Question
At what rate percent per annum of compound interest, will a sum of money become four times of itself in two years ?
Answer: Option A
$$\eqalign{
& {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr
& \,\,\,\,\,\,\,\,\,{\text{1}}\,\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\,\,\,{\text{4}} \cr
& \Rightarrow 4 = 1{\left( {1 + \frac{r}{{100}}} \right)^2} \cr
& \Rightarrow 4 = {\left( {1 + \frac{r}{{100}}} \right)^2} \cr
& \Rightarrow r = 100\% \cr
& \cr
& {\text{Alternate}} \cr
& {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr
& \,\,\,\,\,\,\,\,\,\root 2 \of 1 \,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\root 2 \of 4 \cr
& \,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,2 \cr
& \Rightarrow {\text{Rate of interest}} \cr
& {\text{ = }}\frac{{\left( {2 - 1} \right)}}{1} \times 100 = 100\% \cr} $$
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$$\eqalign{
& {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr
& \,\,\,\,\,\,\,\,\,{\text{1}}\,\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\,\,\,{\text{4}} \cr
& \Rightarrow 4 = 1{\left( {1 + \frac{r}{{100}}} \right)^2} \cr
& \Rightarrow 4 = {\left( {1 + \frac{r}{{100}}} \right)^2} \cr
& \Rightarrow r = 100\% \cr
& \cr
& {\text{Alternate}} \cr
& {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr
& \,\,\,\,\,\,\,\,\,\root 2 \of 1 \,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\root 2 \of 4 \cr
& \,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,2 \cr
& \Rightarrow {\text{Rate of interest}} \cr
& {\text{ = }}\frac{{\left( {2 - 1} \right)}}{1} \times 100 = 100\% \cr} $$
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