# Problems on Compound Interest

Q1. Find the compound interest on Rs. 5000 at 6% per annum for 2 years.

(a) 602

(b) 618

(c) 653

(d) 669

**Answer:** (b) 618

Here P = Rs. 5000 , r = 6% , t = 2 years

∴ Amount = P ( 1 + | r | ) ^{t} |

100 |

= 5000 (1 + | 6 | ) ^{2} |

100 |

= 5000 X | 106 | X | 106 |

100 | 100 |

= 5618

∴ Compund Interest = Rs (5618 - 5000) = Rs 618

Q2. The difference between the simple interest and the compond interest on Rs 4000 at 10% per annum for 2 years is

(a) 20

(b) 30

(c) 40

(d) 50

**Answer:** (c) 40

Simple Interest = Rs. | 4000 X 10 X 2 | = Rs. 8000 |

100 |

Compound Interest = Rs. { 4000 ( 1 + | 10 | ) ^{2} - 4000 } |

100 |

= Rs. { 4000 X | 11 | X | 11 | - 4000 } |

10 | 10 |

= Rs. (4840 - 4000)

= Rs. 840

∴ Difference = Rs. (840 - 800)

= Rs. 40

Q3. The difference between compound interest and simple interest on Rs. 8000 at 5 % per annum for 3 years is

(a) 57

(b) 61

(c) 65

(d) 69

**Answer:** (b) 61

Simple Interest = | 8000 X 5 X 3 | = 1200 |

100 |

Compound Interest = Rs. { 8000 ( 1 + | 5 | ) ^{3} - 8000 } |

100 |

= Rs. { 8000 ( | 105 | )^{3} |
- 8000 } |

100 |

= Rs. { 8000 X | 21 | X | 21 | X | 21 | - 8000 } |

20 | 20 | 20 |

= Rs. (9261 - 8000) = Rs. 1261

∴ C.I - S.I = Rs. (1261 - 1200)

= Rs. 61

Q4. A tree increases annually by 1/16 of its height. By how much it increases after 2 years if it stands today 32 cm heigh ?

(a) 21.10 cm

(b) 24.26 cm

(c) 32.13 cm

(d) 36.12 cm

**Answer:** (d) 36.12 cm

For the first year, the height of the tree is = 32 + 32 X (1/16) cm

=32 + 2 cm = 34 cm

For the 2nd year, the of the tree is = 34 + 34 X (1/16) cm

= 34 + 2.12 cm

= 36.12 cm

Q5. What will be the compound interest on Rs. 24000 after 2 years at 10% per annum

(a) 5000

(b) 5015

(c) 5040

(d) 5045

**Answer:** (c) 5040

Here P = 24000 , t = 2 years, r = 10%

∴ Compound Interest = { 24000 ( 1 + | 10 | )^{2} } - 24000 |

100 |

= 24000 X | 110 | X | 110 | - 24000 |

100 | 100 |

= 240 X 121 - 24000

= 29040 - 24000

= 5040

Q6. How much would a sum of Rs. 14000 approximately amount to in 2 years at 10 % per annum compounded half yearly

(a) 16025

(b) 16126

(c) 17017

(d) 17198

**Answer:** (c) 17017

Here P = Rs. 14000 , t = 4 years, r = (10/2)% = 5%

∴ Amount = Rs. { 14000 ( 1 + | 5 | )^{4} } |

100 |

= Rs. { 14000 X | 105 | X | 105 | X | 105 | X | 105 | } |

100 | 100 | 100 | 100 |

= Rs. { 14000 X | 21 | X | 21 | X | 21 | X | 21 | } |

20 | 20 | 20 | 20 |

= Rs. 17017 (approx)

Q7. The difference between compound interest and simple interest at the same rate on Rs. 5000 for 2 years is Rs. 72. The rate of interest per annum is

(a) 12 %

(b) 16 %

(c) 17 %

(d) 19 %

**Answer:** (a) 12 %

C.I - S.I = 70

⇒ { 5000 ( 1 + | r | )^{2} - 5000 } - |
5000 X r X 2 | =72 |

100 | 100 |

⇒ { 5000 ( | 100 + r | )^{2} - 5000 } - 100r |
= 72 |

100 |

⇒ 5000 { ( | 100 + r | )^{2} - 1 } - 100r |
= 72 |

100 |

⇒ 5000 X | 10000 + 200r + r^{2} - 10000 |
- 100r | = 72 |

10000 |

⇒ 5 X | 200r + r^{2} |
- 100r | = 72 |

10 |

⇒ | 200r + r^{2} - 200r |
= 72 |

2 |

⇒ | r^{2} |
= 72 |

2 |

⇒ r^{2} = 144

⇒ r = 12 %

Q8. The effective annual rate of interest, corresponding to a nominal rate of 4% per annum,payable half yearly is

(a) 2.30 %

(b) 3.45 %

(c) 4.04 %

(d) 5.12 %

**Answer:** (c) 4.04 %

Let, the sum be Rs. 100

Now, P = Rs. 100, r = 2%, t = 2

∴ Amount = 100 ( 1 + | 2 | )^{2} |

100 |

= 100 X | 102 | X | 102 |

100 | 100 |

=Rs. 104.04

∴ Effective annual rate = 4.04%

Q9. A man deposited Rs. 8000 in a bank at 5% per annum simple interest. Another man deposited Rs. 6000 at 6% per annum compound interest. After 2 years the difference of their interest will be

(a) 20 Rs

(b) 25 Rs

(c) 31 Rs

(d) 35 Rs

**Answer:** (a) 20 Rs

S.I = Rs. | 8000 X 5 X2 | = Rs. 800 |

100 |

C.I = Rs. { 8000 (1 + | 5 | )^{2} - 8000 } |

100 |

= Rs. { 8000 X | 105 | X | 105 | - 8000 } |

100 | 100 |

= Rs. {8820 - 8000}

= Rs. 820

∴ C.I - S.I = Rs. (820 - 800) = Rs. 20

Q10. A sum of money placed at compound interest doubles itself in 5 years. In how many years, it would amount to 8 times of itself at the same rate of interest ?

(a) 8 years

(b) 10 years

(c) 13 years

(d) 15 years

**Answer:** (d) 15 years

Let, the sum be Rs x

Now, x (1 + | r | )^{5} = 2x |

100 |

⇒ ( 1 + | r | )^{5} = 2 -------> (1) |

100 |

Let, the required time t

∴ x (1 + | r | )^{t} = 8x |

100 |

⇒ (1 + | r | )^{t} = 8 |

100 |

⇒ (1 + | r | )^{t} = 2^{3} |

100 |

⇒ (1 + | r | )^{t} = {(1 + |
r | )^{5} }^{3} -------- From (1) |

100 | 100 |

⇒ t = 15 years

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