The compound interest (compounding annually) on a certain sum at the rate of 8 percent per annum for two years is Rs. 6656. What…

Question

The compound interest (compounding annually) on a certain sum at the rate of 8 percent per annum for two years is Rs. 6656. What would be the simple interest on the same sum at the same rate of interest for two years?

1. A. Rs. 6224
2. B. Rs. 6400 (Correct answer)
3. C. Rs. 5600
4. D. Rs. 6336

Correct Answer

Option B — Rs. 6400

Detailed Solution & Explanation

The correct answer is Rs. 6400.

Key Points

• First recover the principal from the two-year compound interest, then compute the simple interest.
• For 2 years at 8%, the CI multiplier is (1.08)² − 1 = 1.1664 − 1 = 0.1664. Given CI = Rs. 6656:
• P × 0.1664 = 6656 → P = 6656 ÷ 0.1664 = Rs. 40,000.
• Now the simple interest for 2 years at 8%:
• SI = (P × R × T)/100 = (40000 × 8 × 2)/100 = Rs. 6400.
• for 2 years, CI = P[(1 + R/100)² − 1] and SI = 2 × (P × R/100).
• CI always exceeds SI because compound interest earns 'interest on interest' in the second year.

Exam Tip

• the difference CI − SI for 2 years = P(R/100)² — here 40000 × (0.08)² = Rs. 256 = 6656 − 6400, a quick way to cross-check the two figures.