Question

A sum of money becomes $\frac{8}{5}$ of itself in $5$ years at a certain rate of simple interest . Find the rate of interest.

Answer 1

Given: Time, $T=5$ years

Let the principal be $P$

Rate of interest $=R$

Amount, $A=\frac{8P}{5}$

Simple Interest, $S.I=$ Amount $-$ Principal
$=\frac{8P}{5}-P$

$=\frac{3P}{5}$

$\therefore S.I=\frac{3P}{5}$
Again, $S.I=\frac{P\times R\times T}{100}$

$\Rightarrow \frac{3P}{5}=\frac{P\times R\times 5}{100}$

$\Rightarrow \frac{3}{5}=\frac{5R}{100}$

$\Rightarrow \frac{3}{5}=\frac{R}{20}$

$\Rightarrow R=3\times \frac{20}{5}$

$\Rightarrow R=3\times 4$

$\therefore R=12.$

The required rate of interest is $12\%.$