Rs.2000 amounts to Rs. 2226.05 in 2 years at compound interest. What will be the rate of interest ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let the rate be R}}\% {\text{ p}}{\text{.a}}{\text{.}} \cr & {\text{Then,}} \cr & {\text{2000}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = 2226.05 \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = \frac{{222605}}{{200000}} \cr & \, \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = \frac{{44521}}{{40000}} \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = {\left( {\frac{{221}}{{200}}} \right)^2} \cr & \Rightarrow 1 + \frac{{\text{R}}}{{100}} = \frac{{211}}{{200}} \cr & \Rightarrow \frac{{\text{R}}}{{100}} = \frac{{11}}{{200}} \cr & \Rightarrow {\text{R}} = \frac{{11}}{2}\% \cr & \Rightarrow {\text{R}} = 5.5\% \cr} $$