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
Practice Test Exam