Multiple choice

A sum of money at compound interest is doubled in $20$ years. Then the number of years required to tripple itself are

  1. $32$ years
  2. $35$ years
  3. $40 $years
  4. $45$ years
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A Correct answer
Explanation

If the amount doubles in 20 years, the growth factor after t years is 2^(t/20). For tripling, 2^(t/20) = 3, so t = 20 log2(3) ≈ 31.7 years. Rounded to the nearest whole year, this is 32 years.

AI explanation

Using the compound interest formula, if a sum doubles in 20 years, we have 2P = P(1 + r)^20, which gives (1 + r)^20 = 2. To find the time to triple, we set 3P = P(1 + r)^n, meaning (1 + r)^n = 3. Dividing the second equation by the first gives (1 + r)^(n - 20) = 1.5, and testing n = 32 yields a highly accurate approximation for standard rates, though mathematically the exact time t is 20 multiplied by the logarithm of 3 over the logarithm of 2, which is 31.7 years. The result is 32 years.

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