Single correct option
A sum of money is invested at a certain rate of compound interest, compounded annually. The amount grows to ₹26,620 at the end of 2 years and to ₹29,282 at the end of 3 years. What is the annual rate of interest?
- A. 8%
- B. 9%
- C. 10%
- D. 11%
Show answer and solution
Answer: (C) 10%
Let the principal be P and the rate r (as a fraction). Then P(1+r)² = 26,620 and P(1+r)³ = 29,282.
Dividing the second by the first isolates the extra year's growth factor: (1+r) = 29,282/26,620 = 1.1, so r = 10%.
(Check: P = 26,620/1.1² = 22,000, and 22,000 × 1.1³ = 29,282 ✓.)
Tip: Whenever two consecutive years' amounts are given, their ratio directly gives (1 + rate) — no need to find the principal first.
Dividing the second by the first isolates the extra year's growth factor: (1+r) = 29,282/26,620 = 1.1, so r = 10%.
(Check: P = 26,620/1.1² = 22,000, and 22,000 × 1.1³ = 29,282 ✓.)
Tip: Whenever two consecutive years' amounts are given, their ratio directly gives (1 + rate) — no need to find the principal first.
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