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A sum becomes eight times in 3 years compounded annually. In how much time will it become sixteen times at the same rate?

1. 6 years
2. 4 years
3. 8 years
4. 5 years

Correct answer: 4 years

Solution

If a sum becomes 8 times in 3 years, then the annual growth factor satisfies \((1+r)^3 = 8\), so \(1+r = 2\). To become 16 times, we need \(2^4 = 16\), which takes 4 years.

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