Compound Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Given,}}\,{\text{Principal}},\,P = Rs.\,2800 \cr & {\text{Compound}}\,{\text{rate}},\,R = 10\% \,{\text{per}}\,{\text{annum}} \cr & = \frac{{10}}{2} = 5\% \,{\text{half - yearly}} \cr & {\text{Amount}} \cr & = {\text{Rs}}{\text{.}}\left[ {2800 \times \left( {1 + \frac{{10}}{{100}}} \right)\left( {1 + \frac{{5}}{{100}}} \right)} \right] \cr & = {\text{Rs.}}\left( {2800 \times \frac{{11}}{{10}} \times \frac{{21}}{{20}}} \right) \cr & = {\text{Rs. }}3234 \cr & \therefore {\text{C}}{\text{.I}}{\text{. = Rs.}}\left( {3234 - 2800} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}434 \cr} $$

$$\eqalign{ & {\text{Rate = 5% }} \cr & {\text{Time = 3 years}} \cr & {\text{Compound Interest Rs. 252}}{\text{.20}} \cr & {\text{Effective rate% of CI for 3 years}} \cr & {\text{ = 15}}{\text{.7625% }} \cr & {\text{Effective rate% of SI for 3 years}} \cr & {\text{ = 5}} \times {\text{3 = 15% }} \cr & {\text{Required SI }} \cr & {\text{ = }}\frac{{252.20}}{{15.7625}} \times 15 \cr & = 240 \cr} $$

$$\eqalign{ & {\text{CI for 2 years}}\,{\text{ = Rs. 282}}{\text{.15}} \cr & {\text{SI for 2 year}}\,{\text{ = Rs. 270}} \cr & {\text{SI for 1 year = }}\frac{{270}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs.}}\,135 \cr & {\text{Difference between CI and SI}} \cr & {\text{ = }}\left( {282.15 - 270} \right) \cr & {\text{ = Rs. 12}}{\text{.15}} \cr & {\text{Required rate % }} \cr & {\text{ = }}\frac{{12.15}}{{135}} \times 100 = 9\% \cr} $$
Note : Always remainder for first year CI and SI will be same.

$$\eqalign{ & {\text{ = Rs}}.10000\left[ {\left( {1 + \frac{4}{{100}}} \right)\left( {1 + \frac{5}{{100}}} \right)\left( {1 + \frac{6}{{100}}} \right)} \right] \cr & = {\text{Rs}}.\left( {10000 \times \frac{{26}}{{25}} \times \frac{{21}}{{20}} \times \frac{{53}}{{50}}} \right) \cr & = {\text{Rs}}.\left( {\frac{{57876}}{5}} \right) = {\text{Rs}}.11575.20 \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {11575.20 - 10000} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}.1575.20 \cr} $$

$$\eqalign{ & {\text{P = Rs}}.10000, \cr & {\text{R}} = 20\% \,p.a. \cr & \,\,\,\,\,\,\, = 10\% \,{\text{per}}\,{\text{half year}} \cr & T = 2\,{\text{years}} = 4\,{\text{half}}\,{\text{years}} \cr & {\text{Amount}} \cr & {\text{ = Rs}}.\left[ {10000 \times {{\left( {1 + \frac{{10}}{{100}}} \right)}^4}} \right] \cr & = {\text{Rs}}.\left( {10000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{{11}}{{10}}} \right) \cr & = {\text{Rs}}.14641 \cr & \therefore {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {14641 - 10000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,4641 \cr} $$

Interest on 650 for one year = 676 - 650 = 26
$$\eqalign{ & 26 = \frac{{650 \times r \times 1}}{{100}} \cr & r = 4\% \cr & 650 = P\left[ {1 + \frac{4}{{100}}} \right] \cr & \Rightarrow 650 = P \times \frac{{26}}{{25}} \cr & \Rightarrow p = \frac{{650 \times 25}}{{26}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,625 \cr} $$

$$\eqalign{ & 4\% = \frac{1}{{25}} \cr & \,\,\,\,\,\,\,\,\, = \frac{{26 \to {\text{Amount}}}}{{25 \to {\text{Principal}}}} \cr & {\text{Time = 2 years}} \cr & {\text{Principal}}\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,\,\,{\text{25}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{26}} \cr & \,\,\,\,\,\,\,\,\,{\text{25}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{26}} \cr & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \cr & \,\,\,\,\,\,\,\,625\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,676 \cr & \,\,\,\, \downarrow \times 0.4\,\,\,\,\,\, \downarrow \times 0.4 \cr & \,\,\,\,\,\,\,\,\,250\,\,\,\,\,\,\,\,\,\,\,\,270.40 \cr & {\text{Hence required principal}} \cr & {\text{ = Rs.250}} \cr} $$

$$\eqalign{ & {\text{ = Rs}}.\left[ {1600 \times {{\left( {1 + \frac{5}{{2 \times 100}}} \right)}^2} + 1600 \times \left( {1 + \frac{5}{{2 \times 100}}} \right)} \right] \cr & {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}} \times \frac{{41}}{{40}} + 1600 \times \frac{{41}}{{40}}} \right] \cr & {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}}\left( {\frac{{41}}{{40}} + 1} \right)} \right] \cr & {\text{ = Rs}}.\left( {\frac{{1600 \times 41 \times 81}}{{40 \times 40}}} \right) \cr & {\text{ = Rs}}.\,3321 \cr & \therefore {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {3321 - 3200} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,121 \cr} $$

$$\eqalign{ & {\text{Amount}} \cr & {\text{ = Rs}}.\left[ {20000{{\left( {1 + \frac{{10}}{{100}}} \right)}^2}\left( {1 + \frac{{20}}{{100}}} \right)} \right] \cr & = {\text{Rs}}.\left( {20000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{6}{5}} \right) \cr & = {\text{Rs}}.29040 \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {29040 - 20000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 9040 \cr} $$

Difference in CI and SI for 2 years
$$\eqalign{ & = \left( {40.80 - 40} \right) \cr & = {\text{Rs 0}}{\text{.80}} \cr & {\text{SI for first year }} \cr & {\text{ = }}\frac{{40}}{2} = {\text{Rs}}{\text{.}}\,20 \cr & {\text{Required Rate }}\% \cr & {\text{ = }}\frac{{0.80}}{{20}} \times 100 = 4\% \cr} $$