Answer: Option C
$$\eqalign{
& {\text{Let}}, \cr
& {\text{Principal}} = Rs.\,100\% \cr
& {\text{Amount}} = Rs.\,200 \cr
& {\text{Rate}} = r\% \cr
& {\text{Time}} = 4\,{\text{years}} \cr
& {\text{Now}}, \cr
& A = P \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^n} \cr
& 200 = 100 \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} \cr
& 2 = {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} - - - - - - \left( i \right) \cr
& {\text{If}}\,{\text{sum}}\,{\text{become}}\,{\text{8}}\,{\text{times}}\,{\text{in}}\,{\text{the}}\,{\text{time}}\,n\,{\text{years}} \cr
& {\text{then,}} \cr
& 4 = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr
& {2^2} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} - - - - - - \left( {ii} \right) \cr
& {\text{Using}}\,{\text{eqn}}\,\left( i \right)in\left( {ii} \right),\,{\text{we}}\,{\text{get}} \cr
& {\left( {{{\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]}^4}} \right)^2} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr
& {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^{8}} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr
& {\text{Thus}},\,n = 8\,{\text{years}}. \cr} $$