Question
A man borrow Rs. 4000 at 15%, compound rate of interest. At the end of each year he pays back Rs. 1500. How much amount should be pay at the end of the third year to clear all his dues ?
Answer: Option A
$$\eqalign{
& {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {4000\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {4000 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {4600 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}3100 \cr
& {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {3100\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {3100 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {3565 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}2065 \cr
& {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {2065\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {2065 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {2374.75 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}874.75 \cr} $$
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$$\eqalign{
& {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {4000\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {4000 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {4600 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}3100 \cr
& {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {3100\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {3100 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {3565 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}2065 \cr
& {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {2065\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {2065 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {2374.75 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}874.75 \cr} $$
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