Question

The difference between the compound interest and the simple interest on Rs. 9,500 for 2 years is Rs. 95 at the same rate of interest per year. Find the rate of interest.

Answer 1

Let the rate of interest be $r\%$
$\therefore$ S.I. In 2 years $=\frac{9500\times r\times 2}{100}=Rs.190r$
And, C.I. in 2 years = A - P
$=Rs.9500{(1+\frac{r}{100})}^2-9500$
Given : C.I. - S. I. = Rs.95
$\Rightarrow [9500{(1+\frac{r}{100})}^2-9500]-190r=95$
$\Rightarrow 9500(1+\frac{r^2}{10000}+\frac{2r}{100})-9500-190r=95$
$\Rightarrow 9500+\frac{{95r}^2}{100}+190r-9500-190r=95$
$\frac{{95r}^2}{100}=95\Rightarrow r^2=95\times \frac{100}{95}=100andr=10$
$\therefore$ Rate of interest $=10\%$