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Example 22: Find the interest and the total amount to be paid on `15000 at 5% per annum after
2 years.

Solution: Here, Principal (P) = `15000, Rate of interest (R) = 5% p.a. and Time (T) = 2 years
Let us find simple interest (SI) and the total amount (A) as follows:
PR T 15000 52
×
××
×
We know, SI = = = `1500
100 100
So, Amount (A) = P + SI = `15000 + `1500 = `16500
In simple interest, the principal amount is always the same. The interest that the banks, post offices
and other financial institutions charge/pay is not simple because the interest, as it falls due over
some time, is added to the original principal to form a new principal to earn further interest. This
can be repeated for several time periods. The difference between the original principal and the
final amount at the end of the last period is known as Compound Interest (CI).
The time period after which interest is added each time to form a new principal is called the
conversion period. It may be one year, half year, three months, a month or even on a daily basis. In
such cases, the interest is said to be compounded annually, semi-annually (half-yearly), quarterly,
monthly or daily respectively.

Calculation of Compound Interest

Let us learn how to calculate compound interest as repeated simple interest through an example.
A sum of `10,000 is borrowed from a company by David for 3 years at an interest of 10%
compounded annually.

In the case of simple interest, P = `10000, T = 3 years and R = 10% p.a.
×
×
×
PR T 10000 × 10 3
So, SI = = = `3000 and A = `10000 + `3000 = `13000
100 100
But the interest is compounded annually, so we need to calculate it in a different way.
For the first year: P = `10000, T = 1 year and R = 10% p.a.
1
Therefore, interest for the 1st year
PR T 10000 × 10 1
×
×
×
SI = = = `1000 and A = `10000 + `1000 = `11000
1
1
100 100
For the second year: P = A = `11000, T = 1 year and R = 10% p.a.
1
2
Therefore, interest for the 2nd year
PR T 11000 × 10 1
×
×
×
SI = 100 = 100 = `1100 and A = `11000 + `1100 = `12100
2
2
For the third year: P = A = `12100, T = 1 year and R = 10% p.a.
3
2
Therefore, interest for the 3rd year
×
×
PR T 12100 × 10 1
×
SI = = = `1210 and A = `12100 + `1210 = `13310
3
3
100 100
David now owes the company for `13310.
Thus, he pays `13310 – `10000 = `3310 as the compound interest, which is `310 more than the
simple interest of `3000.
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