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Learning objectives of this
article:
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Define and explain the simple
interest.
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How is it calculated?
Contents:
There are two ways to calculate interest. One is
the simple interest and other is the compound
interest. In this article simple interest is
defined, explained and calculated. The concept of
compound interest is explained on
future value of a single sum page.
Interest is a fee which is paid for
having the use of money. We pay interest on
mortgages for having the use of the bank's money. We
use the bank's money to pay a contractor or person
from whom we are purchasing a home. Similarly, the
bank pays us interest on money invested in savings
accounts or certificates of deposit because it has
temporary access to our money. The amount of money
that is lent or invested is called the principle.
Interest is usually paid in proportion to the
principle and the period of time over which the
money is used. The interest rate specifies the rate
at which interest accumulates. The interest rate is
typically stated as a percentage of the principle
per period of time, for example, 18 percent per year
or 1.5 percent per month.
Interest that is paid solely on the
amount of the principle is called simple
interest. Simple interest is usually
associated with loans or investments which are
short-term in nature.
The calculation of simple interest
is based on the following formula:
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Simple interest = Principle
×
Interest rate per time period
× Number
of time periods
Or
I
= Pin
Where;
- I = Simple interest, dollars
- P = Principle, dollars
- i = Interest rate per time period
- n = Number of time periods of
loan
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In the above formula, it is essential that the
time periods for i and n be consistent with
each other. That is, if i is expressed as a
percentage per year, n should be expressed in
number of years. Similarly, if i is expressed
as a percentage per month, n must be stated
in number of months.
Example 1:
A credit union has issued a 3-year loan of
$5,000. Simple interest is charged at a rate of 10
percent per year. The principle plus interest is to
be repaid at the end of the third year. Compute the
interest for three year period. What amount will be
repaid at the end of the third year?
Solution:
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I = Pin
I = ($5,000)(0.10)(3)
= $1,500
The amount to be repaid is
the principle plus the accumulated interest,
that is:
$5,000 + $1,500
$6,500 |
Example 2:
A person lends $10,000 to a corporation by
purchasing a bond from the corporation. Simple
interest is computed quarterly at a rate of 3
percent per quarter, and a check for the interest is
mailed each quarter to all bondholders. The bonds
expire at the end of 5 years, and the final check
includes the original principle plus interest earned
during the last quarter. Compute the interest earned
each quarter and the total interest which will be
earned over 5-year life of the bonds.
Solution:
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In this problem P = $10,000, i = 0.03 per
quarter, and the period of the loan is 5
years. Since the time period for i is a
quarter (of a year), we must consider 5
years as 20 quarters. And since we are
interested in the amount of interest earned
over one quarter, we must let n = 1.
Therefore quarterly interest equals:
I = Pin
I = ($10,000)(0.03)(1)
= $300
To compute the total interest over the
five year period, we multiply the
per-quarter interest of $300 by the number
of quarters, 20, to obtain
Total interest = $300
× 200
= $6000 |
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