1. A certain some of money and Rs. 2420 in 2 years and Rs. 2662 in 3 years at same rate of compound interest, compounded annually. The rate of interest per annum is =

a) 6%

b) 8%

c) 9%

d) 10%

Explanation:

$$\eqalign{ & {\text{Amount after three years}} {\text{ = Rs. 2662}} \cr & {\text{Amount after two years}} {\text{ = Rs. 2420}} \cr & {\text{Net interest earned in the }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & {\text{ = }}\,{\text{2662}} - {\text{2420}} \cr & {\text{ = Rs}}{\text{. 242}} \cr & {\text{Rate of interest (r)}} \cr & {\text{ = }}\frac{{242}}{{2420}} \times {\text{100 = 10% }} \cr} $$

(2

^{nd}year's amount is principal for 3

^{rd}year)

2. Kamal took Rs. 6800 as a loan which along with interest is to be repaid in two equal annual installment. If the rate of interest is $$12\frac{1}{2}$$ % compounded annually, then the value of each installment is =

a) Rs. 8100

b) Rs. 4150

c) Rs. 4050

d) Rs. 4000

Explanation:

$$\eqalign{ & {\text{Rate of interest}} \cr & {\text{r}} = {\text{12}}\frac{1}{2}\% = \frac{1}{8} \cr} $$

Year | Principal | Installment | |

I | 8_{×9} → |
9_{×9} |
......(i) |

II | 64 → | 81 | ......(ii) |

Total principal = 72 + 64 = 136 units

136 units → 6800

1 units → 50

81 units → 4050

Each installment = Rs. 4050

3. A man invests Rs 4000 for 3 years at compound interest. After one year the money amounts to Rs. 4320. What will be the amount (to the nearest rupee) due at the end of 3 years ?

a) Rs. 4939

b) Rs. 5039

c) Rs. 5789

d) Rs. 6129

Explanation:

$$\eqalign{ & {\text{Le the rate be R }}\% {\text{ p}}{\text{.a}}{\text{.}} \cr & {\text{4000}}\left( {1 + \frac{{{\text{R }}}}{{100}}} \right) = 4320 \cr & 1 + \frac{{{\text{R }}}}{{100}} = \frac{{4320}}{{4000}} = \frac{{108}}{{100}} \cr & \frac{{{\text{R }}}}{{100}} = \frac{8}{{100}} \cr & {\text{R }} = 8 \cr & {\text{Amount after 3 yeras}} \cr & {\text{ = Rs}}{\text{. }}\left[ {4000 + {{\left( {1 + \frac{8}{{100}}} \right)}^3}} \right] \cr & {\text{ = Rs}}{\text{. }}\left( {4000 \times \frac{{27}}{{25}} \times \frac{{27}}{{25}} \times \frac{{27}}{{25}}} \right) \cr & {\text{ = Rs}}{\text{. }}\left( {\frac{{629856}}{{125}}} \right) \cr & {\text{ = Rs}}{\text{. }}5038.848 \approx 5039 \cr} $$

4. A sum of Rs. 13360 was borrowed at $${\text{8}}\frac{3}{4}$$ % per annum compound interest and paid back in two years in two equal annual installments. What was the amount of each installment ?

a) Rs. 5769

b) Rs. 7569

c) Rs. 7009

d) Rs. 7500

Explanation:

$$\eqalign{ & {\text{Rate of interest (r)}} \cr & {\text{ = 8}}\frac{3}{4}\% = \frac{7}{{80}} = \frac{{87 \to {\text{ Installment}}}}{{80 \to {\text{Principal}}}} \cr} $$

⇒ | I | 80_{×87} |
→ | 87_{×87} |
......(i) |

⇒ | II | 6400 | → | 7569 | ......(ii) |

Total principal = 6960 + 6400 = 13360

13360 units = Rs. 13360

1 units = Rs. 1

7569 units = Rs. 7569

Each installment = Rs. 7569

5. An amount of Rs. 10000 becomes Rs. 14641 in 2 years if the interest is compounded half yearly. What is the rate of compound interest p.c.p.a. ?

a) 10%

b) 12%

c) 16%

d) 20%

Explanation:

$$\eqalign{ & {\text{Let the rate be R% p}}{\text{.a}}{\text{. }} \cr & {\text{10000}}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^4} = 14641 \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{200}}} \right)^4} = \frac{{14641}}{{10000}} = {\left( {\frac{{11}}{{10}}} \right)^4} \cr & 1 + \frac{{\text{R}}}{{200}} = \frac{{11}}{{10}} \cr & \frac{{\text{R}}}{{200}} = \frac{1}{{10}} \cr & {\text{R}} = {\text{20% }} \cr} $$

6. What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?

a) Rs. 9000.30

b) Rs. 9720

c) Rs. 10123.20

d) Rs. 10483.20

Explanation:

$$\eqalign{ & {\text{Amount}} = Rs.\,\left[ {25000 \times {{\left( {1 + \frac{{12}}{{100}}} \right)}^3}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {25000 \times \frac{{28}}{{25}} \times \frac{{28}}{{25}} \times \frac{{28}}{{25}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,35123.20 \cr & {\text{C}}{\text{.I}}{\text{.}} = Rs.\left( {35123.20 - 25000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,10123.20 \cr} $$

7. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

a) 6%

b) 6.5%

c) 7%

d) 7.5%

Explanation:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{rate}}\,{\text{be}}\,R\% \,p.a. \cr & 1200 \times {\left( {1 + \frac{R}{{100}}} \right)^2} = 1348.32 \cr & \Rightarrow {\left( {1 + \frac{R}{{100}}} \right)^2} = \frac{{134832}}{{120000}} = \frac{{11236}}{{10000}} \cr & {\left( {1 + \frac{R}{{100}}} \right)^2} = {\left( {\frac{{106}}{{100}}} \right)^2} \cr & 1 + \frac{R}{{100}} = \frac{{106}}{{100}} \cr & R = 6\% \cr} $$

8. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is

a) 3

b) 4

c) 5

d) 6

Explanation:

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

9. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?

a) Rs. 8600

b) Rs. 8620

c) Rs. 8820

d) None of these

Explanation:

$$\eqalign{ & {\text{Amount}} = Rs.\left[ {8000 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {8000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,8820 \cr} $$

10. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:

a) 6.06%

b) 6.07%

c) 6.08%

d) 6.09%

Explanation:

$$\eqalign{ & {\text{Amount}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{100}}\,{\text{for}}\,{\text{1}}\,{\text{year}}\,{\text{when}}\, {\text{compounded}}\,{\text{half - yearly}} \cr & = Rs.\,\left[ {100 \times {{\left( {1 + \frac{3}{{100}}} \right)}^2}} \right] \cr & = Rs.\,106.09 \cr & {\text{Effective}}\,{\text{rate}} = \left( {106.09 - 100} \right)\% \cr & = 6.09\% \cr} $$