Multiple choice

On a sum of Rs. 1000, the compound interest for 2 years is twice the simple interest for 2 years when the rate is 11%. Find the rate at which the interest is compounded annually.

  1. 10%

  2. 15%

  3. 20%

  4. 25%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest (SI) = 1000 * 0.11 * 2 = 220. Compound Interest (CI) = 2 * 220 = 440. CI = P((1 + r/100)^2 - 1) = 1000((1 + r/100)^2 - 1) = 440. (1 + r/100)^2 = 1.44. 1 + r/100 = 1.2, so r = 20%.

AI explanation

For a principal of Rs. 1000 over 2 years, the simple interest at 11% is (1000 * 11 * 2) / 100 = 220. The compound interest for the same period is twice this, meaning CI = 440, so the total amount is 1440. Using the formula A = P(1 + R/100)^n, we have 1000(1 + R/100)^2 = 1440, which gives (1 + R/100)^2 = 1.44; taking the square root gives 1 + R/100 = 1.2, so R equals 20.

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