Banks, post offices, and insurance companies calculate the interest for one year and then yearly interest is added to the principal. The amount we get becomes the principal for second-year interest calculation. This process is repeated until the amount is calculated for the whole loan period.
Thus, the difference between the final amount and the original principal is called the compound interest. It is written as C.I.
C.I = A − P
Note: The principal remains constant for the whole loan period in case of simple interest calculation, but the principal keeps on changing every year for compound interest calculation.
Example 1. Calculate the compound interest on 20,000 rupees for 2 years at 4% per annum.
Solution. Here, rate of interest = 4%, principal for the first year = Rs. 20,000.
Interest for the first year = 20,000 × 4 × 1⁄100
= Rs. 800
Amount at the end of first year = 20,000 + 800 = Rs. 20,800.
Principal for the second year = Rs. 20,800
Interest for the second = 20,800 × 4 × 1⁄100 = Rs. 832
Amount at the end of second year = 20,800 + 832 = Rs. 21,632
Compound interest for 2 years = final amount − original
= 21,632 − 20,000 = Rs. 1632.
Deducing a Formula for Compound Interest
To find out compound interest in a shorter way, following formulae we should use. Let’s discuss how formulae are formed.
Suppose a sum of P rupees is compounded annually at a rate of R% per annum for n year. The amount at the end of n years must be calculated by using formulae
A = P(1 + R⁄100)n
Compound Interest (C.I) = A − P
Let’s see some solved examples for a better understanding
Example 1. What principal of money will amount to Rs. 2205 in two years at 7% per annum compound interest?
Solution. Here, A = Rs. 2205, R= 5%, n = 2 years
A = P(1 + R⁄100)n
⇒ 2205 = P(1 + 5⁄100)2
⇒ 2205 = P(21⁄20) × (21⁄20)
⇒ P = 2205(21⁄20) × (21⁄20)
= Rs. 2000
Hence the principal is Rs. 2000.
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