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Learning objectives of this
article:
-
What is difference between simple
interest and compound interest.
-
What are the characteristics of compound
interest?
Contents:
Usually, interest is calculated using two
methods. One is the simple interest method and other
is the compound interest method. Both the methods
are popular and are in practice.
When the simple interest method is used, the
interest is calculated only on the principal amount
(original amount). The amount of interest is not
added to the principal amount for the purpose of
calculating interest. When compound interest method
is used, the interest is added to the principal
amount (original amount) for the purpose of
calculating interest. This method is
widely used by banks, credit unions, corporations,
government agencies, and other financial
institutions.
The following example explains these two methods:
A loan of $8,000 is issued for a period of 4
years. The interest is calculated @ 2%. Whole amount (principal + interest) is paid at the
end of 4-year period. Calculate the amount to repay if:
- The interest is calculated using simple
interest method.
- The interest is calculated using compound
interest method.
Solution:
1. When interest is simple:
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Principal amount =
$8,000
Annual interest =
$8,000 ×
0.02
= $160
Interest for 4 years:
= $160
× 4
= 640
Amount to repay at
the end of 4-year period:
= $5,000 + $640
= $5,640 |
2. When interest is compounded:
|
Year |
(P) Principle |
(I) Interest |
(S = P + I) Compound Amount |
| 1 |
$8,000.00 |
$160.00 |
$8,000.00 |
+ |
$160.00 |
= |
$8,160.00 |
| 2 |
$8,160.00 |
$163.00 |
$8,160.00 |
+ |
$163.00 |
= |
$8,323.20 |
| 3 |
$8,323.20 |
$166.46 |
$8,323.20 |
+ |
$166.46 |
= |
$8,489.66 |
| 4 |
$8,489.66 |
$169.79 |
$8,489.66 |
+ |
$169.79 |
= |
$8,659.46 |
Amount to repay at the end of 4-year
period:
= [$8,000 + ($160.00+$163.00+$166.46+$169.79)]
= $8659.46
Alternatively this
amount of payment can also be computed
using compound interest formula
S = P(1 + i)n
Where;
S = P(1 + i)n
S = 8,000 (1 + 0.02)4
S = 8,000
×
1.08243*
= $8659.4
*Future
value of $1 table - (1 + i)n
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The difference between simple interest and
compound interest is $659.46 - $640 = $19.46.
Compound interest exceeds simple interest in this
example by $19.46 over the four year period.
In this example interest is compounded annually.
But in real businesses the interest may be
compounded quarterly, semiannual or annually.
When the compound interest method is used the
following points should be kept in mind:
- The
frequency of compounding of interest has an effect
on the value of an investment. The frequency refers
to how often interest is computed and earned. The
value of an investment increases with increased
frequency of compounding.
- Another characteristic of compound interest
is that, compared with the effects of simple
interest, the effects of compounding of interest
become more significant as the period of
investment becomes longer.
- Rate if interest has also a great influence
on the compounding procedure. The higher the
interest rate, the greater the interest earned
each compounding period and the greater the rate
of growth in the investment.
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