A sum of ₹4,000 is invested at 10% per annum, compounded annually. What will the difference between the compound interest (in ₹) earned in the second year and the first year be?

Correct option is D

Given:

Principal (P) = ₹4,000

Rate of interest (R) = 10% per annum

Formula Used:

The formula for compound interest is:

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

Where:

A is the amount after T years

P is the principal amount

R is the annual interest rate

T is the time in years

Solution:

Compound Interest in the First Year: For the first year, the principal is ₹4,000, and the interest rate is 10%.

​$$A_1 = 4000 \times \left( 1 + \frac{10}{100} \right) = 4000 \times 1.10 = ₹4,400$$​​

The compound interest for the first year is:

​$$\text{CI}_1 = A_1 - P = 4400 - 4000 = ₹400$$​​

Compound Interest in the Second Year:
After the first year, the new principal becomes ₹4,400 (the amount at the end of the first year).

​$$A_2 = 4400 \times \left( 1 + \frac{10}{100} \right) = 4400 \times 1.10 = ₹4,840$$​​

The compound interest for the second year is:

​$$\text{CI}_2 = A_2 - A_1 = 4840 - 4400 = ₹440$$​​

Difference =$$\text{CI}_2 - \text{CI}_1 = 440 - 400 = ₹40$$​​