## Compound Interest Questions and Answers Part-6

1. A certain amount money at R% compounded annually after two and three years becomes Rs. 1440 and Rs. 1728 respectively, R% is ?
a) 5%
b) 10%
c) 15%
d) 20%

Explanation: 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}

2. 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 = ?
a) $$7\frac{1}{2}$$%
b) 5%
c) 10%
d) 6%

Explanation:
\eqalign{ & {\text{Required rate }}\% \cr & {\text{ = }}\frac{{\left( {238.50 - 225} \right)}}{{225}} \times 100 \cr & = 6\,\% \cr}

3. 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 ?
a) Rs. 12000
b) Rs. 12100
c) Rs. 12200
d) Rs. 12300

Explanation:
\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}

4. 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 = ?
a) Rs. 4096
b) Rs. 4260
c) Rs. 4335
d) Rs. 4360

Explanation: S.I. on Rs. 4624 for 1 year
\eqalign{ & {\text{ = Rs. }}\left( {4913 - 4624} \right) \cr & {\text{ = Rs. 289}} \cr & {\text{Rate}} = \left( {\frac{{100 \times 289}}{{4624 \times 1}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\frac{1}{4}\% \cr & {\text{Now, }} x{\left( {1 + \frac{{25}}{{400}}} \right)^2} = 4624 \cr & x \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} = 4624 \cr & x = \left( {4624 \times \frac{{16}}{{17}} \times \frac{{16}}{{17}}} \right) \cr & x = 4096 \cr}

5. A sum of Rs. 12000 deposited at compound interest become double after 5 years. After 20 years it will become ?
a) Rs. 96000
b) Rs. 120000
c) Rs. 124000
d) Rs. 192000

Explanation:
\eqalign{ & 12000 \times {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 24000 \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 2 \cr & {\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}

6. The compound interest on Rs. 4000 for 4 years at 10% per annum will be =
a) Rs. 1856.40
b) Rs. 1600
c) Rs. 1856
d) Rs. 1756.60

Explanation:
\eqalign{ & {\text{10}}\% {\text{ = }}\frac{1}{{10}} \cr & {\text{Principal}}\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \underbrace {\overline {\,\,\,10000\,\,\,\,\,\,{\text{:}}\,\,\,\,\,{\text{14641}}\,\,\,} }_{{\text{CI = 4641}}} \cr & {\text{Principal = 10000 units}} \cr & {\text{ = Rs}}{\text{. 4000 (given)}} \cr & {\text{1 unit = }}\frac{2}{5} \cr & {\text{CI = 4641 unit}} \cr & {\text{ = Rs}}{\text{. }}\left( {\frac{2}{5} \times 4641} \right) \cr & = {\text{Rs}}{\text{. }}1856.40 \cr}

7. 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 ?
a) Rs. 230.550
b) Rs. 234.375
c) Rs. 250.129
d) Rs. 324.357

Explanation:
\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 }}{\text{ = Rs}}{\text{. }}\left( {3984.375 - 3750} \right) \cr & = {\text{Rs}}{\text{. }}234.375 \cr}

8. The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 525.The simple interest on the same sum of money for double the time at half the rate percent per annum is ?
a) Rs. 1000
b) Rs. 500
c) Rs. 200
d) Rs. 800

Explanation: Let the sum of money be rs. P
\eqalign{ & \left[ {P{{\left( {1 + \frac{R}{{100}}} \right)}^t} - P} \right] = {\text{C}}{\text{.I}}{\text{.}} \cr & \left[ {P{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - P} \right] = 525 \cr & P{\left( {\frac{{11}}{{10}}} \right)^2} - 1 = 525 \cr & P\left( {\frac{{121}}{{100}} - 1} \right) = 525 \cr & P\left( {\frac{{21}}{{100}}} \right) = 525 \cr & P = \frac{{525 \times 100}}{{21}} \cr & P = {\text{Rs}}{\text{.}}\,2500 \cr}
Simple interest on the same sum Rs. 2500 for 4 (double the time) years at 5% (half the rate of percent per annum) is
\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{2500 \times 5 \times 4}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 500}} \cr}

9. 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 ?
a) Rs. 7000
b) Rs. 7200
c) Rs. 7500
d) Rs. 7700

Explanation: 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
$${\text{ = 2}} + {\text{2}} + \frac{{2 \times 2}}{{100}} = 4.04\%$$
(100 + 4.04)% of sum = Rs. 7803
\eqalign{ & {\text{Sum = }}\frac{{7803}}{{104.04}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}7500 \cr}

10. The difference between CI and SI for 3 years Rs. 992. If rate of interest is 10%. Find the Principal ?
a) Rs. 22000
b) Rs. 30000
c) Rs. 28000
d) Rs. 32000

\eqalign{ & {\text{Rate}} = 10\% ,\, \cr & {\text{Let}}\,{\text{Principal}} = P \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times 10 \times 3}}{{100}} = \frac{{3P}}{{10}} \cr & {\text{C}}{\text{.I}}{\text{.}} = P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} - 1} \right\} \cr & {\text{C}}{\text{.I}}{\text{.}}\,\, - \,\,{\text{S}}{\text{.I}}{\text{.}} = 992 \cr & P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} - 1} \right\} - \frac{{3P}}{{10}} = 992 \cr & P\left\{ {{{\left( {\frac{{11}}{{10}}} \right)}^3} - 1 - \frac{3}{{10}}} \right\} = 992 \cr & P\left\{ {\frac{{\left( {1331 - 1000 - 300} \right)}}{{1000}}} \right\} = 992 \cr & P\left( {\frac{{31}}{{1000}}} \right) = 992 \cr & P = 32000 \cr}