Question
When principal = Rs. S, rate of interest = 2r % p.a., then a person will get after 3 years at compound interest = ?
Answer: Option B
$$\eqalign{
& {\text{According to the question}} \cr
& {\text{Principal = Rs S}} \cr
& {\text{Rate }}\% {\text{ = 2r}}\,\% {\text{ p}}{\text{.a}}{\text{.}} \cr
& {\text{Time = 3 years}} \cr
& \therefore {\text{A = P}}{\left( {1 + \frac{{\text{r}}}{{100}}} \right)^T} \cr
& \Leftrightarrow {\text{A = S}}{\left( {1 + \frac{{{\text{2r}}}}{{100}}} \right)^3} \cr
& \Leftrightarrow {\text{A = S}}{\left( {1 + \frac{{\text{r}}}{{50}}} \right)^3} \cr} $$
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$$\eqalign{
& {\text{According to the question}} \cr
& {\text{Principal = Rs S}} \cr
& {\text{Rate }}\% {\text{ = 2r}}\,\% {\text{ p}}{\text{.a}}{\text{.}} \cr
& {\text{Time = 3 years}} \cr
& \therefore {\text{A = P}}{\left( {1 + \frac{{\text{r}}}{{100}}} \right)^T} \cr
& \Leftrightarrow {\text{A = S}}{\left( {1 + \frac{{{\text{2r}}}}{{100}}} \right)^3} \cr
& \Leftrightarrow {\text{A = S}}{\left( {1 + \frac{{\text{r}}}{{50}}} \right)^3} \cr} $$
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