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Balesoro, John Lesther S. FIN185

The document provides 6 examples of time value of money calculations involving topics such as future and present value, annuities, interest rates, loan amortization, and calculating deposits needed to accumulate a future sum. Detailed calculations are shown for each example, such as determining the future value of $800 after 5 years at 6% interest or calculating the effective annual interest rate for a nominal 8% rate compounded annually, semiannually, and quarterly. Step-by-step work is displayed for finding the loan payments on a $6,000 loan at 10% interest over 4 years through annuity calculations.

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77 views3 pages

Balesoro, John Lesther S. FIN185

The document provides 6 examples of time value of money calculations involving topics such as future and present value, annuities, interest rates, loan amortization, and calculating deposits needed to accumulate a future sum. Detailed calculations are shown for each example, such as determining the future value of $800 after 5 years at 6% interest or calculating the effective annual interest rate for a nominal 8% rate compounded annually, semiannually, and quarterly. Step-by-step work is displayed for finding the loan payments on a $6,000 loan at 10% interest over 4 years through annuity calculations.

Uploaded by

Less Balesoro
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Balesoro, John Lesther S.

FIN185

Time Value of Money Exercises:

Directions: Solve the problem-solving exercises and submit your answers via e-mail
(rlpancho2020@gmail.com) or via personal messenger, not in our messenger group.

1. Future Value of a Single Amount:

Ms. Jane places $800 in a savings account paying 6% interest compounded annually. She wants to know
how much money will be in the account at the end of five years. Find the future value?

After 5 years:

FV5 = PV (1 + I) 5

= $800 (1.06) 5

= $1,070.58

2. Present Value of a Single Amount:

Ms. Pam wishes to find the present value of $1,700 that will be received 8 years from now. Pam’s
opportunity cost is 8%. Find the present value?

PV = FVN / (1 + I) N

PV = FV8 / (1.08) 8

= $1,700 / (1.08) 8

= $918.46
3. Finding the Present Value of an Ordinary Annuity:

Brod Company, a small producer of plastic toys, wants to determine the most it should pay to purchase
a particular annuity. The annuity consists of cash flows of $700 at the end of each year for 5 years. The
firm requires the annuity to provide a minimum return of 8%. Use the Long Method for Finding the
Present Value of an Ordinary Annuity.

PVA = $700 (PVIFA,8%,5)

= $2,794.90

4. Nominal and Effective Annual Rates (EAR) of Interest:

Mr. Moreno wishes to find the effective annual rate associated with an 8% nominal annual rate (r =
0.08) when interest is compounded (1) annually (m = 1); (2) semiannually (m = 2); and (3) quarterly (m =
4). Find the EAR for annually, semi-annually, and quarterly?

EFF% for 8% annual interest EFF% for 8% semiannual interest

EFF%= (1 + INOM/M) M – 1 EFF%= (1 + INOM/M) M – 1

= (1 + 0.08 / 1) 1 – 1 = (1 + 0.08 / 2) 2 – 1

= 8.00% = 8.16%

EFF% for 8% monthly interest

EFF%= (1 + INOM/M) M – 1

= (1 + 0.08 / 3) 3 – 1

= 8.24%

5. Special Applications of Time Value: Deposits Needed to Accumulate a Future Sum:


Suppose you want to buy a house 5 years from now, and you estimate that an initial down payment of
$30,000 will be required at that time. To accumulate the $30,000, you will wish to make equal annual
end-of-year deposits into an account paying annual interest of 6 percent. Calculate the annual cash
payment?

PMT = $30,000/5.637

= $5,321.89

6. Special Applications of Time Value: Loan Amortization:

Say you borrow $6,000 at 10 percent and agree to make equal annual end-of-year payments over 4
years. To find the size of the payments, the lender determines the amount of a 4-year annuity
discounted at 10 percent that has a present value of $6,000. Calculate the equal periodic loan payment?

Required Annual Payment

N=4 I/YR = 10% PV = -6,000 PMT = 1,892.82 FV = 0

Interest Paid in Year 1 Principal Repaid in Year 1 Ending Balance after Year 1

INTt = Beg balt(I) PRIN = PMT – INT END BAL= BEG BAL – PRIN

INT1 = $6,000 (0.10) = $1,892.82 - $600 = $6,000 – $1,292.82

INT1 = $600 = $1,292.82 = $4,707.18

YEAR BEG BAL PMT INT PRIN END BAL


1 $6,000 $1,893 $600 $1,293 $4,707
2 4,707 1,893 471 1,422 3,285
3 3,285 1,893 329 1,564 1,721
4 1,721 1,893 172 1,721 0
TOTAL ----- 7,572 1,572 6,000 -----

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