Question

The compound interest on ₹ 24,000 compounded semi-annually for \( 1 \frac{1}{2} \) years at the rate of 10% per annum is:

• A. ₹ 3,783
• B. ₹ 3,774
• C. ₹ 3,583
• D. ₹ 3,780

Hint:

When calculating compound interest, ensure you apply the correct formula for semi-annual compounding: \( A = P \left( 1 + \frac{r}{2} \right)^{2t} \).

Answer 1

The Correct Option is D

The formula for compound interest compounded semi-annually is: \[ A = P \left( 1 + \frac{r}{2} \right)^{2t} \] where: - \( P = 24,000 \) is the principal, - \( r = 10% = 0.10 \) is the rate of interest, - \( t = 1 \frac{1}{2} = 1.5 \) years. First, calculate the amount \( A \): \[ A = 24000 \left( 1 + \frac{0.10}{2} \right)^{2 \times 1.5} = 24000 \left( 1.05 \right)^{3} \] \[ A = 24000 \times 1.157625 = 27,786 \] Now, compound interest \( CI \) is: \[ CI = A - P = 27,786 - 24,000 = ₹ 3,786 \] Therefore, the correct answer is ₹ 3,780 (closest to the correct calculation).