Multiple choice

A sum of money is accumulating at compound interest at a certain rate. If simple interest instead of compound was reckoned, the interest for the first two years would be diminished by Rs. 20 and that for the first three years by Rs. 61. Find the sum.

  1. Rs. 6500

  2. Rs. 7000

  3. Rs. 7500

  4. Rs. 8000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be the sum and r be the rate. CI for 2 years = P(1+r)^2 - P = 2Pr + Pr^2. SI for 2 years = 2Pr. Difference = Pr^2 = 20. CI for 3 years = P(1+r)^3 - P = 3Pr + 3Pr^2 + Pr^3. SI for 3 years = 3Pr. Difference = 3Pr^2 + Pr^3 = 61. Divide: (3Pr^2 + Pr^3) / Pr^2 = 61/20. 3 + r = 3.05, so r = 0.05. Pr^2 = 20 => P(0.05)^2 = 20 => P(0.0025) = 20 => P = 8000.

AI explanation

The difference between compound interest and simple interest for the second year is the interest on the first year's interest, which is 20 rupees. The difference for the third year is 61 minus 20, which is 41 rupees, representing the interest on the accumulated difference up to the second year. The difference ratio of 20 to 41 indicates an interest rate slightly over 100 percent, which contradicts standard problem parameters; using the exact formula for the first three years where the difference is P times R squared times (3 plus R) divided by 1000000 equals 61, and substituting the approximate rate derived from 20 equals P times R squared divided by 10000, reveals no consistent standard rate. The exact solution for the sum is Rs. 8,000 assuming a rate of 5 percent, since 8000 times 0.05 squared times 3.05 equals 61.

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