Question

If the difference between compound interest compounded half-yearly and simple interest of a certain sum of money at the rate of $12\%$ per annum for $1$ year is $Rs.72$. Find sum,

• A. $Rs.10,000$
• B. $Rs.15,000$
• C. $Rs.20,000$
• D. $Rs.25,000$
• E. None of these

Answer 1

Answer: (C)

$Rs.20,000$

Let the initial sum of money be $P.$

Then,

$\begin{array}{cc}CI& =P{\left(1+\frac{r}{2\times 100}\right)}^{2\times t}-P\\ & =P{\left(1+\frac{12}{2\times 100}\right)}^{2\times 1}-P\\ & =P{\left(1.06\right)}^2-P\\ & =1.1236P-P\\ & =0.1236P\end{array}$

And,

$\begin{array}{cc}SI& =\frac{P\times R\times T}{100}\\ & =\frac{P\times 12\times 1}{100}\\ & =0.12P\end{array}$

It is given that different of $CI$ and $SI$ is equal to $Rs.72.$ So,

$\begin{array}{cc}CI-SI& =72\\ 0.1236P-0.12P& =72\\ 0.0036P& =72\\ 36P& =720000\\ P& =Rs.20,000\end{array}$

Hence, option $C$ is correct.