Question

A man borrowed Rs. 20,000 for 2 years at 8% per year compound interest. Calculate the interest for the first year.

Answer 1

Hint: We have to use the concept of compound interest in this question. The concept is that the interest calculated is not with respect to the principal amount. But instead, it is calculated with the total amount at the end of each year. So, the interest does not increase linearly as in simple interest. The formula used will be-
${\text{A}} = {\text{P}} \times {\left( {1 + \dfrac{{\text{R}}}{{100}}} \right)^{\text{T}}}$
where A is the final amount, P is the principal amount, R is the rate of interest and T is the time in years.

Complete step by step answer:
We have to find the interest for the first year, so first we will calculate the amount at the end of first year which is given by-
${\text{A}} = {\text{P}} \times {\left( {1 + \dfrac{{\text{R}}}{{100}}} \right)^{\text{T}}}$
${\text{A}} = 20000 \times {\left( {1 + \dfrac{8}{{100}}} \right)^1}$
A = 20000 + 1600 = Rs. 21,600
Now the interest at the end of the first year is the total amount minus the principal amount.
So the interest will be-
= A - P
= 21,600 - 20,000
=Rs. 1600
This is the required answer.
Note: For the first year, the compound interest and the simple interest will be the same, because the initial principal amount is the same in both the cases. This can be calculated as-
$Interest = \dfrac{{PRT}}{{100}} = \dfrac{{20000 \times 8 \times 1}}{{100}} = Rs.\;1600$