Multiple choice

A sum of money doubles itself at certain rate of compound interest in 15 years. In how many years will it become eight times of itself with the same rate?

  1. 30

  2. 45

  3. 48

  4. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In compound interest, amount doubles in 15 years: 2P = P(1+r)¹⁵, so (1+r)¹⁵ = 2. For 8 times: 8P = P(1+r)ⁿ, so (1+r)ⁿ = 8 = 2³. Since (1+r)¹⁵ = 2, we need (1+r)ⁿ = [(1+r)¹⁵]³ = (1+r)⁴⁵, so n = 45 years.

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