The Time Value of Money
Interest: the Cost of Money
Majority of engineering economy studies
involves commitment of capital for extended
periods of time, so the effect of time must be
considered
Capital
Refers to wealth in the form of money or
property than can be used to produce more
wealth
Present Value of Money Concept
a peso earned today is worth more than a
peso earned in the future.
In typical situations, if capital is invested in a
project, investors would expect, as a minimum
to receive a return at least equal to the
amount they have sacrificed by not using it in
some other available opportunity of
comparable risk
Whether borrowed capital or equity capital is
involved, there is a cost for the capital employed
in the sense that the project and venture must
provide a return sufficient to be financially
attractive to suppliers of money or property
Whenever capital is required in engineering and
other business projects and ventures, it is
essential that proper consideration be given to its
cost
Interest
Defined as the amount of money paid for the
use of borrowed capital for a certain period of
time
Simple Interest
If the interest to be paid (for borrowed
money) is directly proportional to the length
of time the amount or principal is borrowed
Principal
Amount of money borrowed and on which
interest is charged
Rate of interest
Amount earned by one unit of principal during
a unit of time
Formula for simple interest
I= Pin
I = Total interest earned by the principal
P = amount of the principal
i = rate of interest
n = number of interest periods
Total amount to F to be repaid is equal to the
sum of the principal and the total interest and
is given by the formula
F = P + I = P (1+in)
Simple Interest
Ordinary simple interest
Exact simple interest
Ordinary
Computed on the basis of one banker's year,
which is 360 days (12 months, each consisting
of 30 days)
Exact
Based on the exact number of days, 365 for an
ordinary year and 366 for a leap year
Ordinary simple interest
I= Pi
360
Exact simple interest
I= Pi (for ordinary year)
365
I= Pi (for leap year)
366
Example 1
Determine the ordinary simple interest on Php
10,000 for 9months and 10 days if the rate of
interest is 12%.
Example 2
A bank charges 12% simple interest on a Php
300,000 loan. How much will be repaid if the
loan is paid back in one lump-sum amount
after three years?
Example 3
If you borrowed money from your friend with
simple interest of 12%, find the present worth
of Php 50,000 which is due at the end of 7
months.
Example 4
A man borrows Php 10,000 from a loan firm.
The rate of simple interest is 15%, but the
interest is to be deducted from the loan at the
time the money is borrowed. At the end of
one year, he has to pay back Php 10,000.
What is the actual rate of interest?
Compound Interest
In compound interest, the interest earned by
the principal is not paid at the end of each
interest period, but is considered as added to
the principal, and therefore will also earn
interest for the succeeding periods.
Compound Interest
The interest earned by the principal when
invested at compound interest is much more
than that earned by the same principal when
invested at simple interest for the same
number of periods.
Using the same nomenclature as that for
simple interest, the total amount due after n
for compound interest is given by the formula:
F = P(1+i)n
Where: (1+i)n = Single Payment Compound
Amount Factor (SPCAF)
Example No. 1
The amount of Php 50,000 was deposited in
the bank earning an interest of 7.5% per
annum. Determine the total amount at the
end of 5 years, if the principal and interest
were not withdrawn during the period?
Example No. 2
Find the present worth of a payment of Php
30,000 to be made in five years with an
interest rate of 8% per annum.
Example No. 3
A sum of Php 1,000 is invested now and left
for eight years, at which time the principal is
withdrawn. The interest that has accrued is
left for another eight years. If the effective
annual interest rate is 5%, what will be the
withdrawal amount at the end of the 16th
year?
Example No. 4
A student plan to deposit Php 1,500 in the
bank now and another Php 3,000 after two
years. If he plans to withdraw Php 5,000
threee years after his last deposit for the
purpose of buying shoes, what will be the
amount of money left in the bank after one
year of his withdrawal? Effective annual
interest rate is 10%
Example No. 5
How long will it take money to triple itself if
invested at 8% compounded annually?
