Multiple choice

Directions : Select the correct alternative from the given choices. If the difference between the total compound interest and the total simple interest accrued on a certain sum at a certain rate of interest at the end of two years is 6.25% of the principal, find the number of years in which the sum will quadruple under simple interest.

  1. 12

  2. 16

  3. 20

  4. 24
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A Correct answer
Explanation

CI - SI = P(r/100)^2 = 0.0625P => (r/100)^2 = 0.0625 => r/100 = 0.25 => r = 25%. Simple interest formula for quadrupling: Amount = 4P, Interest = 3P. 3P = P * 0.25 * t => t = 3 / 0.25 = 12 years.

AI explanation

Using the difference formula for two years, r squared divided by 100 equals 6.25, giving an interest rate of 25%. Under simple interest, quadrupling the sum means the total interest equals 300% of the principal, which requires 300 divided by 25 years. The sum will quadruple in 12 years.

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