1. A sum of money invested at compound interest amounts to Rs. 650 at the end of first year and Rs. 676 at the end of second year. The sum of money is =

a) Rs. 540

b) Rs. 560

c) Rs. 625

d) Rs. 600

Explanation: Interest on 650 for one year = 676 - 650 = 26

$$\eqalign{ & 26 = \frac{{650 \times r \times 1}}{{100}} \cr & r = 4\% \cr & 650 = P\left[ {1 + \frac{4}{{100}}} \right] \cr & \Rightarrow 650 = P \times \frac{{26}}{{25}} \cr & \Rightarrow p = \frac{{650 \times 25}}{{26}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,625 \cr} $$

2. On a certain sum of money the compound interest for 2 years is Rs. 282.15 and the simple interest for the same period of time is Rs. 270. The rate of interest per annum is =

a) 6.07%

b) 9%

c) 10%

d) 12.15%

Explanation:

$$\eqalign{ & {\text{CI for 2 years}}\,{\text{ = Rs. 282}}{\text{.15}} \cr & {\text{SI for 2 year}}\,{\text{ = Rs. 270}} \cr & {\text{SI for 1 year = }}\frac{{270}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs.}}\,135 \cr & {\text{Difference between CI and SI}} \cr & {\text{ = }}\left( {282.15 - 270} \right) \cr & {\text{ = Rs. 12}}{\text{.15}} \cr & {\text{Required rate % }} \cr & {\text{ = }}\frac{{12.15}}{{135}} \times 100 = 9\% \cr} $$

3. If the difference between the compound interest and simple interest on a sum of 5% rate of interest per annum for three years is Rs. 36.60, then the sum is = ?

a) Rs. 8000

b) Rs. 4400

c) Rs. 8400

d) Rs. 4800

Explanation:

Rate % = 5%

Effective Rate of CI for 3 years = 15.7625%

Effective Rate of SI for 3 years = 5 × 3 = 15%

According to the question

$$\eqalign{ & \left( {15.7625 - 15} \right)\% \,{\text{of sum}} {\text{ = Rs. 36}}{\text{.60}} \cr & {\text{0}}{\text{.7625% of sum}} {\text{ = Rs. 36}}{\text{.60}} \cr & {\text{Sum = }}\frac{{36.60}}{{0.7625}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}4800 \cr} $$

4. Compound interest on a sum of money for 2 years at 4% per annum is Rs. 2448. simple interest on the same sum of money at the same rate of interest for 2 years will be = ?

a) Rs. 2360

b) Rs. 2400

c) Rs. 2250

d) Rs. 2500

Explanation:

Time (t) = 2 years

Rate % = 4%

Effective rate of CI of 2 years

$$\eqalign{ & {\text{ = 4 + 4 + }}\frac{{4 \times 4}}{{100}} \cr & = 8.16\% \cr} $$

Effective Rate of SI for 2 years = 8%

According to the question

$$\eqalign{ & {\text{8}}{\text{.16% of sum}} \cr & {\text{ = Rs. 2448}} \cr & {\text{1% of sum}} \cr & {\text{ = Rs. }}\frac{{2448}}{{8.16}} \cr & {\text{8% of sum}} \cr & {\text{ = }}\frac{{2448}}{{8.16}} \times {\text{8}} \cr & {\text{ = Rs. 2400 }} \cr} $$

5. A man gets a simple interest on Rs. 1000 on a certain principal at the rate of 5 p.c.p.a. in 4 years. What compound interest will the man get on twice the principal in 2 years at the same rate ?

a) Rs. 1005

b) Rs. 1000

c) Rs. 10125

d) None of the above

Explanation:

$$\eqalign{ & {\text{Principal}} \cr & {\text{ = Rs}}{\text{.}}\left( {\frac{{100 \times 1000}}{{5 \times 4}}} \right) \cr & = {\text{Rs}}{\text{. 5}}000 \cr & {\text{Now, P = Rs}}{\text{.}}\,10000, \cr & {\text{T = 2 years,}} \cr & {\text{R = 5% }} \cr & {\text{Amount}} \cr & {\text{ = Rs}}{\text{.}}\left[ {10000 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr & = {\text{Rs}}{\text{.}}\left( {10000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr & = {\text{Rs}}. 11025 \cr & \therefore {\text{C}}{\text{.I}}{\text{. = }}\left( {11025 - 10000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 1025 \cr} $$

6. Mr. Duggal invested Rs. 20000 with rate of interest @ 20 p.c.p.a. The interest was compounded half-yearly for first one year and in the next year it was compounded yearly. What will be the total interest earned at the end of 2 year ?

a) Rs. 9040

b) Rs. 8800

c) Rs. 9800

d) Rs. 8040

Explanation:

$$\eqalign{ & {\text{Amount}} \cr & {\text{ = Rs}}.\left[ {20000{{\left( {1 + \frac{{10}}{{100}}} \right)}^2}\left( {1 + \frac{{20}}{{100}}} \right)} \right] \cr & = {\text{Rs}}.\left( {20000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{6}{5}} \right) \cr & = {\text{Rs}}.29040 \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {29040 - 20000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 9040 \cr} $$

7. A sum of money doubles itself in 4 years compound interest. It will amount to 8 times itself at the same rate of interest in = ?

a) 24 years

b) 16 years

c) 12 years

d) 18 years

Explanation:

$$\eqalign{ & {\text{Let Principal = P}} \cr & {\text{Rate = R% }} \cr & {\text{T = 4 years}} \cr & \therefore {\text{Amount = 2P}} \cr & {\text{Case (I) 2P = P}}{\left( {1 + \frac{R}{{100}}} \right)^4} \cr & 2 = {\left( {1 + \frac{R}{{100}}} \right)^4}.....(i) \cr & {\text{Case (II) Let after t years it will be 8 times}} \cr & {\text{8P = P}}{\left( {1 + \frac{R}{{100}}} \right)^t} \cr & {\left( 2 \right)^3} = {\left( {1 + \frac{R}{{100}}} \right)^t}.....(ii) \cr & {\text{By using equation (i) & equation (ii)}} \cr & {\left( {1 + \frac{R}{{100}}} \right)^{12}} = {\left( {1 + \frac{R}{{100}}} \right)^t} \cr & {\text{By comparing both sides,}} \cr & {\text{t = 12 years}} \cr} $$

8. If the compound interest on a sum of money for 3 years at the rate of 5% per annum is Rs. 252.20, the simple interest on the same sum at the same rate and for the same time is ?

a) Rs. 240

b) Rs. 245

c) Rs. 220

d) Rs. 250

Explanation:

$$\eqalign{ & {\text{Rate = 5% }} \cr & {\text{Time = 3 years}} \cr & {\text{Compound Interest Rs. 252}}{\text{.20}} \cr & {\text{Effective rate% of CI for 3 years}} \cr & {\text{ = 15}}{\text{.7625% }} \cr & {\text{Effective rate% of SI for 3 years}} \cr & {\text{ = 5}} \times {\text{3 = 15% }} \cr & {\text{Required SI }} \cr & {\text{ = }}\frac{{252.20}}{{15.7625}} \times 15 \cr & = 240 \cr} $$

9. The difference between simple interest and compound interest on Rs. P at R% p.a in 2 years is = ?

a) $${\text{Rs}}{\text{.}}\,\frac{{P{R^2}}}{{100}}$$

b) $${\text{Rs}}{\text{.}}\,\frac{{2PR}}{{100}}$$

c) $${\text{Rs}}{\text{.}}\,\frac{{PR}}{{100}}$$

d) $${\text{Rs}}{\text{.}}\,\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}$$

Explanation:

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{P \times R \times 2}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left( {\frac{{2PR}}{{100}}} \right) \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {P \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - P} \right] \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right] \cr & \therefore {\text{Difference}} \cr & {\text{ = Rs}}{\text{.}}\left[ {\left\{ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right\} - \frac{{2PR}}{{100}}} \right] \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}} \right] \cr} $$

10. What would be the compound interest accrued on an amount of Rs. 8400 @ 12.5 p.c.p.a at the end of 3 years ?

a) Rs. 2584.16

b) Rs. 3820.14

c) Rs. 3560.16

d) Rs. 4205.62

Explanation:

$$\eqalign{ & {\text{Amount}} \cr & {\text{ = Rs}}{\text{.}}\left[ {8400 \times {{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^3}} \right] \cr & = {\text{Rs}}{\text{.}}\left( {8400 \times \frac{9}{8} \times \frac{9}{8} \times \frac{9}{8}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{382725}}{{32}}} \right) \cr & = {\text{Rs}}.11960.156 \approx {\text{Rs}}.11960.16 \cr & {\text{C}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {11960.16 - 8400} \right) \cr & = {\text{Rs}}{\text{.}}\,3560.16 \cr} $$