Compound Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & {\text{ = Rs}}{\text{. }}\left[ {4000\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left[ {\left( {4000 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left( {4600 - 1500} \right) \cr & = {\text{Rs}}{\text{. }}3100 \cr & {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & {\text{ = Rs}}{\text{. }}\left[ {3100\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left[ {\left( {3100 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left( {3565 - 1500} \right) \cr & = {\text{Rs}}{\text{. }}2065 \cr & {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & {\text{ = Rs}}{\text{. }}\left[ {2065\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left[ {\left( {2065 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left( {2374.75 - 1500} \right) \cr & = {\text{Rs}}{\text{. }}874.75 \cr} $$

$${\text{Rate 8% = }}\frac{2}{{25}}$$

Principal	Amount
25	27
25	27
625	729
↓ × 8	↓ × 8
5000	5832

Hence required sum = Rs. 5000

$$\eqalign{ & {\text{Principal = Rs 6000}} \cr & {\text{Rate }}\% {\text{ = 10}}\% \cr & {\text{Time (t) = 1}}\frac{1}{2}{\text{ years}} \cr} $$

$$\eqalign{ & {{\text{2}}^{{\text{nd}}}}{\text{ year CI = 660}} \cr & {\text{6 months }}{{\text{2}}^{{\text{nd}}}}{\text{ year CI}} \cr & {\text{ = }}\frac{{660}}{2}{\text{ = 330}} \cr & {\text{Total CI}} \cr & {\text{ = }}\left( {600 + 330} \right) \cr & \,\, = 930 \cr} $$

$$\eqalign{ & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & {\text{= }}\,{\text{Rs}}{\text{.}}\left[ {5000\left( {1 + \frac{5}{{100}}} \right) - 5000} \right]{\text{ }} \cr & = {\text{Rs}}{\text{. }}\left( {5250 - 5000} \right) \cr & = {\text{Rs}}{\text{. 250}} \cr & {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{. }}\left( {5250 - 20\% {\text{ of }}250} \right) \cr & = {\text{Rs}}{\text{.}}\left( {5250 - 50} \right){\text{ }} \cr & {\text{= }}\,{\text{Rs}}{\text{.}}\,{\text{5200 }} \cr & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{.}}\left[ {5200\left( {1 + \frac{5}{{100}}} \right) - 5200} \right]{\text{ }} \cr & = {\text{Rs}}{\text{. }}\left( {5460 - 5200} \right) \cr & = {\text{Rs}}{\text{.260 }} \cr & {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & {\text{= Rs}}{\text{. }}\left( {5460 - 20\% {\text{ of }}260} \right) \cr & {\text{= Rs}}{\text{. }}\left( {5460 - 52} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{5408 }} \cr & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & {\text{= Rs}}{\text{. }}\left[ {5408\left( {1 + \frac{5}{{100}}} \right) - 5408} \right] \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 5408} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{270}}{\text{.40 }} \cr & {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 20\% \,{\text{of }}270.40} \right) \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 54.08} \right) \cr & = {\text{Rs}}{\text{. 5624}}{\text{.32}} \cr} $$

$$\eqalign{ & {\text{SI for 1 year}} \cr & {\text{ = Rs 260}} \cr & {\text{SI for 2 year}} \cr & {\text{ = 260}} \times {\text{2}} \cr & {\text{ = Rs}}{\text{. 520 }} \cr & {\text{Difference in (CI}} - {\text{SI)}} \cr & \left( {540.80 - 520} \right){\text{ = Rs 20}}{\text{.8}} \cr & {\text{Required rate % }} \cr & {\text{ = }}\frac{{20.8}}{{260}} \times {\text{100}} \cr & {\text{ = 8% }} \cr} $$

$$\eqalign{ & {\text{Rate }}\% {\text{ = 4}}\% \cr & {\text{Time (}}{{\text{t}}_1}) = 2\,{\text{years}} \cr & {\text{SI for 2 years}} \cr & {\text{ = 4}} \times {\text{2 = 8}}\% \cr & {\text{CI for 2 years}} \cr & {\text{ = 4 + 4 + }}\frac{{4 \times 4}}{{100}} \cr & = 8.16\% \cr & \operatorname{Required} \,CI \cr & = \frac{{80}}{8} \times 8.16 \cr & = Rs.\,81.60 \cr} $$

$$\eqalign{ & {\text{Amount = Rs}}{\text{. }}\left( {30000 - 4347} \right) \cr & {\text{Amount = Rs}}{\text{. }} 34347 \cr & {\text{Let the time be }}n{\text{ years}} \cr & {\text{Then,}} \cr & {\text{30000}}{\left( {1 + \frac{7}{{100}}} \right)^n} = 34347 \cr & \Leftrightarrow {\left( {\frac{{107}}{{100}}} \right)^n} = \frac{{34347}}{{30000}} \cr & \Leftrightarrow {\left( {\frac{{107}}{{100}}} \right)^n} = \frac{{11449}}{{10000}} = {\left( {\frac{{107}}{{100}}} \right)^2} \cr & \therefore n = {\text{ 2 years}} \cr} $$

$$\eqalign{ & {\text{Effective rate of CI for 2 years}} \cr & {\text{= 5 + 5 + }}\frac{{5 \times 5}}{{100}} \cr & = 10.25\% \cr & {\text{Effective rate of SI for 3 years}} \cr & {\text{= 6}} \times {\text{3 = 18% }} \cr & {\text{According to question}} \cr & {\text{Required SI}} \cr & {\text{= }}\frac{{246}}{{10.25}} \times 18 \cr & = {\text{Rs. 432}} \cr} $$

$$\eqalign{ & \Rightarrow P\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1 - \frac{3}{{20}}} \right] = 122 \cr & \Rightarrow P\left[ {\frac{{{{21}^3} - {{20}^3} - 3 \times {{20}^2}}}{{{{20}^3}}}} \right] = 122 \cr & \Rightarrow P\left[ {\frac{{9261 - 8000 - 1200}}{{8000}}} \right] = 122 \cr & \Rightarrow P \times \frac{{61}}{{8000}} = 122 \cr & \Rightarrow P = \frac{{8000 \times 122}}{{61}} \cr & \Rightarrow P = {\text{Rs}}{\text{.}}\,16000 \cr} $$

$$\eqalign{ & {\text{Let the rate be R}}\% {\text{ p}}{\text{.a}}{\text{.}} \cr & {\text{Then,}} \cr & {\text{2000}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = 2226.05 \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = \frac{{222605}}{{200000}} \cr & \, \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = \frac{{44521}}{{40000}} \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} = {\left( {\frac{{221}}{{200}}} \right)^2} \cr & \Rightarrow 1 + \frac{{\text{R}}}{{100}} = \frac{{211}}{{200}} \cr & \Rightarrow \frac{{\text{R}}}{{100}} = \frac{{11}}{{200}} \cr & \Rightarrow {\text{R}} = \frac{{11}}{2}\% \cr & \Rightarrow {\text{R}} = 5.5\% \cr} $$