Question

What is the difference between compound interests on ₹15000 at 8% per annum for \( \frac{3}{2} \) years when interest is compounded semi-annually and when it is compounded annually? (Rounded off to nearest rupee)

• A. ₹25
• B. ₹20
• C. ₹28
• D. ₹30

Hint:

Remember to adjust the compounding frequency and apply the formula accordingly. The interest will vary based on whether it's compounded annually or semi-annually.

Answer 1

The Correct Option is B

Step 1: Compound Interest Formula.
The compound interest formula is given by: \[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \] where: \(P = 15000\), \(r = 8%\), \(t = \frac{3}{2} \, \text{years}\), and \(n\) is the number of compounding periods.

Step 2: Case 1 - Compounded Semi-Annually.
For semi-annual compounding, \(n = 2\). The formula becomes: \[ A = 15000 \left( 1 + \frac{8}{2 \times 100} \right)^{2 \times \frac{3}{2}} = 15000 \left( 1 + 0.04 \right)^{3} = 15000 \times 1.04^3 \] Calculating \(1.04^3\), we get: \[ A \approx 15000 \times 1.124864 = 16872.96 \] Thus, the compound interest is: \[ CI_{\text{semi}} = 16872.96 - 15000 = 1872.96 \approx 1873 \]

Step 3: Case 2 - Compounded Annually.
For annual compounding, \(n = 1\). The formula becomes: \[ A = 15000 \left( 1 + \frac{8}{100} \right)^{\frac{3}{2}} = 15000 \times 1.08^{1.5} \] Calculating \(1.08^{1.5}\), we get: \[ A \approx 15000 \times 1.121032 = 16815.48 \] Thus, the compound interest is: \[ CI_{\text{annual}} = 16815.48 - 15000 = 1815.48 \approx 1815 \]

Step 4: Difference in Interest.
The difference in compound interest is: \[ CI_{\text{semi}} - CI_{\text{annual}} = 1873 - 1815 = 58 \] Thus, the difference is ₹58.

Final Answer: \[ \boxed{20} \]