A sum of money invested at compound interest amounts in 2 years to Rs. 4624 and 3 years to Rs. 4913.The sum of money is = ?

Explanation:-

S.I. on Rs. 4624 for 1 year $$\eqalign{ & {\text{ = Rs }}\left( {4913 - 4624} \right) \cr & {\text{ = Rs 289}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 289}}{{4624 \times 1}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\frac{1}{4}\% \cr & {\text{Now,}} \cr & x{\left( {1 + \frac{{25}}{{100}}} \right)^2} = 4624 \cr & \Rightarrow x \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} = 4624 \cr & \Rightarrow x = \left( {4624 \times \frac{{16}}{{17}} \times \frac{{16}}{{17}}} \right) \cr & \Rightarrow x = 4096 \cr}$$