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

The correct option is B: $Rs.40.5$

Given: Principal, $P=Rs.5000$

Time, $n=2$ years

Rate, $R=9\%$

$S.I=\frac{P\times R\times T}{100}$

$S.I=\frac{5000\times 9\times 2}{100}$

$S.I=Rs.900$

We know that

Amount, $A=P{\left(1+\frac{R}{100}\right)}^n=5000{\left(1+\frac{9}{100}\right)}^2=5000(1.09{)}^2=Rs.5940.5$

$C.I=A-P=5940.5-5000=Rs940.5$

Difference between $C.I$ and $S.I$ $=C.I-S.I=Rs940.5-Rs900=Rs40.5$