Question

The Simple interest on a sum of money is $\frac{4}{9}$ of the principle, and the number of years is equal to the rate $\%$. p.a. Find the rate $\%$.

Answer 1

Let the principal be $P$.

Rate of interest be $R\%$

According to the question, Time$=R$

Simple interest $=\frac{4P}{9}$.

$SI=\frac{\left(PTR\right)}{100}$

$\Rightarrow \frac{4P}{9}=\frac{\left(PTR\right)}{100}$

$\Rightarrow \frac{4P}{9}=\frac{(P\times R\times R)}{100}$

$\Rightarrow \frac{4P}{9}=\frac{(P\times R^2)}{100}$

$\Rightarrow \frac{4}{9}=\frac{R^2}{100}$

$\Rightarrow R^2=100\times \frac{4}{9}$

$\Rightarrow R=10\times \frac{2}{3}=\frac{20}{3}$

Therefore, rate of interest is $\frac{20}{3}\%$ or $6\frac{1}{3}\%$.