The difference between the compound interest and simple interest for the sum of ₹5,000 at 10% per annum for two years is:

Correct option is D

Given:

Principal (P) = ₹5,000

Rate (R) = 10% per annum

Time (T) = 2 years
We need: Difference between Compound Interest (CI) and Simple Interest (SI).

Formula Used:

Simple Interest (SI):

SI =$$\frac{P \times R \times T}{100}$$​

Compound Interest (CI):

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

Difference between CI and SI for 2 years:

Difference = P $$\times \left(\frac{R}{100}\right)^2$$​

Solution:​

SI =$$\frac{5000 \times 10 \times 2}{100} = 1000$$​​

CI = $$5000 \times \left(1 + \frac{10}{100}\right)^2 - 5000$$​​

= 5$$000 \times (1.1)^2 - 5000 = 5000 \times 1.21 - 5000 = 6050 - 5000 = 1050$$​

Difference = 1050 – 1000 = 50

Alternate Method:

Difference = 500$$0 \times \left(\frac{10}{100}\right)^2 = 5000 \times \frac{1}{100} = 50$$​