Rs. 1000 is invested at 5% per annum simple interest. If the interest is added to the principal after every years, the amount will become Rs. 2000 after = ?

Explanation:-

$$\eqalign{ & {\text{Principal = Rs}}{\text{. 1000 }} \cr & {\text{Rate = 5}}\% \cr & {\text{Interest for first 10 years}} \cr & = \frac{{1000 \times 5 \times 10}}{{100}} \cr & = {\text{Rs}}{\text{. 500}} \cr & {\text{After 10 years principal}} \cr & = {\text{(1000}} + {\text{500)}} \cr & {\text{ = Rs}}{\text{. 1500}} \cr & {\text{Remaining interest}} \cr & {\text{ = Rs}}{\text{. (2000}} - {\text{1500)}} \cr & {\text{ = Rs}}{\text{. 500}} \cr & {\text{Required time }} \cr & {\text{ = }}\frac{{500}}{{1500}} \times \frac{{100}}{5} \cr & \Rightarrow \frac{{100}}{5} = \frac{{20}}{3} \cr & \Rightarrow 6\frac{2}{3}{\text{years}} \cr & {\text{Total time}} \cr & = \left( {10 + 6\frac{2}{3}} \right){\text{years}} \cr & {\text{ = 16}}\frac{2}{3}{\text{years}} \cr}$$