Practice MCQ Questions and Answer on Compound Interest

Solution: Rate = 20% p.a = 5% Quarterly = $$\frac{1}{{20}}$$ Time = 1 year = 4 quarter

Solution: $$\eqalign{ & 2{\text{ year}} \to {\text{CI}} \cr & = 10 + 10 + \frac{{10 \times 10}}{{100}} = 21\% \cr & {\text{In 2}}\frac{1}{2}{\text{ year CI}} \cr & = 21 + 5 + \frac{{21 \times 5}}{{100}} = 27.05\% \cr & P \times \frac{{27.05}}{{100}} = 1623 \cr & P = {\text{Rs}}{\text{. 6000}} \cr} $$

Solution: $$\eqalign{ & {\text{Principal = Rs. 2000}} \cr & {\text{Amount = Rs. 2420}} \cr & {\text{Rate = 10% }} \cr & {\text{By using formula,}} \cr & \Rightarrow 2420 = 2000{\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{2420}}{{2000}} = {\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{121}}{{100}} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow {\left( {\frac{{11}}{{10}}} \right)^2} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow n = 2 \cr & {\text{Hence,}} \cr & {\text{required time = 2 years}} \cr} $$ Alternative Note : In such type of questions to save your valuable time follow the given below method.     Principal   :   Amount Ratio   →   2000   :   2420     100   :   121 $${\text{Rate = 10% = }}\frac{1}{{10}}$$     Principal   :   Amount 1st year   →   10   :   11 2nd year   →   10   :   11 Ratio   →   100   :   121 Note : Now after 2nd year both the principal and amount will be in the same ratio. Hence required time = 2 years

Solution: $$\eqalign{ & P{\left( {1 + \frac{{20}}{{100}}} \right)^n} > 2P\,\,\, \Rightarrow \,\,\,{\left( {\frac{6}{5}} \right)^n} > 2 \cr & {\text{Now}},\left( {\frac{6}{5} \times \frac{6}{5} \times \frac{6}{5} \times \frac{6}{5}} \right) > 2 \cr & So,\,n = 4\,{\text{years}} \cr} $$

Solution: Let the sum be = 400x Simple Interest = $$\frac{{PTR}}{{100}}$$ S.I = $$\frac{{400x \times 2 \times 5}}{{100}}$$ = 40x for Compond Interest 5% = $$\frac{{1}}{20}$$ C.I = 20x + 20x + x = 41x Difference = 41x - 40x = 20 i.e. x = 20 ∴ Sum is = 400 × 20 = 8000

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

Solution: $$\eqalign{ & 1{\text{ year CI}} = 1{\text{ year SI}} \cr & {\text{SI}} = \frac{{P \times R \times T}}{{100}} \cr & = \frac{{50000 \times 8 \times 1}}{{100}} \cr & = 4000 \cr & {\text{Compound interest at half yearly}} \cr & {\text{Rate}} = \frac{8}{2} = 4\% \cr & {\text{Time}} = 1 \times 2 = 2{\text{ years}} \cr & A = P{\left( {1 + \frac{R}{{100}}} \right)^n} \cr & A = 50000{\left( {1 + \frac{4}{{100}}} \right)^2} \cr & A = 50000 \times \frac{{104}}{{100}} \times \frac{{104}}{{100}} \cr & A = 5 \times 10816 \cr & A = 54080 \cr & {\text{CI}} = 54080 - 50000 = 4080 \cr & {\text{Difference between the interest of on year}} \cr & = 4080 - 4000 \cr & = 80 \cr} $$

Solution: Rate % = 10%, Time = 1 year Case (I) : When interest is calculated yearly, Rate = 10% Case (II) : When interest is calculated half yearly $$\eqalign{ & \Rightarrow {\text{New rate }}\% = \frac{{10}}{2} = 5\% \cr & {\text{Time = 1}} \times {\text{2}} = {\text{2 years}} \cr & {\text{Effective rate}}\% \cr & {\text{ = 5 + 5 + }}\frac{{5 \times 5}}{{100}} = 10.25\% \cr & {\text{Difference in rates}} \cr & {\text{ = }}\left( {10.25 - 10} \right)\% = 0.25\% \cr & {\text{According to the question,}} \cr & {\text{0}}{\text{.25% of sum = Rs 180}} \cr & {\text{Sum = }}\frac{{180}}{{0.25}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}72000 \cr} $$

Solution: $$\eqalign{ & {\text{C}}{\text{.I}}{\text{.}}\, = Rs.\,\left[ {4000 \times {{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - 4000} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {4000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} - 4000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,840 \cr & \therefore {\text{Sum}} = Rs.\,\left( {\frac{{420 \times 100}}{{3 \times 8}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1750 \cr} $$

Solution: $$\left[ {15000 \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - 15000} \right]$$       $$ - $$ $$\left( {\frac{{15000 \times R \times 2}}{{100}}} \right)$$    $$ = 96$$ $$ \Rightarrow 15000\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^2} - 1 - \frac{{2R}}{{100}}} \right] = 96$$ $$ \Rightarrow 15000$$  $$\left[ {\frac{{{{\left( {100 + R} \right)}^2} - 10000 - \left( {200 \times R} \right)}}{{10000}}} \right]$$       $$ = 96$$ $$\eqalign{ & \Rightarrow {R^2} = {\frac{{96 \times 2}}{3}} = 64 \cr & \Rightarrow R = 8 \cr & \therefore {\text{Rate}} = 8\% \cr} $$