Multiple choice

The compound interest on a certain sum for 2 years at a certain rate of interest is Rs 1025 and simple interest on the same sum, same time and same rate of interest is Rs 1000. Then find the compound interest for the same sum in 3 years.

  1. $1575.25$
  2. $1576.25$
  3. $1576.75$
  4. $1575.75$

  5. None of these
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B Correct answer
Explanation

Let P be principal, r be rate. SI = P × r × 2 = 1000, so P × r = 500. CI = P(1+r)² - P = 1025. Expanding: P(2r + r²) = 1025. Substituting P × r = 500: 2(500) + P × r² = 1025, so P × r² = 25. Dividing by P × r: r = 25/500 = 0.05 (5%). Then P = 500/0.05 = 10000. CI for 3 years = 10000(1.05)³ - 10000 = 10000(1.157625) - 10000 = 1576.25.

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