Single correct option
A sum of money invested at compound interest (compounded annually) amounts to ₹13,310 in 2 years and to ₹14,641 in 3 years. What is the sum invested?
- A. ₹11,500
- B. ₹11,000
- C. ₹10,500
- D. ₹10,000
Show answer and solution
Answer: (B) ₹11,000
The amount in year 3 is the amount in year 2 plus one year's interest on it.
Rate: 14641/13310 = 1.10, so r = 10% p.a.
Principal P satisfies P × 1.10² = 13310 → P = 13310/1.21 = ₹11,000.
Check: 11000 × 1.10³ = 14641 ✓.
Tip: the ratio of consecutive compound amounts directly gives (1 + r).
Rate: 14641/13310 = 1.10, so r = 10% p.a.
Principal P satisfies P × 1.10² = 13310 → P = 13310/1.21 = ₹11,000.
Check: 11000 × 1.10³ = 14641 ✓.
Tip: the ratio of consecutive compound amounts directly gives (1 + r).
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