A sum becomes ₹6,600 in 2 years and ₹7,920 in 3 years at compound interest. What is the original principal?

Question

A sum becomes ₹6,600 in 2 years and ₹7,920 in 3 years at compound interest. What is the original principal?

1. A. ₹4,000.33
2. B. ₹5,583.33
3. C. ₹4,583.33 (Correct answer)
4. D. ₹6,583.33

Correct Answer

Option C — ₹4,583.33

Detailed Solution & Explanation

The correct answer is ₹4,583.33.

Key Points

• The one-year growth from ₹6,600 to ₹7,920 gives the rate: (7920 − 6600)/6600 × 100 = 20%.
• Since ₹6,600 is the amount after 2 years, the principal P satisfies P × 1.2² = 6600, so P = 6600 / 1.44 = ₹4,583.33.
• Consecutive-year compound amounts reveal the rate from their ratio; then discount back by (1 + r)ⁿ to recover the principal.