Question

The simple interest on a sum of money is $\frac{4}{9}$ of the principal and the no of years is equal to the rate of interest p.a. Find the rate of interest p.a.

Answer 1

Consider the problem

Let $P$ be the principle and $r$ be the rate of interest p.a

Then,

$\begin{array}{c}S.I=\frac{4}{9}P\\ t=r\end{array}$

Therefore,

$S.I=\frac{p\times r\times t}{100}$

$\Rightarrow \frac{4}{9}p=\frac{p\times r\times r}{100}$

$\Rightarrow r^2=\frac{400}{9}$

$\Rightarrow r=\frac{20}{3}$

$\Rightarrow r=6.67\%$