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

Solution(By Examveda Team)

S.I. on Rs. 4624 for 1 year
$$\eqalign{ & {\text{ = Rs. }}\left( {4913 - 4624} \right) \cr & {\text{ = Rs. 289}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 289}}{{4624 \times 1}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\frac{1}{4}\% \cr & {\text{Now,}} \cr & x{\left( {1 + \frac{{25}}{{400}}} \right)^2} = 4624 \cr & \Rightarrow x \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} = 4624 \cr & \Rightarrow x = \left( {4624 \times \frac{{16}}{{17}} \times \frac{{16}}{{17}}} \right) \cr & \Rightarrow x = 4096 \cr} $$