Question

Find the difference between the simple interest and the compound interest on $Rs.5000$ for $2$ years at $9\%$ per annum.

Answer 1

Principal $\left(P\right)=Rs.5000$

Rate $\left(R\right)=9\%$ p.a.

Time $\left(n\right)=2$ years

$\therefore S.I=\frac{P\times R\times T}{100}=\frac{5000\times 9\times 2}{100}=Rs.900$

Now, Amount at $C.I=P{(1+\frac{R}{100})}^n$

$=Rs.5000{(1+\frac{9}{100})}^2$

$=Rs.5000\times \frac{109}{100}\times \frac{109}{100}$

$=Rs.\frac{11881}{2}=Rs.5940.50$

$\therefore C.I=A-P=Rs.5940.50-Rs.5000$

$=Rs.5940.50-5000=Rs.940.50$

$\therefore$ Difference between $C.I.$ and $S.I$

$=Rs.940.50-Rs.900=Rs.40.50$