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# Difference Between Simple Interest and Compound Interest:

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1. What is difference between simple interest and compound interest.
2. What are the characteristics of compound interest?

Contents:

## Explanation of the Difference:

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:

## Example:

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:

1. The interest is calculated using simple interest method.
2. The interest is calculated using compound interest method.

### Solution:

##### 1. When interest is simple:
 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;

• P = Principal, dollars

• i = Interest rate per compounding period

• n = Number of compounding periods (number of periods in which the principal has earned interest)

• S = Compound amount

S = P(1 + i)n

S = 8,000 (1 + 0.02)4

S = 8,000 × 1.08243*

= \$8659.4

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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## More study material from this topic:

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