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 ?

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Solution

The correct option is C 12
Let the rate per cent p.a.be r. Then,
$S . I . = R s . (5000 \times \frac{r}{100} \times 2) = R s .100 r$
$C . I . = R s . ⎡ ⎣ 5000 {(1 + \frac{r}{100})}^{2} - 5000 ⎤ ⎦$
$= R s .5000 [{(1 + \frac{r}{100})}^{2} - 1]$
$= R s .5000 [(1 + \frac{r^{2}}{10000} + \frac{2 r}{100}) - 1]$
$= R s .5000 (\frac{r^{2}}{10000} + \frac{r}{50}) = R s . \frac{5000 (r^{2} + 200 r)}{10000}$
$= R s . (\frac{r^{2}}{2} + 100 r)$
$∴ C . I . - S . I . = 72$
$\Rightarrow \frac{r^{2}}{2} + 100 r - 100 r = 72$
$\Rightarrow \frac{r^{2}}{2} = 72$
$\Rightarrow r^{2} = 144$
$\Rightarrow r = 12 % p . a .$

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