A certain sum was invested at the rate of 10% for a period of 2 years at compound interest and compounded annually. The same sum was invested for the same period and same rate of interest at simple interest. If the difference of compound interest and simple interest was Rs.200, find the sum.

Correct option is D

Given:

Rate of interest = 10% per annum

Time period = 2 years

Difference between compound interest and simple interest = Rs. 200

We need to find the sum (principal).

Formula Used:

The formula for compound interest (CI) compounded annually is:

​$$CI = P(1 + \frac{R}{100})^T - P$$​​

Where, P = principal, R = rate of interest, T = time period

The formula for simple interest (SI) is:

​$$SI =\frac{ PRT} { 100}$$​​

The difference between compound interest and simple interest for 2 years is:

Difference = CI – SI

Solution:

Compound interest for 2 years:

​$$CI = P(1 + \frac{10}{100})^2 - P = P(1.1)^2 - P$$​​

= P(1.21) - P = 0.21P

Simple interest for 2 years:

​$$SI = \frac{(P × 10 × 2)}{ 100} = 0.2P$$​​

Difference between CI and SI:

Difference = 0.21P - 0.2P = 0.01P

Given that the difference is Rs. 200, we have:

0.01P = 200

Solving for P:

P = 200 / 0.01 = Rs. 20,000

Thus, the sum (principal) is Rs. 20,000.

Alternative Method: