Question

A sum of money at compound interest amounts to three times of itself in three years. In how many years will it be nine times of itself ? 

(a) 6 years 

(b) 5 years 

(c) 9 years 

(d) 7 years

Answer 1

(a) 6 years

Given, 3P = P\(\big(1+\frac{r}{100}\big)^3\)

\(\Rightarrow\) \(\big(1+\frac{r}{100}\big)^3\) = 3

Let t be the time in years in which the sum will be nine times of itself. Then,

9P = P\(\big(1+\frac{r}{100}\big)^t\) \(\Rightarrow\) \(\big(1+\frac{r}{100}\big)^t\) = 9 = 3²

\(\Rightarrow\) \(\big(1+\frac{r}{100}\big)^t\) = \(\Big[\big(1+\frac{r}{100}\big)^3\Big]^2\) (From (i))

\(\Rightarrow\) \(\big(1+\frac{r}{100}\big)^t\) = \(\big(1+\frac{r}{100}\big)^6\)

\(\Rightarrow\) t = 6 years.