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

$\text{Principal (p) = Rs. 5000}\text{Rate (R) =}9\%p.a.\text{Time (n) = 2 years}\therefore S.I=\frac{PRT}{100}=\frac{5000\times 9\times 2}{100}=Rs.900\text{Now amount at C.I = P}{(1+\frac{R}{100})}^n=Rs.5000{(1+\frac{9}{100})}^2=Rs.5000\times \frac{109}{100}\times \frac{109}{100}=Rs.\frac{11881}{2}=Rs.5940.50\therefore C.I=A-P=Rs.5940.50-Rs.5000=Rs.5940.50-5000=Rs.940.50\therefore \text{Difference between C.I. and S.I}=Rs.940.50-Rs.900=Rs.40.50$