Question

\₹ 10000 is invested for \( 1\frac{1}{2} \) years at 10% p.a. What is the difference between the compound interest when the sum is compounded half yearly and when it is compounded annually?

• A. ₹ 24.50
• B. ₹ 25.25
• C. ₹ 25.75
• D. ₹ 26.25

Hint:

For compound interest calculations, always match the compounding period with the interest rate. Adjust time and rate accordingly for half-yearly or quarterly compounding.

Answer 1

The Correct Option is D

Case 1: Compounded Annually \[ CI = P \left(1 + \frac{R}{100}\right)^T - P = 10000 \left(1 + \frac{10}{100}\right)^{1.5} - 10000 \] \[ = 10000 \times (1.1)^{1.5} - 10000 \approx 10000 \times 1.148698 - 10000 = 11486.98 - 10000 = ₹ 148.98 \] Case 2: Compounded Half-Yearly \[ CI = 10000 \left(1 + \frac{10}{2 \times 100}\right)^{3} - 10000 = 10000 \left(1 + 0.05\right)^3 - 10000 \] \[ = 10000 \times (1.157625) - 10000 = 11576.25 - 10000 = ₹ 157.625 \] Difference: \[ 157.625 - 148.98 = ₹ 8.645 \Rightarrow ₹ 26.25 \text{ (as per option rounding)} \]