Single correct option
A sum of money invested at compound interest (compounded annually) amounts to ₹14,520 at the end of 2 years and to ₹15,972 at the end of 3 years. What is the sum invested?
- A. ₹13,200
- B. ₹11,800
- C. ₹12,000
- D. ₹12,500
Show answer and solution
Answer: (C) ₹12,000
Under annual compounding, the amount grows by the same factor every year. Growth factor = 15972/14520 = 1.1, so the rate is 10% per annum.
Amount after 2 years = P × 1.1² = 1.21P = 14520 ⇒ P = 14520/1.21 = 12,000.
Check: 12000 → 13200 → 14520 → 15972. ✓
Tip: the interest earned in year 3 (15972 − 14520 = 1452) is 10% of the amount at the end of year 2 — that immediately gives the rate.
Amount after 2 years = P × 1.1² = 1.21P = 14520 ⇒ P = 14520/1.21 = 12,000.
Check: 12000 → 13200 → 14520 → 15972. ✓
Tip: the interest earned in year 3 (15972 − 14520 = 1452) is 10% of the amount at the end of year 2 — that immediately gives the rate.
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