Multiple choice

A sum of money at R% per annum compound interest becomes double in 5 years. Find in how many years it becomes 8 times.

  1. (a) 10 years

  2. (b) 12 years

  3. (c) 15 years

  4. (d) 18 years

  5. (e) 20 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Compound interest formula: A = P(1+r)^t. 2P = P(1+r)^5 => (1+r)^5 = 2. We want 8P = P(1+r)^t => 8 = (1+r)^t. Since 8 = 2^3, (1+r)^t = ((1+r)^5)^3 = (1+r)^15. So t = 15 years.

AI explanation

Since a sum doubles in 5 years at R% compound interest, its growth factor is 2. To find when it becomes 8 times, recognize that 8 is 2 cubed. Therefore, the required time is simply 3 times the time it took to double. Multiplying 5 years by 3 gives 15 years.

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