Question

A sum becomes $Rs.$ $4800$ after two years and $Rs.$ $6400$ after four years at compound interest per annum compounded annually. Find the sum.

Answer 1

Let the sum be $x$ and the rate be $r$

Given, Amount in 2 years $=x{(1+\frac{r}{100})}^2=4800...\left(I\right)$

and the amount in 4 years $=x{(1+\frac{r}{100})}^4=6400...\left(II\right)$

Let us divide equation $\left(I\right)$ by equation $\left(II\right)$

$\Rightarrow \frac{x{(1+\frac{r}{100})}^2}{x{(1+\frac{r}{100})}^4}=\frac{4800}{6400}$

$\Rightarrow {(1+\frac{r}{100})}^2=\frac{4}{3}$

$\Rightarrow 1+\frac{r}{100}=\frac{2}{\sqrt{3}}$

$\Rightarrow \frac{r}{100}=\frac{2}{\sqrt{3}}-1$

from $\left(I\right),$

$\Rightarrow x{(1+\frac{2}{\sqrt{3}}-1)}^2=4800$

$\Rightarrow x\times \frac{4}{3}=4800$

$\therefore x=Rs.3600$