Exact Simple Interest is based on the exact number of
ENGINEERING ECONOMY
days in a year, 365 days for an ordinary year and 366
days for a leap year.
INTEREST AND MONEY-TIME RELATIONSHIPS
The term capital refers to wealth in the form of money
or property that can be used to produce more wealth.
The majority of engineering economy studies involve
commitment of capital for extended periods of time, so
the effect of time must be considered. In this regard, it
is recognized that a dollar today is worth more than a
dollar one or more years from now because of the
interest (or profit) it can earn.
1 interest period = 365 or 366 days
Cash Flow Diagrams
A cash flow diagram is simply a graphical
representation of cash flow drawn on a time scale.
Cash flow diagram for economic analysis problems is
analogous to that of free body diagram for mechanics
problems.
receipt (positive cash flow or cash inflow)
Therefore, money has a time value.
Why Consider Return to Capital?
There are fundamental reasons why return to capital
in the form of interest and profit is an essential
ingredient of engineering economy studies.
 Interest and profit pay the providers of capital for
forgoing its use during the time the capital is
being used.
 Interest and profit are payments for the risk the
investor takes in permitting another person, or an
organization, to use his or her capital.
A loan of P100 at a simple interest of 10% will become
P150
after 5 disbursement (negative cash flow or cash
outflow)
years.
P150
0
1
2
3
4
5
Interest is the amount of money paid for the use of
borrowed capital or the income produced by money
which has been loaned.
Simple Interest
Fig 1. Cash flow diagram on the viewpoint of the lender
Simple interest is calculated using the principal only,
ignoring any interest that had been accrued in
preceding periods. In practice, simple interest is paid
on short-term loans in which the time of the loan is
measured in days.
P100
P100
1
2
3
4
5
0
𝐼 = 𝑃𝑛𝑖
𝐹 = 𝑃 + I = 𝑃 + 𝑃𝑛𝑖
P150
𝐹 = 𝑃 (1 + 𝑛𝑖)
where:
I = interest
Fig 2. Cash flow diagram on the viewpoint of the borrower
P = principal or present worth
n = number of interest periods
i = rate of interest per interest period
F = accumulated amount or future worth
Compound Interest
In calculations of compound interest, the interest for
an interest period is calculated on the principal plus
total amount of interest accumulated in previous
periods. Thus compound interest means “interest on
top of interest”
Ordinary simple interest is computed on the basis of
12 months of 30 days each or 360 days a year.
P
1 interest period = 360 days
0
1
2
3
n-1
n
F
Fig 3. Compound Interest (Borrower’s Viewpoint)
Interest Principal
Period
at
Beginning
of Period
1
P
2
P(1+i)
3
P(1+i)2
…
4
…
P(1+i)n-1
Interest
Earned
During
Period
Pi
P(1+i)i
Amount at End of
Period
P + Pi = P(1+i)
P(1+i) + P(1+i)i
= P(1+i)2
2
P(1+i) i
P(1+i)2 + P(1+i) 2
= P(1+i)3
…
…
n-1
P(1+i) i P(1+i)n
𝐹 = 𝑃(1 + 𝑛)𝑛
The quantity (1+i)n is commonly called the “single
payment compound amount factor and is designated
by the functional symbol F/P, i%, n. Thus
𝐹
𝐹 = 𝑃 ( , 𝑖%, 𝑛)
𝑃
SAMPLE PROBLEMS
1. What is the annual rate of interest if P265 is
earned in four months on an investment of
P15, 000?
2. A loan of P2, 000 is made for a period of 13
months, from January 1 to January 31 the
following year, at a simple interest of 20%.
What is the future amount is due at the end of
the loan period?
3. If you borrow money from your friend with
simple interest of 12%, find the present worth
of P20, 000, which is due at the end of nine
months.
4. Determine the exact simple interest on P5,
000 for the period from Jan.15 to Nov.28,
1992, if the rate of interest is 22%.
5. A man wishes his son to receive P200, 000 ten
years from now. What amount should he
invest if it will earn interest of 10%
compounded annually during the first 5 years
and 12% compounded quarterly during the
next 5 years?