Question

A sum of money lent out at C.I. at a certain rate per annum doubles itself in 5 years. Find in how many years will the money become eight times of itself at the same rate of interest p.a.

Answer 1

Let Principal = Rs. x = Amount in 5 years = Rs .2x
$A=P{(1+\frac{r}{100})}^n\Rightarrow 2x=x{(1+\frac{r}{100})}^5$
$\Rightarrow 2={(1+\frac{r}{100})}^5$
For the second part : P= Rs x and A = Rs. 8x
$\therefore A=P{(1+\frac{r}{100})}^n\Rightarrow 8x=x{(1+\frac{r}{100})}^n$
$\Rightarrow 8={(1+\frac{r}{100})}^n$
i.e. ${\left(2\right)}^3={(1+\frac{r}{100})}^n\Rightarrow {\left[{(1+\frac{r}{100})}^5\right]}^3={(1+\frac{r}{100})}^n[\because 2={(1+\frac{r}{100})}^5]$
$\Rightarrow {(1+\frac{r}{100})}^{15}={(1+\frac{r}{100})}^n$
$\Rightarrow n=15$
i.e. Time Required = 15 years