In what time will 10000 amount to 14641 at 10% per annum compound interest compounded annually?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let the rate be R% p}}{\text{.a}}{\text{. }} \cr & {\text{Then,}} \cr & {\text{10000}}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^4} = 14641 \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{200}}} \right)^4} = \frac{{14641}}{{10000}} = {\left( {\frac{{11}}{{10}}} \right)^4} \cr & \Rightarrow 1 + \frac{{\text{R}}}{{200}} = \frac{{11}}{{10}} \cr & \Rightarrow \frac{{\text{R}}}{{200}} = \frac{1}{{10}} \cr & \Rightarrow {\text{R}} = {\text{20% }} \cr} $$