Multiple choice

If the compound interest earned on a certain sum for 2 years is twice the amount of simple interest for 2 years, then the rate of interest per annum is _____ percent.

  1. 200%

  2. 2%

  3. 4%

  4. 400%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

CI = P(1 + r/100)^2 - P. SI = P * r * 2 / 100. Given CI = 2 * SI. P((1 + r/100)^2 - 1) = 2 * (2Pr/100). (1 + 2r/100 + r^2/10000 - 1) = 4r/100. r^2/10000 = 2r/100. r = 200.

AI explanation

The simple interest for 2 years is 2PR/100, and the compound interest for 2 years is P(1 + R/100)^2 - P, which simplifies to 2PR/100 + PR^2/10000. Setting the compound interest equal to twice the simple interest gives 2PR/100 + PR^2/10000 = 4PR/100, which reduces to R^2/10000 = 2R/100. Solving this equation results in a rate of 200 percent.

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