
4 _,074 .4823 .1863 .3863 5.368 __589 L.:74 3.299 4
5 __488 .4019 .1344 .3344 7.442 __ 991 1.64 1 4.906 5
6 2.986 .3349 .1007 .3007 9.930 3.326 1.979 6.581 6
7 3.583 .2791 .0774 .2774 1-.9 16 3.605 L90 8.255 7
8 4.300 .2326 .0606 .2606 16.499 3.837 2.576 9.883 8
~ 5. 160 .1938 .048 1 .2481 20.799 4.031 2.836 11.434 9
10 6.1 92 .1615 .0385 .2385 :lS.959 4.192 3.(H4 12.887 ]0
11 7.430 .1346 .031 1 .2311 3 __150 4.327 L89 14.233 n
12 8.916 .1122 .0253 .2253 39581 4.439 3.484 15.467 12
13 10.699 .0935 .0206 .2206 48.497 4.533 3.660 16.588 13
14 L839 .0779 .0169 .2169 59.1 96 4.611 3.817 17.601 ]4
15 15.407 .0649 .0139 .2139 72.035 4.675 3.959 18.509 ]5
16 18.488 .0541 .011 4 .2114 87.442 4.730 4 .085 19.321 ]6
17 __J 86 .045 1 .00944 .2094 I05 ..9 I 4.775 4.198 20.M2 l7
18 26 ..623 .0376 .0078 1 .2078 128. 11 7 4.812 4--98 2.0.680 ]8
1~ 31.948 .0313 .00646 .2065 154.740 4.843 4.386 2 1.244 19
w 38.338 .0261 .00536 .2054 186.688 4.870 4.464 - 1.739 20
21 46.005 .0217 .00444 .2044 225.026 4.891 4 .533 -2.174 21
22 55. 206 .Ol81 .00369 .2037 271:031 4.909 4.594 22.555 22
23 66.247 .01 5 1 .00 07 .2031 326.237 4.925 4.647 22.887 23
24 79.497 .0126 .00255 .2025 392.484 4.937 4.694 23.176 24
25 95.396 .OI05 .002 12 .2021 471..981 4.948 4.735 23.428 25
26 114.475 JJ0874 .001 76 .20l8 567.377 4.956 4 .771 23.646 26
27 137.371 .00728 .00 147 .2015 681.853 4.964 4.802 23.835 27
28 164.845 .00607 .00 122 .201_ 819.223 4.970 4.829 23.999 28
~ 197.814 .00506 .00 102 .2010 984 ..068 4.975 4.853 24.1 41 29
30 237.376 _004_1 .00085 .2008 1181.9 4.979 4.873 24 .263 JD
31 284.852 .00351 .00070 .2007 1419.3 4.982 4. 891 24.368 31
32 341.822 .00293 .00059 .2006 1704.1 4.985 4.906 24.459 32
33 4I0.1 86 .00244 .00049 .2005 2045.9 4.988 4.919 24.537 33
34 492.224 .1)0203 .0004 1 .2004 2 456. l 4.990 4.93 1 24.604 34
35 590.668 .00169 .00034 .2003 2948.3 4.992 4.94] 24.661 35
40 1469.8 .00068 .000 .1.4 .2001 7 343.9 4.997 4 .973 24.847 40
45 36573 .00027 .00005 .2001 ]8 281.3 4.999 4.988 24.932 45
50 9 100.4 .00011 .00002 .2000 45 497.2 4.999 4.995 24.970 50
55 22644.8 .00004 .0000 1 .2000 113219.0 5.000 4.998 24.987 55
60 563475 .00002 .2000 281 732.6 5.000 4.999 24.994 60

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Financial Ratios Derived from Income Statement Data

The profit margin (Equation 17-6) equals net profits divided by net sales revenue. Net sales revenue equals sales minus
returns and allowances.

Pmfit margin = Net profit/ Net ale revenue (17-6)

This ratio provides insight into the cost efficiency of operations as well as a finn 's ability to convert sales into profits.
For Engineered Industries in Figure 17-3, the profit margin is 850, 000/18, 030, 000 = 0.047 = 4.7%. Like other financial
measures, the profit margin is best evaluated by comparisons with other time periods and industry benchmarks, and trends
may be more significant than individual values.
Interest coverage, as given in Equation 17-7, is calculated as the ratio of total income to interest payments--where
total income is total revenues minus all expenses except interest payments.
Interest coverage = Total incorne / lntere t payments (17-7)
The interest coverage ratio (which for industrial fitms should be at least 3.0) indicates how much revenue must drop to
affect the firm's abIHty to finance its debt. With an interest coverage ratio of 3.0, a firm's revenue would have to decrease
by two-thirds (unlikely) before it became impossible to pay the interest on the debt. The larger the interest coverage ratio
the better. Engineered Industries in Figure 17- 3 has an interest coverage ratio of

(18,350,000 - 17 110,000)/120,000 = 10.3

Linking the Balance Sheet-, Income Statement, and Capital Transactions

The balance sheet and the income statement are separate but linked documents. Understanding how the two are linked
together helps clarify each. Accounting describes such links as the articulation between these reports.
The balance sheet shows a finn 's assets, liabilities, and equity at a patticular po1nt 1n time, whereas the income
statement summarizes revenues and expenses over a time interval. These tabulations can be visualized as a snapshot at the
period's beginning (a balance sheet), a video summal'y over the period (the income statement), and a snapshot at the
period's end (another balance sheet). The income statement and changes in the balance sheets summarize the business
transactions that have occurred during that period.
There are many links between these statements and the cash flows that make up business transactions, but for
engineering economic analysis the folJowing are the most important
1. Overall profit or loss (income statement) and the staiting and ending equity (balance sheets).
2.. Acquisition of capita] assets.
3. Depreciation of capital assets.
The overall profit or loss during the year (shown on the income statement) is reflected in the change in retained
earnings between the baJance sheets at the beginning and end of the year. To find the change in retained earnings (RE),
one must also subtract any dividends distributed to the owners and add the value of any new capital stock sold:

RE 00 g + Net income/ Lo + New stock - Dividend = REend

When capital equipment is purchased. the balance sheet changes, but the 1ncome statement does not. If cash is paid,
then the cash asset account decrease equals the increase in the capital equipment account-there is no change in total
assets. If a loan is used, then the capital equipment account increases, and so does the liability item for loans. In both
cases the equity accounts and the income statement are unchanged.
The depreciation of capital equipment is shown as a line on the income statement. The depreciation for that year equals
the change in accumulated depreciation between the beginning and the end of the year----after subtraction of the
accumulated depreciation for any asset that is sold or disposed of during that year.
Examp]e 17- 1 applies these relationships to the data in Figures 17- 1 and 17- 2.

EXAMPLE 17-1
For simplicity, assume that Engineered Industries will not pay dividends in 2018 and did not sen any capital
equipment. It did purchase $400,000 in capital equipment. What can be said about the values on the balance sheet at
the end of 2018, using the linkages just described?

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SOLUTION
First, the net profit of $850,000 will be added to the retained earning~ from the end of 2017 to find the new retained
earnings at the end of 2018:
RE 12/3 1/ 2011 = 850,000 + $8 745.()00 = $9,595,000
Second, the plant and equipment assets shown at the end of 2018 would increase from $6,500,000 to $6,900,000.
Third, the accumulated depreciation would increase by the $450,000 in depreciation shown in the 2018 income
statement from the $2,350,000 posted in 2017. The new accumulated depreciation on the 2018 balance sheet would be
$2,800,000. Combined with the change in the amount of capital equipment, the new fixed asset total for 2018 would
equal:
$335,000 + $6,900 000 - $2,800 000 = 4,435 000

TRADITIONAL COST ACCOUNTING

A firm's cost-accounting system collects, analyzes, and reports operational performance data (costs, utilization rates, etc.).
Cost-accounting data are used to develop product costs to determine the mix of labor, materials, and other costs in a
production setting, and to evaluate outsourcing and subcontracting possibilities.

Direct and Indirect Costs

Costs incurred to produce a product or service are traditionally classified as either direct or indil'lect (overhead),. Direct
costs come from activities directly associated with the final product or servke produced. Examples include material costs
and labor costs for engineering design, component assembly, painting, and drilling.
Some organizational activities are difficult to link to specific projects, products, or services. For example, the receiving
and shipping areas of a manufacturing plant are used by all incoming materials and all outgoing products. Materials and
products differ in their weight, size., fragility, va]ue, number of units, packaging, and so on, and the receiving and shipping
costs depend on all these fae1ors. Also, different materials atTive together and different products are shipped together, so
these costs are intermingled and often cannot be tied directly to each product or material.
Other costs, such as the organization's management, sales, and administrative expenses, are difficult to link directly to
individual products or services. These indirect or overhead expenses also include machine depreciation, engineering and
technical support, and customer warranties.

Indirect Cost Allocation

To allocate indirect costs to different departments, products, and services, accountants use quantities such as direct-labor
hours, direct-labor costs, matetial costs, and total direct cost. One of these is chosen to he the burden vehicle. The total of
all indirect or overhead costs is divided by the total for the hurden vehicle. For example, if direct-labor hours is the burden
vehicle, then oved1ead will be aUocated based on oved1ead doUar per direct-labor hour. Then each product, project, or
depa1tment will absorb (or be allocated) overhead costs, based on the number of direct-labor hours each has.
This is the basis for calling tradi.tional costing systems absorption costing. For decision making, the problem is that
the ahsorbed costs represent average, not incremental, perfonnance.
Four common ways of a1locating overhead are direct-labor hours, direct-labor cost, direct-materials cost, and total
dired cost. The first two differ significantly only if the cost per hour of labor differs for different products. Example 17-2
uses direct-labor and direct-matetials cost to illustrate the different choices of burden vehide.

EXAMPLE 17-2
Industrial Robots does not manufacture its own motors or computer chips. Its premium product differs from its
standard product in having heavier-duty motors and more computer chips for greater flexibility.
As a result. Industrial Robots manufactures a higher fraction of the standard product's value itself, and it purchases a
higher fraction of the premium product's value. Use the following data to allocate $850,000 in overhead on the basis of
labor cost and materials cost.
IStandard IPremium I
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Standard Premium
umber of units p.er year 750 400
Labor cost (each) $400 $500
aterfals cost (each) 50 900

SOLUTION
First, the labor and material costs for the standard product, the premium. product, and in total are calculated.

Standard P remium Total

umber of units per year 750 400

Labor cost (each) $400 $500
aterials cost (each) 550 900
Labor cost 300,000 200,000 $500,000
aterials cost 412,500 360,000 772,500

Then the allocated cost per labor dollar, $1.70, is found by dividing the $850,000 in overhead by the $500,000 in
total Jabor cost. The allocated cost per material dollar, $1.100324, is found by dividing the $8S0,000 in overhead by the
$772,500 in materials cost. ow, the $850,000 in allocated overhead is split between the two products using labor costs
and mate1i.al costs.

Standard Premium Total

Labor cost $300,000 $200,000 $500,.000

Overhead/labor 1.70 1.70
Allocation by labor 510,000 340,000 850,000

aterial cost 412,500 360,000 0

Overhead/material 1.1003 1.1003
Al.location by material 453,884 396,116 850,000

If labor cost is the burden vehicle, then 60% of the $850,000 in overhead is allocated to the standard product. If
material cost is the burden vehide, then 53.4% is allocated to the standard product. In both cases, the $850,000 has
been split between the two products. Using total direct costs would produce another overhead allocation between these
two values. However., for decision making about product mix and product prices, incremental overhead costs must be
analyzed. AU the aUocation or burden vehicles are based on an average cost of overhead per unit of burden vehicle.

Proble1ns with Traditionall Cost Accounting

Allocation of indirect costs can distmt product costs and the decisions based on those costs. To be accurate, the analyst
must determine which indirect or overhead expenses will be changed because of an engineering project. In other words,
what are the incremental cash flows? For example, vacation and sick leave accrual may be patt of overhead, but will they
change if the labor content is changed? The changes in costs incurred must be estimated. Loadings, or allocations, of
overhead expenses cannot be used .
This issue has become vety important because in some finns, automation has reduc ed direct-labor content to Jess than
5% of the product's cost Yet in some of these firms, the basis for allocating overhead is stilJ direct-labor hours or cost.
Other firms are shifting to activity-based costing (ABC), where each activity is linked to spedfic cost drivers, and the
number of doUars all ocated as overhead is minimized (see Liggett. Trevino, and Lavelle, 1992). Figure 17-4 illustrates
the difference between activity-based costing and traditional overhead alJocations (see Tippet and Hoekstra, 1993).

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Direct Direct
Labor Material

Product Cost

FIGURE 17-4 Activity-based costing versus traclitiona] overhead allocation. (Based on an example by Kim Lascola
Needy.)

Other Problen1s to Watch For

Project managers have often accused centralized accounting systems of being too slow or being "untimely." Because
engineering economy is not concerned with the problem of daily project control, this is a less critical issue. However, if an
organization establishes multiple files and systems so that project managers (and others) have the timely data they need,
then the level of accuracy in one or all systems may be low. As a result, analysts making cost estimates will have to
consider other intemal data sources.
There are several cases in which data on equipment or inventory values may be questionable. When inventory fa
valued on a "Jast in, first out" basis, the remaining inventory may be valued too low. SimHady, land valued at its
acquisition cost is like]y to be significantly undervalued. Finally, capital equipment may be valued at either a low or a
high va]ue, depending on allowable depreciation techniques and company policy.

SUMMARY
This chapter has provided several key concepts from the accounting field. These provide additional perspective when
conducting engineering economic analyses. Data from accounting records form the bases for many needed estimates.
Management decisions rely on both professions to keep the finn profitable.
Engineering economic analysis: requires the estimation of future costs and benefits. These are often detived from
histmi cal data. Projects are evaluated over their life cycle using methods such as present worth, equivalent worth,
and rate of return. The effects of taxes, inflation, and risk and uncertainty may be included. Analyses assist the firm
in making future dedsions .
Accounting: determines the economic impact of past business decisions, and thus provides irnpmtant historical data
for making future ones. Tools such as the balance sheet and income statement capture important measures.
Management: alJocates constrained resources of the firm to promote economic growth/stability and strategic
objectives. Management requires data, analysis, and communication from both the engineering economy (future
view) and accounting (historical view) perspect1ves.
The primary accounting statements are the balance sheet and the income statement. The balance sheet provides a
snapshot in time of the financial position of the firm. This tool is based on the fundamental accounting equation: Assets =
Liabilities - Equity, where assets are items owned by the film and have monetary value, liabilities represent debt
obligations, and equity is the ownership value in the firm. Financial measures such as cun-ent ratio and quick ratio are
fmmed from data on the balance sheet.
The income statement summarizes a firm 's revenue and expenses over an interval of time. This is usually a month,
quarter, or year. Profit (or Joss) is calculated as: Revenues - Expenses= Profit (or loss) . Economic ti-ends over time, from
consecutive income statements, provide mot-e Information than one statement evaluated in isolation. Financial measures
such as profit margin and inte1-est coverage are formed from data from the income statement.
Films' cost accounting systems collect, analyze, and repmt on operational data. These are used for managing assets
and operations. A traditional cost accounting method treats the firm's direct and indirect costs differently than an activity-
based method. The former spreads indirect costs (overhead) over products using very simple assumptions, and the latter
relates costs to the activities that cause those costs. Fim1s that use traditional methods may not have accurate data for
make versus buy, product mix, and other operating decisions.
By understancling accounting principles, engineeting economists are better prepared to perform analyses and improve
decision making for the finn.

STUDENT STUDY GUIDE

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~ .L 'u.1..1.c:.1~ .L .:, .1. u.u I. uu.1..un
These questions are intended for self-study. Click the [solution] box to reveal a detailed solution.
17- Determin e retained earnings for Lavene Manufacturing.
1 Current hab ilities $4,000,000
Long-tenn liabi.lities 2,000,000
Current a.sse,ts 6,500,000
F lxed assets 4, 000,0 00
Other assets 1,500,000
Common stock 2,500,000
Preferred stock 500,000
Capital surplus 1,000,000

17- Billy Bob' s Towing and Repak Service has provided the allowing financial information.
2
Cas h $ 80,000
Accounts receivable 120,000
Accounts payable 200,000
Securities 75,000
Pans inventories 42,000
Prepaid expenses 30,000
Accrued expense 15,000

Determ ine (a) the current ratio, (b) the quick ratio, and (c) the avaifable working capital.

17- Dete.rmi.ne the cun-ent and q uick ratios for Harbor aster Boats, Inc. Does the firm appear to be financially sound?
3 Harbor Master Boats, Inc.
Balance Sheet,. January 1, 20XX
Assets Liabiliti es
Current asse,ts Current liabil.ities
Cash 900,000 Accounts pa)rabl e 2,400,000
Accounts receivable 1,100,000 Notes payable 2,000,000
Inven tory 2,000,000 Accrued expe-nse 900,.0 00
Total current assets 4,000,000 Total current liabi.lities 5,300,000
Fixed assets Long-term debt 3,000,000
Land 300,.0 00 Total liabilities 8,300,000
Plant 2,500,000 Equity
Equipment 6,000,000 Stock 2,000,000
Total fixed assets 8,800,000 Retained eamings 2,500,000
Total net worth 4,500,000
Total assets 12,800,000 Total liabi.lities and net wonh 12,800,.00 0

4i•1•1dce)ki
17- Rapid Delivery's financiaJ information 1ncludes:
4
Aci d-test ratio 1.3867
Cas h on hand $72,000
Accounts receivable 102,000
Market value of securities he ld 34,000
Inventories 14 3,000
Other assets 16,000
Fixed assets 215,000
Total liabilities 400,000

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Determine (a) the current assets,. {b) the current l.iabilities, (c) the total assets, and (d) the owner's equJty.
Wi•ll'dM§•
17- The fonowing information has been taken fro m the financial statements avai.lable for the ABC Company.
5 Accounts payable $4,000
Accounts receivable 12,000
Income ta..xes 6,. 000
Owner's equity 75,000
C.ost of goods sold 42,000
Sel.ling expense 10,000
Sales revenue 80,000

Detenn ine the ne t income.

17- Th.is financial information is from Firerock Industries' income statement:

6
Revenues
Sales 3,200,000
Operating revenue 2,000,000
Nonoperating revenue 3,400,000
Expenses
Total operating expenses 6,700,000
Interest payments 500,000

Taxes paid for the year equaled $110,000. Determine (a) the net income before taxes, (b) the net profit (loss), (c) the interest
coverage, and (d) th,e net profit ratio.
Wi•l•GiM§i
17- Wheeler Industries had sales of $157M and returns and allowances of $2 1 . . Operating expenses were $48M and non-operating
7 revenues and expens.es equaled the interest pa.id of $7M. Using the corporate tax rate fro m the TCJA compute the tax paid by
Wheeler Industries. Consnuct th e income statement.
Wi•li!iidii
17- Wheeler industries (prob]em SG17-7) had the following ennies in its baJance sheet at the end of last year.
8
Plant and equipment $17M
(less accumulated depreciation) 9M
Retained earnings $80M
In addition to the income statement data for tMs year in prob lem SGl ?-7, we also know that the finn purchased $5 mill.ion of
equipment with cash and that depreciation expenses were $4 mjJJion of the $4B million in operating expenses. The £inn paid no
dividends and sold no stock this year. What are the entries in the balance sheet at the end of this year for:
{a} Pfant and equipment?
{b) Accumulated depredatio n?
{c) Retained eamings?
Wi•I •G it•ii
17- Brown Box, Inc., mam1factures shipping boxes for a wide variety of indusnies. Their XLLarge costs:
9 Direct materials costs $0.85/unit
Direct labor costs 3,85/un.it
Overhead for the entire manufacturing plant is $4,000,000 per year, and it is allocated based on direct labor costs. Total dkect
labor costs are $5,500,000. The demand the XLLarge is 200,000 boxes per year. Determ ine the cost per unit.
Wffi•Gi 0ii
17- Abby Man ufacturing produces chHdren's toys and the Dr. Dolittle Farm is a big se11er. Indirect costs of $750 000 are aUocated
10 based on direct materials cost, wlili.ch total $8,350,000 for the facility. The materials used in Dr. DoUttle Fa.rm cost $7.45 per unit
The totaJ labor (both direct and indirect) costs $9.35 per unjt. Tlile production scheduJe is 300,00 0 units for the coming year. If
"· .
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' , ..
Abby desires a 35% profit margin, what should the Farm's wholesa]e price be?
►i•il'PiM§•
17- Denali lndustries makes specialized oil well eq uipme nt. se ~ota] dkect cost as the burden vehicle, and compute the total cost per
11 unit for each model. Total manufacturing indirect costs are $2,500,000, and there are 1000 unjts manufactured per year for Model
A, 600 for ode! K,. and 500 for Model T. Use tota.l dkect cost as the burden vehicle, and compute the Iota.I cost per unit for each
model
Activity Model A Mode l K Mode l T
Direct material cost $800,000 $530,000 $630,000
Direct labor cost $500,000 $320,000 $410,000

PROBLEMS
Key to icons: D = dick to reveal answer; e = Green, which may include environmental ethics; CJ = Ethics other than
green; = autograded problems that are available online in Dashboard; = The icon indicates that a spreadsheet is
recommended.

Accounting
17- Why is it important fo r engineers and managers to understand acco unting principles? arne a few ways that they can do so.
1
17- Explain the accounting function within a firm. What does th.is function do, and why is it important? What types of data does it
2. provide?
17- anipulation of financial data by the Enron Corporation was revealed in October 2001. Firm executives were sentenced to prison.
3 Arthur Andersen, which had been one of the "Big 5" accounting firms and Enron's auditor, su.rrendered its licenses to practice as
G certified public accountants in August 2002. This and other scandals led to the passage of the fe deraJ Sarbanes-Oxley (SarbOx)
legislation in July 2002 . What a.re the key components of thi.s law?
17- How would the informatio n and activities in Figure 17-1 rela~e to potential conhibutions by extemaJ professional services that
4 firms will often hire
•(a) consulting eng.ineers?
(b) management consulting firms?
,(c), accounting firms for auditing?
17- Consider Figure 17- 1 and external professional services that £inns will often hi.re. What ethical questions seem like]y to arise
5 when a firms hires
G •(a) consulting engineers for design?
(b) management consuHing firms?
,(c), acco unting firms for auditing?
17- Inso]vency or cash flow problems in the U.S. banking industry started the financial CJisis of 2007. Have significant changes in
6 accounting standards and practices been forced thro ugh legislation? If so, what are these changes?
17- Accounting and finance are requi red topics for most management degrees, and many engineers do beco me managers during their
7 careers. After graduation with a B.S. in engineering, what courses are avai.lable to you from your or another nearby university?
17- Using the table of contents, compare the coverage of this engineering economy text with a text for the inh"Oductory course in
8 corporate finance (typically a j unior course in BBA programs). What topics do the ~exts have in common? Identify the topics that
seem to be cove11ed in only one--note which topics for which course.

Balance Sheet
17- Develop short definitions for the following terms: balance sheet, income statement, and fundame ntal accounting equation.
9
17- Explain the difference between short-term and long-term ]jabilities.
10
17- Calculate the equity of the Gravel Conshuction Company if it has 10 million worth of assets. Gravel has $1.3 miJUon in rnn"l'llt
11 liabilities and $2.5 million in long-term liabilities.

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17- atbach Industries has $930,000 in cuITent assets and $470,000 in fixed assets l.ess $180,000 in accumulated depreciation. The
12 film's curl'ent liabiUties total $370,000, and the long-term liabilities $115,000.
0 {a) What is the firm 's equity?
(b) If the firm's stock and capital surplus total $305,000, what is the value for retained earnings?
17- CalcTech has $1.3M in current assets and $550,000 in fixed assets less $200,000 in accumulated depreciation . The film's cun--em
13 liabilities total Sl80,000, and the long-te1m l.iabiUties $205,000.
(a) What is the firm 's equity?
(b) If the film's stock and capital surpl us total $202,000, what is the value for retained earnings?
17- Fi.rst Step Baby Monitor Company has curl'ent assets of $5.5 million and current liabjJities of 2.2 million. Give the company's

•
14 working capital and current ratio.

17- From the following data, taken from the balance sheet of Petra's Widget Factory, dete1mjne the working capital, current ratio, and
15 quick ratio.
Cash $110,000
Net accounts and notes receiva ble 325,000
Retailers ' inventories 210,000
Prepaid expenses 6,000
Accounts and notes payable 300,000
(short term)
Accrued expenses 187,000
17- For Gee-Whiz Devices, calculate the following: working capital cun'ent ratio, and quick ratio.

•
16 Gee-Whiz Devices Ba lance Sheet Data
Cash $100,000
Market securities 45,000
Net accounts and notes receivable 150,000
Retailers ' inventories 200,000
P1'epaid expenses 8,000
Accounts and notes payable 315,000
(short term)
Accrued ,expenses 90,000
17- Turbo Start has cun'ent assets totaling $1.5 milUon (this includes $500,000 in current inventory) and current Uabilities totaling
17 $400,000. Find the cunent ratio and quick ratio . Are the ratios at desirable levels? E:xplain.
17- ,(a) For E:vergreen Environmental Engineering (EEE), determine the working capital, cmTent ratio, and q uick ratio. Evaluate the
18 company's economic situation wi th 1--espect to its ability to pay off debt
I EEE Balance Sheet Data ( lOOlts)
m Cash $120,000
Secmities 40,000
Accounts J'e,ceivable 110,000
Inventmies 300,000
P1'epaid expenses 3,000
Accounts payable 351,000
Accrued ,expenses 89,000
{b) The entries to com plete EEE's balance sheet include:Cons truct EEE's balance sheet
More EEE Ba lance Sheet Data ($1000s)
Long-term Uabilities $220,000
Land 25,000
Plant and eq uipment 510,000
Accumulated dep1--eciation 210,000
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] .l""t..LL u u 1u.u1 Lcu ucpl 'C"\.... Lauu1 t jL ..1.u,vuu

More EEE Ba lancie Sbeet Data ($1000s)

Stock 81,000
Capital surplus 15,000
Retained earnings Value not given
(c), What are EEE's values for total assets, total Liabilities, and 11etained earnings?
17- (a) For J&W Graphics Supply, compute the current ratio. Is this a financially healthy company? Explain.
19 J&W Graphics Supply Balance Sheet Data ($1000s)
Assets
Cash $1740
Accounts re;ceivable 2500
Inventmie:s 900
Bad debt provision -75
Liabiliti.e s
Accounts payable 1050
Notes payable 500
Accrued expenses 125
,(b) The entries of completeJ&W's baJance sheet include:
More J&W Balance Sheet Data ($Ul00s)
Long-te;m liabilities $950
Land 475
Plant and equipment 3100
Accumulated depreciation 1060
Stock 680
Capital surplus 45
Retained earnings Value not given
Construct J&W's balance sheet.
(c), What are J&W's values for total assets, total liabilities, and total eamings?
17- For Sutton Manufacturing, determine the current ratio and the quick rati.o. Are these values acceptable? Why or why not?

•
2.0

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Assets Liabilities
Cunent ass.e~ Current [iabili:ties
Cash $ 870 Note payable 500
Accounls 450 Accounts payable 600
receivable
Inventory 1200 Accruals 200
Prepaid expenses 60 Taxes payable 30
Cllfrent portion 100
l'olal current assets 2580 long-term debt
et fixed assets Total curren t
Land 1200 liabilities 1430
Plant and 3800 Long-term debt 2·000
equipment Officer debt 200
(less -IOOO (subordi nated
accumulated Total liabilities 3630
depreciation) Equity
Otl:ter assets Common stock 1670
Notes receivable 200 Capital surplus 400
Intangibles l20 Retained earnings 1200

Total equity 3270

l'olal assets 69(H) Total liabilities 69(H)

and equity

17- If a firm has a current ratio less than 2.0 and a quick ratio Jess than 1.0, will the com pany eventually go ban krupt and ou t of
2.1 business? Explain your answer.
17- What is the advantage of com paring financial statements across periods or against industry benc-hmarks over lookjng at sta temen ts
2.2 associated wi th a single date or period?

Income Staten1ent
17- LaiJa 's Surveying lnc, had revenues of $1.5 m illion in 2016. Expenses totaled $900,000. What was her net profit (or loss) if the
2.3 tax rate is 38%?

17- Bohr Pajnt Company has annual sales of $12 m illion per year. If there is a profit of $5000 per d ay wi th 7 days per week operation,
24 what is the total yearly business expense? AU cakulations are on a before-tax basis.
0
17- For Magdalen Industri es, compute the net in come before taxes and net profi t (or loss). Taxes for the year were $7.5 mJrnon.
25 ,(a) Calculate net profit for the year.
,(b) Construct the income statement.
,(c), Calculate the interest coverage and net p rofit ratio. Is the interest coverage acceptable? Explain why or why not.
Magdalen Industries Income Statement Data ( M)
Revenues
Total operating revenue $124
(incl uding sales of $48 mill.ion)
Total nonoperating flevenue 36
Expens.es
Total operating expenses 70
Total nonoperating expenses 35
(interest payments)

17- Find the net incom e of Turbo Start (Problem 17-17) g iven the fo llowin~ data from the balance sheet and income statem ent.
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J. l - t' J.111.J Ult' 111:! L lllL1.J H H:! U ! 1 U I U U ~ Ldll \ r 1 UIJlt'IU .l I - .l I J g1 V l:!!l Ult' lUU U W tug Ud.Li:I l[UlU LIit' IJdldllLt' 1i!lt'l:!I i:IIIU HILUU.11:!' Sli:llt'U!t'II L

26 Turbo Start Data ($ HI ODs)

•
J J

Turbo Start Data ($UIOOs)

Accounts payable $200
Selling expense 500
Sales revenue 5000
Owner's equity 2400
Income taxes 315
Cost of goods sold 3000
Accounts re,ceivable 500
17- The general ledger of the Fly-Buy-Nite (FBN) Engineering Company contained the following account balances. Construct an
2.7 income statement. Vvhat is the net income before taxes and the net profit (or loss) after taxes? FB has a tax rate of 21%.
Amount ($1000s)
Administrative expenses $2,750
Subcontracted services 15,000
Development expenses 900
Interest expense 200
Sales revenue 35,000
Selling expenses 4,500
17- For Andrew's Electronk Instruments, calculate the interest coverage and net profit ratio. Is Andrew's business healthy?
28
I

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Income Statement f•Dr Andrew's Electronics for Endo( Year 20UJ ($1000s)
Revenues
Operating revenues
Sales $395
(minus) Returns -15
Total operating revenues 380
Nonoperating rev,enues
Interest receipts 50
Stock revenues 25
Total nonoperating revenues 75
Total revenues, R 455
Expenses
Operatin g expenses
Cost of goods and services sold
Labor 200
Materials 34
Indirect cost 68
Selling and promotion 20
Depreciation 30
General and administrative 10
Lease payments 10
Total operating expenses 372
Nonoperating expenses
Interest payments 22
Total nonoperating expenses 22
Total expenses, E 394
Net income before taxes, R - E 61
Incomes taxes 17
Net profit (loss) for the year 2010 44

Linking Balance Sheet and Income Statement

17- Use your own experiences or a search engine to provide specific examp]es where the balance sheet and income statement are
29 linked.
17- Lithium batteries are popular and widely used. Lithium is typically mined from saJt flats where water is scarce, yet litMum mi ning
30 requires large amounts of water. Are the environmental costs of lithium captured in the financial statements of companies that
CD prod uce lithium batteries?
17- Sutton Manufacturing (balance sheet at the end of last year in Problem 17-20) had ilie foUowing entries in thi.s year's income
31 statement.
Depreciation $420,000
Profit 480,000
In addition, we also know the firm purchased $800,000 of equipment witlh. cash. The firm paid $200,000 in dividends this year.
What are the entries in the balance s.heet at the end of th.is year for
(a) pfant and eq uipment?
(b) accumulated depreciation?
(c), retained earnings?
17- agdaJen Industries (Problem 17-25) had the following entries in its balance sheet at the end of last year.
':I.?

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3.2 Plant and equipment $15 million
I (less accumulated depredation) 8 miJUon
Retained earnings 00 miJlion
In addition to the income statement data for this year in Problem 17-25, we also know that the firm purchased $3 mil.lion of
equipment with cash and that depreciation expenses were $2 million of the $70 million in operating expenses listed in Problem
17-26. The firm paid no dividends this year.
What are the entries in the balance sheet at the end of th.is year for
,(a) plant and equipmen t?
,(b) accumulated depreciation?
,(c), retained earnings?

Allocating Costs
17- Categ01ize each of the following costs as direct or indirect. Assume that a trad.itional costing system fa .in place.
3.3 Machine nm costs Cost to markcet the product
Machine depreciation Cost of storage
Ma terial handling costs Insurance costs
Cost of materials Cost of product sa.les force
Overtime expenses Engineering drawings
Machine operator wages Machine labor
Utility costs Cost of tooling and fixtu11es
Support (administrative)
staff salaries
17- RLW-11 Enterprises estimated that indirect manufacturing costs for the year would be $75 million and that 15,000 machine-hours
34 wouJd be used.
I •(a) Compute the predetermined indi.11ect cost applkation rate using machine hours as the burden vehkl,e,.
,(b) Determine the totaJ mst of pro duction fo r a product with direct material costs of $2 minion, direct-labor costs of $2 ,5
mirnon, and 200 machine-hours.
17- Phi.Lippe Francois Inc. produces concrete sundials-5000 were produced in a rece11t production run. The run required 1500
35 machine hours, three "set-ups" of the mixing equipment, and 100 hours of final inspection time. Costs are ,esti.mated as follows:
$50 per machine hom~ $3000 per "set-up," and $20 per inspection hour. Direct materials and direct labor total $95 per sundial
Indirect expenses total 45% of the direct material. and labor costs.
,(a) Determine the "cost to produce" each unit.
,(b) At a 15% profit level what is the unit sa.les price?
,(c), With six runs per year what is the total annual profit for tMs product?
17- LeGarmme Industries ma1 es industrial pipe manufactming equ1pment. Use direct-labor hours as the burden vehicle, and compute
36 the tota.1 cost per unit for each model given in the ta ble. Total manufacturing indirect costs are $1 ,892 000, and there are 100,000
I units manufactu11ed per year for Model S, 50,000 for odel M and 82,250 for Model G,
Item Model s Model llf Model G
Direct-materia.l costs $3,800,000 $1,530,000 $2,105,000
Direct-labor costs 600,000 380,000 420,000
Direct-labor hours 64,000 20,000 32,000

17- Par Golf Equipment Company produces two types of golf bag: the standard and deluxe models. The total 1ndirect cost to be
37 allocated to the two bags is $35,000. Determine the net revenue that Par Golf can expect from the sale of each bag.
,(a) Use direct-labor mst to allocate indirect costs.
(b) Use direct-materials cost to allocate indirect costs,

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Data Item Standard Deluxe

Direct-labor cost $60,000 $70,000
Direct-materiaJ cost 40,000 47,500
Selling price 70 105
Units produced 1800 1400

Minicase
17- Find a reaJ world example where a finn has included environmental remediation costs on its balance sheet or in a note to the
38 balance sheet. Briefly descri be what was done. Wha t percentage of tile firm's assets and net profi t a.re these costs?
CD
CASES
The following cases from Cases in Engineering Economy (www.oup.com/us/newnan) are suggested as matched with
this chapter.

CASE4 BaJder-Dash Inc.

Standard cost and allocated costs v,ersus true marginal cost (IEs).
CASE52 Aunt AUee's Jams and Jellies
Product costing needs activity based costs.

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