If a sum of money placed at compound interest becomes 3 times of itself in 3 years. In how many years will it be 9 times at the same rate of interest?

Q: If a sum of money placed at compound interest becomes 3 times of itself in 3 years. In how many years will it be 9 times at the same rate of interest?

Let the principle be P then amount be 3P ∵ 3P =P(1 + r/100)3 ⇒ 3 = (1 + r/100)3 On squaring on both the sides, ⇒ (3)2 = {(1 + r/100)3}2 ∴ 9 = (1 + r/100)6 Hence,it will become 9 times in 6 years.

6 years
9 years
12 years
5 years

Correct Answer: 6 years

Explanation:

Let the principle be P then amount be 3P
∵ 3P =P(1 + r/100)³
⇒ 3 = (1 + r/100)³
On squaring on both the sides,
⇒ (3)² = {(1 + r/100)³}²
∴ 9 = (1 + r/100)⁶
Hence,it will become 9 times in 6 years.

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