Compound Interest problems
- 1. The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Options- A. Rs. 2.50
- B. Rs. 3
- C. Rs. 3.75
- D. Rs. 4
- E. None of these Discuss
Correct Answer: Rs. 3
Explanation:
| S.I. = Rs | ❨ | 1200 x 10 x 1 | ❩ | = Rs. 120. |
| 100 |
| C.I. = Rs. | [ | 1200 x | ❨ | 1 + | 5 | ❩ | 2 | - 1200 | ] | = Rs. 123. |
| 100 |
∴ Difference = Rs. (123 - 120) = Rs. 3.
- 2. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
Options- A. Rs. 51.25
- B. Rs. 52
- C. Rs. 54.25
- D. Rs. 60 Discuss
Correct Answer: Rs. 51.25
Explanation:
| Sum = Rs. | ❨ | 50 x 100 | ❩ | = Rs. 500. |
| 2 x 5 |
| Amount |
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| = Rs. 551.25 |
∴ C.I. = Rs. (551.25 - 500) = Rs. 51.25
- 3. 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?
Options- A. Rs. 8600
- B. Rs. 8620
- C. Rs. 8820
- D. None of these Discuss
Correct Answer: Rs. 8820
Explanation:
| Amount |
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| = Rs. 8820. |
- 4. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Options- A. 6.06%
- B. 6.07%
- C. 6.08%
- D. 6.09% Also asked in: Bank Exams, Bank PO
Correct Answer: 6.09%
Explanation:
| Amount of Rs. 100 for 1 year when compounded half-yearly |
] | = Rs. | [ | 100 x | ❨ | 1 + | 3 | ❩ | 2 | ] | = Rs. 106.09 |
| 100 |
∴ Effective rate = (106.09 - 100)% = 6.09%
- 5. 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.?
Options- A. Rs. 9000.30
- B. Rs. 9720
- C. Rs. 10123.20
- D. Rs. 10483.20
- E. None of these Discuss
Correct Answer: Rs. 10123.20
Explanation:
| Amount |
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| = Rs. 35123.20 |
∴ C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20
- 6. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Options- A. Rs. 400
- B. Rs. 500
- C. Rs. 600
- D. Rs. 800 Discuss
Correct Answer: Rs. 500
Explanation:
Let the sum be Rs. P.
| Then, | [ | P | ❨ | 1 + | 10 | ❩ | 2 | - P | ] | = 525 |
| 100 |
| ⟹ | P | [ | ❨ | 11 | ❩ | 2 | - 1 | ] | = 525 |
| 10 |
| ⟹ P = | ❨ | 525 x 100 | ❩ | = 2500. |
| 21 |
∴ Sum = Rs . 2500.
| So, S.I. = Rs. | ❨ | 2500 x 5 x 4 | ❩ | = Rs. 500 |
| 100 |
- 7. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Options- A. 6%
- B. 6.5%
- C. 7%
- D. 7.5% Discuss
Correct Answer: 6%
Explanation:
Let the rate be R% p.a.
| Then, 1200 x | ❨ | 1 + | R | ❩ | 2 | = 1348.32 |
| 100 |
| ⟹ | ❨ | 1 + | R | ❩ | 2 | = | 134832 | = | 11236 |
| 100 | 120000 | 10000 |
| ∴ | ❨ | 1 + | R | ❩ | 2 | = | ❨ | 106 | ❩ | 2 |
| 100 | 100 |
| ⟹ 1 + | R | = | 106 |
| 100 | 100 |
⟹ R = 6%
- 8. What is the difference between the compound interests on Rs. 5000 for 1½ years at 4% per annum compounded yearly and half-yearly?
Options- A. Rs. 2.04
- B. Rs. 3.06
- C. Rs. 4.80
- D. Rs. 8.30 Discuss
Correct Answer: Rs. 2.04
Explanation:
| C.I. when interest compounded yearly |
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| = Rs. 5304. |
| C.I. when interest is compounded half-yearly |
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| = Rs. 5306.04 |
∴ Difference = Rs. (5306.04 - 5304) = Rs. 2.04
- 9. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
Options- A. Rs. 120
- B. Rs. 121
- C. Rs. 122
- D. Rs. 123 Discuss
Correct Answer: Rs. 121
Explanation:
| Amount |
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| = Rs. 3321. |
- 10. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
Options- A. 3
- B. 4
- C. 5
- D. 6 Also asked in: Bank Exams, Bank PO
Correct Answer: 4
Explanation:
| P | ❨ | 1 + | 20 | ❩ | n | > 2P | ⟹ | ❨ | 6 | ❩ | n | > 2. |
| 100 | 5 |
| Now, | ❨ | 6 | x | 6 | x | 6 | x | 6 | ❩ | > 2. |
| 5 | 5 | 5 | 5 |
So, n = 4 years.
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