Question

A certain sum of money at compound interest becomes $Rs7,396$ in two years and $7,950.70$ in three years. Find the rate of interest.

Answer 1

Let r% be the rate of interest compounded annually.

$A=P{(1+\frac{r}{100})}^t$

where A is the amount, P is the principal amount, t is time (in years).

Therefore, after $t=2$ years,

$7396=P{(1+\frac{r}{100})}^2........\left(i\right)$

After $t=3$ years,

$7950.70=P{(1+\frac{r}{100})}^3........\left(ii\right)$

Dividing equation (ii) by (i), we get,

$\frac{7950.70}{7396}=\frac{P{(1+\frac{r}{100})}^3}{P{(1+\frac{r}{100})}^2}=(1+\frac{r}{100})=>\frac{7950.70}{7396}=(1+\frac{r}{100})$

$=>r=7.5$%

Therefore, rate of interest is $7.5$% compounded annually.