Multiple choice

If the ratio between the difference between compound interest and simple interest of 3 years and 2 years on a same sum is 16 : 5, then find the rate of interest.

  1. 20%

  2. 25%

  3. 10%

  4. 15%

  5. 12.5%
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A Correct answer
Explanation

For a sum P at rate r%, CI-SI difference for 2 years = Pr²/100² and for 3 years = Pr²(300+r)/100³. Ratio = [Pr²(300+r)/100³] / [Pr²/100²] = (300+r)/100 = 16/5. Solving: 5(300+r) = 1600, so 1500 + 5r = 1600, giving r = 20%. The pattern holds: check SI for 2 years = 2Pr/100, CI = P(1+r/100)² - P = Pr²/100² + 2Pr/100.

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