Question 120

If a certain sum becomes 2 times in 7 years at compound interest, then in how many years, it will become 8 times?

Solution

The sum becomes 2 times in 7 years at compound interest,

$$2P = P(1 + \frac{r}{100})^{7}$$

$$1 + \frac{r}{100} = 2^{1/7}$$ ----------(1)

Let the sum becomes 8 times in T years,

$$8P = P(1 + \frac{r}{100})^{T}$$

$$1 + \frac{r}{100} = 2^{3/T}$$ -------------(2)

Substitute equation (1) in (2)

$$2^{1/7}$$ = $$2^{3/T}$$

$$\frac{1}{7} = \frac{3}{T}$$

$$T = 21$$

Hence, option B is the correct answer.

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