Question
An amount of Rs. 10000 becomes Rs. 14641 in 2 years if the interest is compounded half yearly. What is the rate of compound interest p.c.p.a. ?
Answer: Option D
$$\eqalign{
& {\text{Let the rate be R% p}}{\text{.a}}{\text{. }} \cr
& {\text{Then,}} \cr
& {\text{10000}}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^4} = 14641 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{200}}} \right)^4} = \frac{{14641}}{{10000}} = {\left( {\frac{{11}}{{10}}} \right)^4} \cr
& \Rightarrow 1 + \frac{{\text{R}}}{{200}} = \frac{{11}}{{10}} \cr
& \Rightarrow \frac{{\text{R}}}{{200}} = \frac{1}{{10}} \cr
& \Rightarrow {\text{R}} = {\text{20% }} \cr} $$
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$$\eqalign{
& {\text{Let the rate be R% p}}{\text{.a}}{\text{. }} \cr
& {\text{Then,}} \cr
& {\text{10000}}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^4} = 14641 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{200}}} \right)^4} = \frac{{14641}}{{10000}} = {\left( {\frac{{11}}{{10}}} \right)^4} \cr
& \Rightarrow 1 + \frac{{\text{R}}}{{200}} = \frac{{11}}{{10}} \cr
& \Rightarrow \frac{{\text{R}}}{{200}} = \frac{1}{{10}} \cr
& \Rightarrow {\text{R}} = {\text{20% }} \cr} $$
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