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Quantitative Aptitude > Interest

COMPOUND INTEREST MCQs

Total Questions : 262 | Page 23 of 27 pages
Question 221. A certain sum, invested at 4% per annum compound interest, compounded half yearly, amounts to Rs. 7803 at the end of one year. The sum is ?
  1.    Rs. 7000
  2.    Rs. 7200
  3.    Rs. 7500
  4.    Rs. 7700
 Discuss Question
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
$$\eqalign{
& \therefore {\text{Sum = }}\frac{{7803}}{{104.04}} \times 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}7500 \cr} $$
Question 222. A certain sum of money yields Rs. 1261 as compound interest for three years at 5% per annum. The sum is ?
  1.    Rs. 9000
  2.    Rs. 8400
  3.    Rs. 7500
  4.    Rs. 8000
 Discuss Question
Answer: Option D. -> Rs. 8000
Let the principal be x Rs. Now,
$$\eqalign{
& C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& \Rightarrow 1261 = x\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& \Rightarrow 1261 = x\left( {\frac{{9261}}{{8000}} - 1} \right) \cr
& \Rightarrow 1261 = x\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& \Rightarrow 1261 = \frac{{1261x}}{{8000}} \cr
& \Rightarrow x = \frac{{1261 \times 8000}}{{1261}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,8000 \cr} $$
Question 223. What will be the difference between S.I. and C.I. on a sum of Rs. 15000 for 2 years at the same rate of interest of $$12\frac{1}{2}$$ % per annum ?
  1.    Rs. 230.550
  2.    Rs. 234.375
  3.    Rs. 250.129
  4.    Rs. 324.357
 Discuss Question
Answer: Option B. -> Rs. 234.375
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left( {15000 \times \frac{{25}}{2} \times 2 \times \frac{1}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}3750 \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left[ {15000{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2} - 15000} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {15000 \times \frac{9}{8} \times \frac{9}{8} - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {18948.375 - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}3984.375 \cr
& {\text{Difference }} \cr
& {\text{ = Rs}}{\text{. }}\left( {3984.375 - 3750} \right) \cr
& = {\text{Rs}}{\text{. }}234.375 \cr} $$
Question 224. What will be the difference between the simple interest and compound interest accrued on an amount of Rs. 19200 of 3 years @ 12 p.c.p.a. ?
  1.    Rs. 722.6826
  2.    Rs. 798.1824
  3.    Rs. 802.5144
  4.    Rs. 862.6176
  5.    None of these
 Discuss Question
Answer: Option D. -> Rs. 862.6176
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{19200 \times 12 \times 3}}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.6912}} \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {19200 \times {{\left( {1 + \frac{{12}}{{100}}} \right)}^3} - 19200} \right] \cr
& = {\text{Rs}}{\text{.}}\left[ {\left( {19200 \times \frac{{28}}{{25}} \times \frac{{28}}{{25}} \times \frac{{28}}{{25}}} \right) - 19200} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {\frac{{16859136}}{{625}} - 19200} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {26974.6176 - 19200} \right) \cr
& = {\text{Rs}}{\text{. 7774}}{\text{.6176}} \cr
& \therefore {\text{Difference }} \cr
& {\text{ = Rs}}{\text{.}}\left( {7774.6176 - 6912} \right) \cr
& = {\text{Rs}}{\text{. 862}}{\text{.6176}} \cr} $$
Question 225. A certain amount money at R% compounded annually after two and three years becomes Rs. 1440 and Rs. 1728 respectively, R% is ?
  1.    5%
  2.    10%
  3.    15%
  4.    20%
 Discuss Question
Answer: Option D. -> 20%
Here, b – a = 3 – 2 = 1
B = Rs. 1728, A = Rs.1440
$$\eqalign{
& R\% = \left( {\frac{B}{A} - 1 \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{1728}}{{1440}} - 1 \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{288}}{{1440}} \times 100} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr} $$
Question 226. A sum of money invested at compound interest amounts to Rs. 4624 in 2 years and Rs. 4913 in 3 years. The sum of money is = ?
  1.    Rs. 4096
  2.    Rs. 4260
  3.    Rs. 4335
  4.    Rs. 4360
 Discuss Question
Answer: Option A. -> Rs. 4096
S.I. on Rs. 4624 for 1 year
$$\eqalign{
& {\text{ = Rs. }}\left( {4913 - 4624} \right) \cr
& {\text{ = Rs. 289}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 289}}{{4624 \times 1}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\frac{1}{4}\% \cr
& {\text{Now,}} \cr
& x{\left( {1 + \frac{{25}}{{400}}} \right)^2} = 4624 \cr
& \Rightarrow x \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} = 4624 \cr
& \Rightarrow x = \left( {4624 \times \frac{{16}}{{17}} \times \frac{{16}}{{17}}} \right) \cr
& \Rightarrow x = 4096 \cr} $$
Question 227. A man, borrow Rs 21000 at 10% compound interest. How much he has to pay annually at the end of each year, to settle his loan in two years ?
  1.    Rs. 12000
  2.    Rs. 12100
  3.    Rs. 12200
  4.    Rs. 12300
 Discuss Question
Answer: Option B. -> Rs. 12100
$$\eqalign{
& {\text{Rate }} \Rightarrow {\text{ 10% = }}\frac{1}{{10}} \cr
& {\text{Each installment of 2 years}} \cr
& \Rightarrow \frac{{10}}{{11}} \times \frac{{\left( {10 + 11} \right)}}{{11}} \times {\text{ Installment = P}}{\text{.A}} \cr
& {\text{P}}{\text{.A = 21000}} \cr
& {\text{Each installment = 12100}} \cr} $$
Question 228. The compound interest on a certain sum for 2 successive years are Rs. 225 and Rs. 238.50. The rate of interest per annum is = ?
  1.    $$7\frac{1}{2}$$%
  2.    5%
  3.    10%
  4.    6%
 Discuss Question
Answer: Option D. -> 6%
$$\eqalign{
& {\text{Required rate }}\% \cr
& {\text{ = }}\frac{{\left( {238.50 - 225} \right)}}{{225}} \times 100 \cr
& = 6\,\% \cr} $$
Question 229. A sum of Rs. 12000 deposited at compound interest become double after 5 years. After 20 years it will become ?
  1.    Rs. 96000
  2.    Rs. 120000
  3.    Rs. 124000
  4.    Rs. 192000
 Discuss Question
Answer: Option D. -> Rs. 192000
$$\eqalign{
& 12000 \times {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 24000 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 2 \cr
& \therefore {\left[ {{{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^5}} \right]^4} = {2^4} = 16 \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \cr
& \Rightarrow {\text{P}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}}{\text{ = 16P}} \cr
& \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \times 12000 \cr
& \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 192000 \cr} $$
Question 230. What does Rs. 250 amounts to in 2 years with compound interest at the rate of 4% in the 1st year and 8% in the second year ?
  1.    Rs. 280
  2.    Rs. 280.80
  3.    Rs. 468
  4.    Rs. 290.80
 Discuss Question
Answer: Option B. -> Rs. 280.80
$$\eqalign{
& {\text{Principal = Rs 250}} \cr
& {{\text{R}}_1} = 4\% ,\,\,\,\,\,\,\,\,\,{{\text{R}}_2} = 8\% \cr
& {\text{Amount}}\,{\text{after}}{1^{st}}\,{\text{year}} \cr
& = 250\left( {1 + \frac{4}{{100}}} \right) = {\text{Rs}}{\text{. }}260 \cr
& {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& {\text{ = }}260\left( {1 + \frac{8}{{100}}} \right) \cr
& = {\text{Rs}}{\text{. }}280.80 \cr} $$

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