Multiple choice

A sum of money is invested at compound interest at a certain rate. If the simple interest at the same rate is calculated, then the simple interest for the first two years comes out to be Rs. 20 less than the compound interest for the same number of years, and that for the first three years, comes out be Rs. 61 less than the compound interest for the same number of years. Find the rate.

  1. 10%

  2. 7%

  3. 5%

  4. 3%

  5. 4%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal and r be the rate. CI for 2 years = P(1+r)^2 - P = P(2r + r^2). SI for 2 years = P(2r). Difference = Pr^2 = 20. CI for 3 years = P(1+r)^3 - P = P(3r + 3r^2 + r^3). SI for 3 years = P(3r). Difference = P(3r^2 + r^3) = 61. Dividing the two: (3r^2 + r^3) / r^2 = 61 / 20, so 3 + r = 3.05, which means r = 0.05 or 5%.

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