Question

The simple interest accrued on a sum of certain principal in 8 years at the rate of 13% per year is Rs.6500. What would be the compound interest accrued on that principal at the rate of 8% per year in 2 years?

• A. Rs.1040
• B. Rs.1020
• C. Rs.1060
• D. Rs.1200

Hint:

First recover the principal from the simple interest formula, then apply the compound interest formula.

Answer 1

The Correct Option is A

Step 1: Find the principal using the simple interest formula.
Simple interest is given by \( SI = \frac{P \times T \times R}{100} \). Here \(SI=6500\), \(T=8\) years and \(R=13\%\), so \(6500 = \frac{P \times 8 \times 13}{100}\), which gives \(P = \frac{6500 \times 100}{104} = 6250\).

Step 2: Compute the compound interest on this principal.
Compound interest for 2 years at 8% per year is \( CI = P\left[\left(1+\frac{8}{100}\right)^2 - 1\right] = 6250 \times \left[(1.08)^2 - 1\right] = 6250 \times 0.1664 = 1040 \).

Final Answer:
The compound interest accrued is Rs.1040, which matches option A; options B, C and D do not follow from \(P=6250\). \[ \boxed{Rs.\,1040} \]