Multiple choice

A sum of money at compound interest (period = 1year) is doubled in 20 years. Then the number of years required to treble the sum will be

  1. 31.6 years

  2. 35 years

  3. 40 years

  4. 45 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For compound interest, A = P(1+r)^t. 2P = P(1+r)^20, so (1+r)^20 = 2. We want 3P = P(1+r)^t, so (1+r)^t = 3. Taking logs: t * log(1+r) = log(3) and 20 * log(1+r) = log(2). t = 20 * log(3)/log(2) = 20 * 0.4771/0.3010 = 31.69 years.

AI explanation

Using the compound interest doubling formula, if a sum doubles in 20 years, the rate is found by 2 equals (1 plus R) to the power of 20. To treble the sum, we need 3 equals (1 plus R) to the power of n. Dividing the logarithm of 3 by the logarithm of 1.03526 gives approximately 31.6 years.

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