Simple Interest
Suppose you deposit a certain amount of money into an account. If you are given simple interest the interest is
added to your account just once, at the end of the time you have the investment for. Say you invest $10,000 for
a period of 5 years and you earn simple interest. Then at the end of this 5 year period the interest that you have
earned is added to the $10,000 you deposited.
In case you take out a loan for a particular amount of time at a certain simple interest rate, then you have to pay
interest just once to your bank. You do this at the end of the amount of time you take out the loan for.
The formula to calculate simple interest is I  P  r  t .
(1)
In this formula, I is the actual amount of interest you earn or pay, P is the principal of the investment or loan
(the amount of money you invest or borrow), r is the annual interest rate (expressed as a decimal), and t is the
time you invest the money for or the time for the loan. The time t must be expressed in years. Thus, if you
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deposit money for 3 years you use t  3 , in case you take out a loan for 5 months the value for t is t  , in
12
17
case you need the loan for 17 months you use t 
12
If you deposit money for a certain number of days you have to use the so-called Bankers Rule which sets a year
to 360 days. This is a convention which is often used in the world of finance. Thus taking out a loan for 40 days
40
leads to t 
.
360
Through out this document we shall round all amounts to the nearest cent.
Amount of Interest Calculations
Let us look at a few examples in which formula (1) is used.
Example 1:
Will deposits $5,000 into an account which earns 2.5% annual simple interest for a period of 7 months. What is
the amount of interest that he earns?
Solution 1:
The values for P, r and t are:
P  5,000
r  0.025
t
7
12
Formula (1) thus gives: I  5,000  0.025 
7
 $72.92
12
Example 2:
Lindsey borrowed $12,000 for a period of 275 days at an annual simple interest rate of 4.35%. How much
interest did she pay?
© 2008 UMUC – European Division
Ron Souverein and Nada Wray
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Solution 2:
The values for P, r and t are:
P  12,000
r  0.0435
275
t
360
Formula (1) thus gives: I  12,000  0.0435 
275
 $398.75
360
Example 3:
Chris borrowed $8,500 at a 5% simple interest rate for a period of two and a half years. How much interest did
he pay?
Solution 3:
The values for P, r and t are:
P  8,500
r  0.05
t  2.5
Formula (1) thus gives: I  8,500  0.05  2.5  $1,062.50
Interest Rate Calculations
Example 4:
Elaine invested $12,000 for a period of 3 years and earned $900 in interest at the end of that period. What was
the simple interest rate?
Solution 4:
The values for I, P and t are:
I  $900
P  12,000
t 3
900  12,000  r  3
Formula (1) thus gives: 900  36000  r
r
900
 0.025
36,000
Thus the interest rate was 2.5%.
Example 5:
Cathy needs to borrow $12,000 for a period of 60 days. Given that she has to repay her bank an amount of
$12,090 at the end of the 60 days, what was the simple interest rate on this loan?
Solution 5:
Cathy borrows $12,000 and has to repay $12,090.The difference of these two amounts, $90, is thus the amount
of interest she paid.
The values for I, P and t are:
I  $90
P  12,000
60
t
360
90  12,000  r 
60
360
Formula (1) thus gives: 90  2,000  r
r
90
 0.045
2,000
Thus the interest rate was 4.5%.
© 2008 UMUC – European Division
Ron Souverein and Nada Wray
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Future Value Calculations
We often use the concept of the future value of an investment or loan. The future value is simply the amount of
the investment plus the interest you earned. In case of taking out a loan the future value of the loan is the
amount of the loan plus the interest paid.
In the form of a formula, this can be written as A  P  I
(2)
In formula (2), A stands for the future value. Why A? Well, why not? It is a common practice to use A as the
future value.
The future value of Will's deposit in example 1 is thus $5,000  $72.92  $5,072.92
The future value of Lindsey's loan in example 2 is $12,000  $398.75  $12,398.75
The future value of Chris' loan in example 3 is $8,500  $1062.50  $9,562.50
Present Value Calculations
The principal is sometimes called the Present Value. This is just another name for the same thing as the
principal.
Sometimes the future value of an investment or loan is known and we are asked to calculate the principal. This
can be done by combining formulas (1) and (2) as
(3).
A  P  Pr  t
Example 6:
Robert's investment pays a future value of $8,640 after it has been deposited 2 years ago at an annual simple
interest rate of 4%. What was the amount of money Robert originally deposited?
Solution 6:
The values for A, r and t are:
A  8,640
r  0.04
t2
8,640  P  P  0.04  2
8,640  1  P  0.08  P and after combining the terms on the right
Formula (3) thus gives: 8,640  1.08  P
8,640
P
 $8,000
1.08
© 2008 UMUC – European Division
Ron Souverein and Nada Wray
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Example 7:
Sam took out a loan at an annual simple interest rate of 5% for a period of 6 months. If the future value of this
loan is $10,000, what was the original amount of the loan?
Solution 7:
The values for A, r and t are:
A  10,000
r  0.05
6
t
 0.5
12
10,000  P  P  0.05  0.5
10,000  1  P  0.025  P and after combining the terms on the right
Formula (3) thus gives: 10,000  1.025  P
10,000
P
 $9,756.10
1.025
Example 8:
In two years from now Bob wants to take a long vacation. He estimates that he needs $30,000 for this vacation.
How much should he deposit now into an account that pays 5.5% annual simple interest rate so he'll have the
needed amount of money available for his vacation?
Solution 8:
The values for A, r and t are:
A  30,000
r  0.055
t2
30,000  P  P  0.055  2
30,000  1  P  0.11  P and after combining the terms on the right
Formula (3) thus gives: 30,000  1.11  P
30,000
P
 $27,027.03
1.11
© 2008 UMUC – European Division
Ron Souverein and Nada Wray
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