Question

The difference between compound interest and simple interest at the same rate on Rs.5000 for 2 years is Rs.72 What is the rate of interest per annum ?

• A. 20
• B. 15
• C. 12
• D. 10

Answer 1

The correct option is C 12

Let the rate per cent p.a.be r. Then,

$S.I.=Rs.(5000\times \frac{r}{100}\times 2)=Rs.100r$

$C.I.=Rs.[5000{(1+\frac{r}{100})}^2-5000]$

$=Rs.5000[{(1+\frac{r}{100})}^2-1]$

$=Rs.5000[(1+\frac{r^2}{10000}+\frac{2r}{100})-1]$

$=Rs.5000(\frac{r^2}{10000}+\frac{r}{50})=Rs.\frac{5000(r^2+200r)}{10000}$

$=Rs.(\frac{r^2}{2}+100r)$

$\therefore C.I.-S.I.=72$

$\Rightarrow \frac{r^2}{2}+100r-100r=72$

$\Rightarrow \frac{r^2}{2}=72$

$\Rightarrow r^2=144$

$\Rightarrow r=12\%p.a.$