Question

The difference between $C.I$ and $S.I$ for $2$ years at $10\%$ per annum is $\text{Rs.}50$. Find the sum.

Answer 1

Let the value of the sum be $P$.

First let us calculate simple interest obtained in the period of $2$ years at rate of $10\%$ per year,

$\begin{array}{cc}S.I& =\frac{P\cdot R\cdot T}{100}\\ & =\frac{P\cdot 10\cdot 2}{100}\\ & =\frac{P}{5}\\ & =0.2P\end{array}$

Now we will calculate the compound interest gained in the period of $2$ years compounded annually at the rate of $10\%$,

$C.I=A-P$

$=P(1+r{)}^t-P$

$=P\left(\right(1+0.1{)}^2-1)$

$=P\left(\right(1.1{)}^2-1^2)$

$=P(1.1+1)(1.1-1)$

$=P\left(2.1\right)\left(0.1\right)$

$=0.21P$

Now it is given that the difference between $C.I$ and $S.I$ is equal to $\text{Rs.}50$. So,

$\begin{array}{cc}C.I-S.I& =50\\ 0.21P-0.2P& =50\\ 0.01P& =50\\ P& =\text{Rs.}5000\end{array}$

So, the sum is equal to $\text{Rs.}5000$.