Multiple choice

A sum of money is invested under simple interest at a certain annual rate of interest for 3 years. If the same sum of money is invested under compound interest, at the same rate of interest, compounded annually, it'll fetch ₹360 more than the total simple interest after 2 years, and ₹1140 more than the total simple interest after 3 years. Which of the following gives the value of the sum (in ₹)?

  1. 13200

  2. 21600

  3. 12960

  4. 19440
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C Correct answer
Explanation

Let the sum be P and rate be r. Simple Interest (SI) = P*r*t/100. Compound Interest (CI) = P((1+r/100)^t - 1). Given CI - SI = 360 for t=2 and 1140 for t=3. Using the formulas, P(r/100)^2 = 360 and P(r/100)^2 * (3 + r/100) = 1140. Solving these yields r=5% and P=12960.

AI explanation

The extra interest generated by compound interest over simple interest for 2 years is P * (R/100)^2, and for 3 years it is P * (R/100)^2 * (3 + R/100). The ratio of these differences is 1140 / 360 = 3 + R/100, which simplifies to 19/6 = 18/6 + R/100, giving a rate of 50/3 percent. Substituting this rate back into the 2-year difference formula, 360 = P * (50/300)^2, yields P = 360 * 36 = 12960.

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