Question
In what time will Rs 64000 amounts to Rs 68921 at 5% per annum interest being compounded half yearly ?
Answer: Option A
$$\eqalign{
& {\text{According to the question,}} \cr
& {\text{Amount}} = {\text{ }}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow 68921 = 64000{\left( {1 + \frac{5}{{2 \times 100}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow \frac{{68921}}{{64000}} = {\left( {1 + \frac{1}{{40}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow {\left( {\frac{{41}}{{40}}} \right)^3} = {\left( {\frac{{41}}{{40}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow 2{\text{t = 3}} \cr
& \Rightarrow {\text{t = }}\frac{3}{2} \cr
& \Rightarrow {\text{t = 1}}\frac{1}{2}{\text{ years}} \cr} $$
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$$\eqalign{
& {\text{According to the question,}} \cr
& {\text{Amount}} = {\text{ }}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow 68921 = 64000{\left( {1 + \frac{5}{{2 \times 100}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow \frac{{68921}}{{64000}} = {\left( {1 + \frac{1}{{40}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow {\left( {\frac{{41}}{{40}}} \right)^3} = {\left( {\frac{{41}}{{40}}} \right)^{2 \times {\text{t}}}} \cr
& \Rightarrow 2{\text{t = 3}} \cr
& \Rightarrow {\text{t = }}\frac{3}{2} \cr
& \Rightarrow {\text{t = 1}}\frac{1}{2}{\text{ years}} \cr} $$
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