Question
A man invests Rs 4000 for 3 years at compound interest. After one year the money amounts to Rs. 4320. What will be the amount (to the nearest rupee) due at the end of 3 years ?
Answer: Option B
$$\eqalign{
& {\text{Le the rate be R }}\% {\text{ p}}{\text{.a}}{\text{.}} \cr
& {\text{Then,}} \cr
& {\text{4000}}\left( {1 + \frac{{{\text{R }}}}{{100}}} \right) = 4320 \cr
& \Rightarrow 1 + \frac{{{\text{R }}}}{{100}} = \frac{{4320}}{{4000}} = \frac{{108}}{{100}} \cr
& \Rightarrow \frac{{{\text{R }}}}{{100}} = \frac{8}{{100}} \cr
& \Rightarrow {\text{R }} = 8 \cr
& \therefore {\text{Amount after 3 yeras}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {4000 + {{\left( {1 + \frac{8}{{100}}} \right)}^3}} \right] \cr
& {\text{ = Rs}}{\text{. }}\left( {4000 \times \frac{{27}}{{25}} \times \frac{{27}}{{25}} \times \frac{{27}}{{25}}} \right) \cr
& {\text{ = Rs}}{\text{. }}\left( {\frac{{629856}}{{125}}} \right) \cr
& {\text{ = Rs}}{\text{. }}5038.848 \approx 5039 \cr} $$
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$$\eqalign{
& {\text{Le the rate be R }}\% {\text{ p}}{\text{.a}}{\text{.}} \cr
& {\text{Then,}} \cr
& {\text{4000}}\left( {1 + \frac{{{\text{R }}}}{{100}}} \right) = 4320 \cr
& \Rightarrow 1 + \frac{{{\text{R }}}}{{100}} = \frac{{4320}}{{4000}} = \frac{{108}}{{100}} \cr
& \Rightarrow \frac{{{\text{R }}}}{{100}} = \frac{8}{{100}} \cr
& \Rightarrow {\text{R }} = 8 \cr
& \therefore {\text{Amount after 3 yeras}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {4000 + {{\left( {1 + \frac{8}{{100}}} \right)}^3}} \right] \cr
& {\text{ = Rs}}{\text{. }}\left( {4000 \times \frac{{27}}{{25}} \times \frac{{27}}{{25}} \times \frac{{27}}{{25}}} \right) \cr
& {\text{ = Rs}}{\text{. }}\left( {\frac{{629856}}{{125}}} \right) \cr
& {\text{ = Rs}}{\text{. }}5038.848 \approx 5039 \cr} $$
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