# Problems on Compound Interest

Q11. If the rate of interest be 3% per annum for the first year, 4% per annum for second year and 5% per annum for third year, then the compound interest of Rs. 10,000 for 3 years will be

(a) 1029.66

(b) 1124.53

(c) 1156.89

(d) 1247.60

**Answer:** (d) 1247.60

Amount = Rs. [10000 ( 1 + | 3 | ) X ( 1 + | 4 | ) X ( 1 + | 5 | ) ] |

100 | 100 | 100 |

= Rs. [10000 X | 103 | X | 104 | X | 105 | ] |

100 | 100 | 100 |

= Rs. [100 X 103 X | 26 | X | 21 | ] |

25 | 20 |

= Rs. 11247.60

∴ C.I = Rs. (11247.60 - 10,000)

= Rs. 1247.60

Q12. A sum of money ammounts to Rs. 7690 after 3 years and to Rs. 11035 after 6 years on compound interest. The sum is

(a) 1425.66

(b) 5142.78

(c) 5358.95

(d) 6825.14

**Answer:** (c) 5358.95

Let the sum be Rs. x

Now x(1 + | r | )^{3} = 7690 ---------> (1) |

100 |

And, x(1 + | r | )^{6} = 11035 ---------> (2) |

100 |

(2) ÷ (1) ⇒ | (1 + | r | )^{3} = |
11035 |

100 | 7690 |

⇒ (1 + | r | )^{3} = |
2207 |

100 | 1538 |

(1) ⇒ x X | 2207 | = 7690 |

1538 |

⇒ x = 7690 X | 1538 |

2207 |

= 5358.95

Q13. The compound interest on Rs. 16000 for 9 months at 20% per annum compounded quaterly is

(a) 2522

(b) 2599

(c) 2677

(d) 2682

**Answer:** (a) 2522

P = Rs. 16000

t = 9 months = 3 quaterly

r = | 20% | = 5% |

4 |

C.I = Rs. [16000 (1 + | 5 | )^{3} - 16000] |

100 |

= Rs. [16000 X | 105 | X | 105 | X | 105 | - 16000] |

100 | 100 | 100 |

= Rs. [16000 X | 21 | X | 21 | X | 21 | - 16000] |

20 | 20 | 20 |

= Rs. (18522 - 16000)

= Rs. 2522

Q14. At what rate of interest will Rs. 10,000 become Rs. 12100 after 2 years when interest is compounded annually ?

(a) 8%

(b) 10%

(c) 13%

(d) 15%

**Answer:** (b) 10%

P = Rs. 10,000

A = Rs. 12,100

t = 2y

Now A = P (1 + | r | ) ^{t} |

100 |

⇒ 12,100 = 10,000 (1 + | r | ) ^{2} |

100 |

⇒ | 12100 | = ( 1 + | r | ) ^{2} |

10000 | 100 |

⇒ | 121 | = ( 1 + | r | ) ^{2} |

100 | 100 |

⇒ ( | 11 | )^{2} = (1 + |
r | ) ^{2} |

10 | 100 |

⇒ 1 + | r | = | 11 |

100 | 10 |

⇒ | r | = | 11 | - 1 |

100 | 10 |

⇒ | r | = | 11 - 10 |

100 | 10 |

⇒ r | = | 1 | X 100 = 10% |

10 |

Q15. A money-lender borrows money at 4% per annum and pays interest at the end of the year. He lends it at 6% per annum compound interest compounded half yearly and receives the interest at the end of the year. Thus he gains Rs. 104.50 a year. The amount of money he borrows is

(a) 4000

(b) 5000

(c) 6000

(d) 7000

**Answer:** (b) 5000

Let the money borrowed be Rs. x

Interest paid by the money lender = Rs. (x X (x/100) X 1) = Rs. x/25

Interest received by the money lender = Rs. [ x X (1 + | 3 | ) ^{2} - x] |

100 |

= Rs. ( x X | 103 | X | 103 | - x) |

100 | 100 |

= Rs. | 609x |

10000 |

Gain = Rs. ( | 609x | - | x | ) = Rs. | 209x |

10000 | 25 | 10000 |

∴ | 209x | = 104.50 |

10000 |

⇒ 209x = 1045000

⇒ x = 5000

Q16. The difference between compound interest and simple interest on a sum for 3 years at 5% per annum is Rs. 768. The sum is

(a) 75581

(b) 92564

(c) 95863

(d) 100721

**Answer:** (d) 100721

Let the sum be Rs. x

S.I = | x X 5 X 3 | = | 15x |

100 | 100 |

C.I = Rs. [x (1 + | 5 | )^{3} - x ] |

100 |

A/Q, C.I - S.I = 768

⇒ [x (1 + | 5 | )^{3} - x ] - |
15x | = 768 |

100 | 100 |

⇒ x X | 105 | X | 105 | X | 105 | - x - | 15x | = 768 |

100 | 100 | 100 | 100 |

⇒ x X | 21 | X | 21 | X | 21 | - | 115x | = 768 |

20 | 20 | 20 | 100 |

⇒ | 9261x | - | 115x | = 768 |

8000 | 100 |

⇒ 61x = 768 X 8000 = 6144000

⇒ x = Rs. 100721

Q17. If the compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 840, what would be the simple interest ?

(a) 580

(b) 600

(c) 720

(d) 800

**Answer:** (d) 800

Let the sum be Rs. x

Now C.I = 840

⇒ { x X (1 + | 10 | )^{2} - x } = 840 |

100 |

⇒ { x X | 11 | X | 11 | - x } = 840 |

10 | 10 |

⇒ | 121x | - x = 840 |

100 |

⇒ | 121x - 100x | = 840 |

100 |

⇒ 21x = 8400

⇒ x = 4000

Now S.I = | 4000 X 10 X 2 | = Rs. 800 |

100 |

Q18. A deposited Rs. 6000 in a bank at 5% per annum simple interest. B deposited Rs. 5000 at 8% per annum compound interest. After 2 years, the difference between their interest will be

(a) 232

(b) 256

(c) 298

(d) 318

**Answer:** (a) 232

S.I = | 6000 X 5 X 2 |

100 |

C.I = Rs. {5000 (1 + | 8 | )^{2} - 5000 } |

100 |

= Rs. {5000 X | 108 | X | 108 | - 5000} |

100 | 100 |

= Rs. (5832 - 5000)

= Rs. 832

∴ C.I - S.I = Rs. (832 - 600) = Rs. 232

Q19. The compound interest on Rs. 2600 for 1½ years at 10% per annum is

(a) 390

(b) 403

(c) 483

(d) 513

**Answer:** (b) 403

Here P = Rs. 2600

t = 1½ = 3/2 y

r = 10%

C.I = Rs. {2600 (1 + | 10 | ) X (1 + | 5 | ) - 2600 } |

100 | 100 |

= Rs. {2600 X | 110 | X | 105 | - 2600 } |

100 | 100 |

= Rs. {2600 X | 22 | X | 21 | - 2600 } |

20 | 20 |

= Rs. {3003 - 2600}

= Rs. 403

Q20. Find the compound interest on Rs. 40,000 at 15% per annum for 6 months compounded quaterly

(a) 3900

(b) 4100

(c) 4300

(d) 5100

**Answer:** (b) 4100

Here P = Rs. 40,000

t = 6 months = 2 quaterly

r = (15/3)% = 5%

∴ C.I = Rs. {40000 (1 + | 5 | )^{2} - 40000} |

100 |

= Rs. {40000 X | 105 | X | 105 | - 40000} |

100 | 100 |

= Rs. {40000 X | 21 | X | 21 | - 40000} |

20 | 20 |

= Rs. {44100 - 40000}

= Rs. 4100

**2**