Multiple choice

A sum becomes 5 times itself in 10 years at compound interest, compounded annually. In how many years will it become 125 times itself at the same rate?

  1. 25

  2. 30

  3. 20

  4. 15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In compound interest, if a sum becomes n times in T years, it becomes n^k times in k*T years. Here, 5^1 = 5 in 10 years. We want 125 = 5^3 times, so it takes 3 * 10 = 30 years.

AI explanation

Let the principal be P. Using the compound interest formula Amount = P(1 + R/100)^T, we have P(1 + R/100)^10 = 5P, which means (1 + R/100)^10 = 5. We need to find the time T when the amount is 125P, so P(1 + R/100)^T = 125P. Since 125 = 5^3, we can substitute 5 with (1 + R/100)^10 to get (1 + R/100)^T = ((1 + R/100)^10)^3 = (1 + R/100)^30. Therefore, T = 30.

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