Question

The difference between the compound interest and simple interest on a certain sum of money at $10\%$ per annum for $2$ years is $Rs.500$. Find the sum when the interest is compounded annually.

Answer 1

Let the sum be $Rs.100$

Computation of compound interest:

Prinicpal $=Rs.100$

$R=10\%$ per annum and $n=2$ years.

$Amount=Rs.[100\times {(1+\frac{10}{100})}^2]$

$=Rs.[100\times {\left(\frac{11}{2}\right)}^2]=Rs.121$

Computation of simple interest:

Prinicpal $=Rs.100$

$R=10\%$ and Time $=2$ years.

$\therefore S.I.=Rs.\left(\frac{100\times 10\times 2}{100}\right)=Rs.20$

Thus, difference in C.I. and S.I.$=Rs.(21-20)=Re.1$

Now, if difference between C.I and S.I. is $Re.1$, Then Sum $=Rs.100$

If difference between C.I. and S.I. is $Rs.500$, Then Sum $=Rs.(100\times 500)=Rs.50000$