Single correct option
A sum invested at 20% per annum, compounded annually, earns Rs 512 more interest over 3 years than the same sum would earn at simple interest. Find the sum.
- A. Rs 3,750
- B. Rs 4,000
- C. Rs 4,200
- D. Rs 4,500
Show answer and solution
Answer: (B) Rs 4,000
Let the sum be P.
CI for 3 years = P(1.2³ − 1) = P(1.728 − 1) = 0.728P.
SI for 3 years = P × 0.20 × 3 = 0.6P.
Difference = 0.728P − 0.6P = 0.128P = 512, so P = 512/0.128 = Rs 4,000.
Check: SI = 4000×0.6 = 2,400; CI = 4000×0.728 = 2,912; difference = 512. ✓
CI for 3 years = P(1.2³ − 1) = P(1.728 − 1) = 0.728P.
SI for 3 years = P × 0.20 × 3 = 0.6P.
Difference = 0.728P − 0.6P = 0.128P = 512, so P = 512/0.128 = Rs 4,000.
Check: SI = 4000×0.6 = 2,400; CI = 4000×0.728 = 2,912; difference = 512. ✓
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