At what rate percent compound interest does a sum of money becomes 16 times in 4 years

Solution(By Examveda Team)

$$\eqalign{ & {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,\,\,{\text{1}}\,\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\,\,\,{\text{4}} \cr & \Rightarrow 4 = 1{\left( {1 + \frac{r}{{100}}} \right)^2} \cr & \Rightarrow 4 = {\left( {1 + \frac{r}{{100}}} \right)^2} \cr & \Rightarrow r = 100\% \cr & \cr & {\text{Alternate}} \cr & {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,\,\,\root 2 \of 1 \,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\root 2 \of 4 \cr & \,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,2 \cr & \Rightarrow {\text{Rate of interest}} \cr & {\text{ = }}\frac{{\left( {2 - 1} \right)}}{1} \times 100 = 100\% \cr} $$