Question
The difference between $C.I.$ payable annually and $S.I.$ on $Rs.50,000$ for two years is $Rs.125$ at the same rate of interest per annum. Find the rate of interest.
✓
Answer
Let the rate of interest per year be $r \%$.
$ \text { S.I.}$ in $2$ years $=\text { Rs. } \frac{50000 \times r \times 2}{100}$
$=\text { Rs. } 1000\ r$
And,$\text { C.I.}$ in $ 2$ years
$=\text { A }-P$
$=\text { Rs. } 50000\left(1+\frac{r}{100}\right)^2-\text { Rs. } 50000$
Given$,\text { C.I. }- \text { S.I. }=\text { Rs. } 125$
$\Rightarrow 50000\left(1+\frac{r}{100}\right)^2-50000-1000 r=125$
$\Rightarrow 50000\left(1+\frac{r^2}{10000}+\frac{2 r}{100}\right)-50000-1000 r=125$
$\Rightarrow 50000+5 r^2+1000 r-50000-1000 r=125$
$\Rightarrow 5 r^2=25$
$\Rightarrow r 2=25$
$\Rightarrow r= \pm 5 $
But the rater of interest cannot ne negative.
$\therefore$ Rate of interest is $5 \%$.
$ \text { S.I.}$ in $2$ years $=\text { Rs. } \frac{50000 \times r \times 2}{100}$
$=\text { Rs. } 1000\ r$
And,$\text { C.I.}$ in $ 2$ years
$=\text { A }-P$
$=\text { Rs. } 50000\left(1+\frac{r}{100}\right)^2-\text { Rs. } 50000$
Given$,\text { C.I. }- \text { S.I. }=\text { Rs. } 125$
$\Rightarrow 50000\left(1+\frac{r}{100}\right)^2-50000-1000 r=125$
$\Rightarrow 50000\left(1+\frac{r^2}{10000}+\frac{2 r}{100}\right)-50000-1000 r=125$
$\Rightarrow 50000+5 r^2+1000 r-50000-1000 r=125$
$\Rightarrow 5 r^2=25$
$\Rightarrow r 2=25$
$\Rightarrow r= \pm 5 $
But the rater of interest cannot ne negative.
$\therefore$ Rate of interest is $5 \%$.
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