Quantitative Aptitude > Interest
COMPOUND INTEREST MCQs
Total Questions : 262
| Page 23 of 27 pages
Answer: Option C. -> Rs. 7500
Time (t) = 1 years
Rate % = 4%
Amount = Rs. 7803
When interest is compounded half yearly
New Rate = $$\frac{4}{2}$$ = 2%
Time = 1 × 2 = 2 years
Required rate% for 2 years CI
$${\text{ = 2}} + {\text{2}} + \frac{{2 \times 2}}{{100}} = 4.04\% $$
According to question,
(100 + 4.04)% of sum = Rs. 7803
$$\eqalign{
& \therefore {\text{Sum = }}\frac{{7803}}{{104.04}} \times 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}7500 \cr} $$
Time (t) = 1 years
Rate % = 4%
Amount = Rs. 7803
When interest is compounded half yearly
New Rate = $$\frac{4}{2}$$ = 2%
Time = 1 × 2 = 2 years
Required rate% for 2 years CI
$${\text{ = 2}} + {\text{2}} + \frac{{2 \times 2}}{{100}} = 4.04\% $$
According to question,
(100 + 4.04)% of sum = Rs. 7803
$$\eqalign{
& \therefore {\text{Sum = }}\frac{{7803}}{{104.04}} \times 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}7500 \cr} $$
Answer: Option D. -> Rs. 8000
Let the principal be x Rs. Now,
$$\eqalign{
& C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& \Rightarrow 1261 = x\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& \Rightarrow 1261 = x\left( {\frac{{9261}}{{8000}} - 1} \right) \cr
& \Rightarrow 1261 = x\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& \Rightarrow 1261 = \frac{{1261x}}{{8000}} \cr
& \Rightarrow x = \frac{{1261 \times 8000}}{{1261}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,8000 \cr} $$
Let the principal be x Rs. Now,
$$\eqalign{
& C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& \Rightarrow 1261 = x\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& \Rightarrow 1261 = x\left( {\frac{{9261}}{{8000}} - 1} \right) \cr
& \Rightarrow 1261 = x\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& \Rightarrow 1261 = \frac{{1261x}}{{8000}} \cr
& \Rightarrow x = \frac{{1261 \times 8000}}{{1261}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,8000 \cr} $$
Answer: Option B. -> Rs. 234.375
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left( {15000 \times \frac{{25}}{2} \times 2 \times \frac{1}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}3750 \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left[ {15000{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2} - 15000} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {15000 \times \frac{9}{8} \times \frac{9}{8} - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {18948.375 - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}3984.375 \cr
& {\text{Difference }} \cr
& {\text{ = Rs}}{\text{. }}\left( {3984.375 - 3750} \right) \cr
& = {\text{Rs}}{\text{. }}234.375 \cr} $$
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left( {15000 \times \frac{{25}}{2} \times 2 \times \frac{1}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}3750 \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left[ {15000{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2} - 15000} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {15000 \times \frac{9}{8} \times \frac{9}{8} - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {18948.375 - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}3984.375 \cr
& {\text{Difference }} \cr
& {\text{ = Rs}}{\text{. }}\left( {3984.375 - 3750} \right) \cr
& = {\text{Rs}}{\text{. }}234.375 \cr} $$
Answer: Option D. -> Rs. 862.6176
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{19200 \times 12 \times 3}}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.6912}} \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {19200 \times {{\left( {1 + \frac{{12}}{{100}}} \right)}^3} - 19200} \right] \cr
& = {\text{Rs}}{\text{.}}\left[ {\left( {19200 \times \frac{{28}}{{25}} \times \frac{{28}}{{25}} \times \frac{{28}}{{25}}} \right) - 19200} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {\frac{{16859136}}{{625}} - 19200} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {26974.6176 - 19200} \right) \cr
& = {\text{Rs}}{\text{. 7774}}{\text{.6176}} \cr
& \therefore {\text{Difference }} \cr
& {\text{ = Rs}}{\text{.}}\left( {7774.6176 - 6912} \right) \cr
& = {\text{Rs}}{\text{. 862}}{\text{.6176}} \cr} $$
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{19200 \times 12 \times 3}}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.6912}} \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {19200 \times {{\left( {1 + \frac{{12}}{{100}}} \right)}^3} - 19200} \right] \cr
& = {\text{Rs}}{\text{.}}\left[ {\left( {19200 \times \frac{{28}}{{25}} \times \frac{{28}}{{25}} \times \frac{{28}}{{25}}} \right) - 19200} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {\frac{{16859136}}{{625}} - 19200} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {26974.6176 - 19200} \right) \cr
& = {\text{Rs}}{\text{. 7774}}{\text{.6176}} \cr
& \therefore {\text{Difference }} \cr
& {\text{ = Rs}}{\text{.}}\left( {7774.6176 - 6912} \right) \cr
& = {\text{Rs}}{\text{. 862}}{\text{.6176}} \cr} $$
Answer: Option D. -> 20%
Here, b – a = 3 – 2 = 1
B = Rs. 1728, A = Rs.1440
$$\eqalign{
& R\% = \left( {\frac{B}{A} - 1 \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{1728}}{{1440}} - 1 \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{288}}{{1440}} \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr} $$
Here, b – a = 3 – 2 = 1
B = Rs. 1728, A = Rs.1440
$$\eqalign{
& R\% = \left( {\frac{B}{A} - 1 \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{1728}}{{1440}} - 1 \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{288}}{{1440}} \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr} $$
Answer: Option A. -> Rs. 4096
S.I. on Rs. 4624 for 1 year
$$\eqalign{
& {\text{ = Rs. }}\left( {4913 - 4624} \right) \cr
& {\text{ = Rs. 289}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 289}}{{4624 \times 1}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\frac{1}{4}\% \cr
& {\text{Now,}} \cr
& x{\left( {1 + \frac{{25}}{{400}}} \right)^2} = 4624 \cr
& \Rightarrow x \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} = 4624 \cr
& \Rightarrow x = \left( {4624 \times \frac{{16}}{{17}} \times \frac{{16}}{{17}}} \right) \cr
& \Rightarrow x = 4096 \cr} $$
S.I. on Rs. 4624 for 1 year
$$\eqalign{
& {\text{ = Rs. }}\left( {4913 - 4624} \right) \cr
& {\text{ = Rs. 289}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 289}}{{4624 \times 1}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\frac{1}{4}\% \cr
& {\text{Now,}} \cr
& x{\left( {1 + \frac{{25}}{{400}}} \right)^2} = 4624 \cr
& \Rightarrow x \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} = 4624 \cr
& \Rightarrow x = \left( {4624 \times \frac{{16}}{{17}} \times \frac{{16}}{{17}}} \right) \cr
& \Rightarrow x = 4096 \cr} $$
Answer: Option B. -> Rs. 12100
$$\eqalign{
& {\text{Rate }} \Rightarrow {\text{ 10% = }}\frac{1}{{10}} \cr
& {\text{Each installment of 2 years}} \cr
& \Rightarrow \frac{{10}}{{11}} \times \frac{{\left( {10 + 11} \right)}}{{11}} \times {\text{ Installment = P}}{\text{.A}} \cr
& {\text{P}}{\text{.A = 21000}} \cr
& {\text{Each installment = 12100}} \cr} $$
$$\eqalign{
& {\text{Rate }} \Rightarrow {\text{ 10% = }}\frac{1}{{10}} \cr
& {\text{Each installment of 2 years}} \cr
& \Rightarrow \frac{{10}}{{11}} \times \frac{{\left( {10 + 11} \right)}}{{11}} \times {\text{ Installment = P}}{\text{.A}} \cr
& {\text{P}}{\text{.A = 21000}} \cr
& {\text{Each installment = 12100}} \cr} $$
Answer: Option D. -> 6%
$$\eqalign{
& {\text{Required rate }}\% \cr
& {\text{ = }}\frac{{\left( {238.50 - 225} \right)}}{{225}} \times 100 \cr
& = 6\,\% \cr} $$
$$\eqalign{
& {\text{Required rate }}\% \cr
& {\text{ = }}\frac{{\left( {238.50 - 225} \right)}}{{225}} \times 100 \cr
& = 6\,\% \cr} $$
Answer: Option D. -> Rs. 192000
$$\eqalign{
& 12000 \times {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 24000 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 2 \cr
& \therefore {\left[ {{{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^5}} \right]^4} = {2^4} = 16 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \cr
& \Rightarrow {\text{P}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}}{\text{ = 16P}} \cr
& \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \times 12000 \cr
& \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 192000 \cr} $$
$$\eqalign{
& 12000 \times {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 24000 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 2 \cr
& \therefore {\left[ {{{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^5}} \right]^4} = {2^4} = 16 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \cr
& \Rightarrow {\text{P}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}}{\text{ = 16P}} \cr
& \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \times 12000 \cr
& \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 192000 \cr} $$
Answer: Option B. -> Rs. 280.80
$$\eqalign{
& {\text{Principal = Rs 250}} \cr
& {{\text{R}}_1} = 4\% ,\,\,\,\,\,\,\,\,\,{{\text{R}}_2} = 8\% \cr
& {\text{Amount}}\,{\text{after}}{1^{st}}\,{\text{year}} \cr
& = 250\left( {1 + \frac{4}{{100}}} \right) = {\text{Rs}}{\text{. }}260 \cr
& {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& {\text{ = }}260\left( {1 + \frac{8}{{100}}} \right) \cr
& = {\text{Rs}}{\text{. }}280.80 \cr} $$
$$\eqalign{
& {\text{Principal = Rs 250}} \cr
& {{\text{R}}_1} = 4\% ,\,\,\,\,\,\,\,\,\,{{\text{R}}_2} = 8\% \cr
& {\text{Amount}}\,{\text{after}}{1^{st}}\,{\text{year}} \cr
& = 250\left( {1 + \frac{4}{{100}}} \right) = {\text{Rs}}{\text{. }}260 \cr
& {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& {\text{ = }}260\left( {1 + \frac{8}{{100}}} \right) \cr
& = {\text{Rs}}{\text{. }}280.80 \cr} $$