The Simple Interest on a sum of money for 2 years is Rs.50 and the Compound Interest on the same sum at the same rate for the same time is Rs.51.25. Find the rate of interest per annum.

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

50 = $$\frac{P \times R \times 2}{100}$$

PR =2500  

compound interest = $$P(1+\frac{R}{100})^n$$

51.25=$$P(1+\frac{R}{100})^2$$

        =$$P(1+\frac{R}{100})(1+\frac{R}{100})$$

          =$$(P+ \frac{PR}{100})(1+ \frac{R}{100})$$

         =$$(P+ \frac{2500}{100})(1+ \frac{R}{100})$$   

         = $$(P+ 25)(1+ \frac{R}{100})$$   

    51.25\times 100=    $$(P+ 25)(100+ R)$$

      5125 =  $$(P+ 25)(100+ R)$$

        5125  = $$P100 +PR+2500 +25R$$

          5125    = $$P100 +2500+2500 +25R$$

125 = $$P100 +25R$$

   125     = 25(4P +R)

5 = $$(4\frac{R}{2500}+ R)$$

R = 4.99 = 5%