Compound Interest problems
- 1. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
Options- A. Rs. 2160
- B. Rs. 3120
- C. Rs. 3972
- D. Rs. 6240
- E. None of these Discuss
Correct Answer: Rs. 3972
Explanation:
| ∴ R = | ❨ | 100 x 60 | ❩ | = 10% p.a. |
| 100 x 6 |
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
| ∴ C.I. |
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| = 3972. |
- 2. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
Options- A. 2
- B.
2 1 2 - C. 3
- D. 4 Discuss
Correct Answer: 2
Explanation:
Let the time be n years.
| Then, 30000 | ❨ | 1 + | 7 | ❩ | n | = 34347 |
| 100 |
| ⟹ | ❨ | 107 | ❩ | n | = | 34347 | = | 11449 | = | ❨ | 107 | ❩ | 2 |
| 100 | 30000 | 10000 | 100 |
∴ n = 2 years.
- 3. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
Options- A. 8
- B. 10
- C. 12
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 8
Explanation:
| [ | 15000 x | ❨ | 1 + | R | ❩ | 2 | - 15000 | ] | - | ❨ | 15000 x R x 2 | ❩ | = 96 | |
| 100 | 100 |
| ⟹ 15000 | [ | ❨ | 1 + | R | ❩ | 2 | - 1 - | 2R | ] | = 96 |
| 100 | 100 |
| ⟹ 15000 | [ | (100 + R)2 - 10000 - (200 x R) | ] | = 96 |
| 10000 |
| ⟹ R2 = | ❨ | 96 x 2 | ❩ | = 64 |
| 3 |
⟹ R = 8.
∴ Rate = 8%.
- 4. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
Options- A. Rs. 1550
- B. Rs. 1650
- C. Rs. 1750
- D. Rs. 2000 Discuss
Correct Answer: Rs. 1750
Explanation:
| C.I. |
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| = Rs. 840. |
| ∴ Sum = Rs. | ❨ | 420 x 100 | ❩ | = Rs. 1750. |
| 3 x 8 |
- 5. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
Options- A. 625
- B. 630
- C. 640
- D. 650 Also asked in: Bank Exams, Bank PO
Correct Answer: 625
Explanation:
| C.I. = | [ | x | ❨ | 1 + | 4 | ❩ | 2 | - x | ] | = | ❨ | 676 | x | - x | ❩ | = | 51 | x. |
| 100 | 625 | 625 |
| S.I. = | ❨ | x x 4 x 2 | ❩ | = | 2x | . |
| 100 | 25 |
| ∴ | 51x | - | 2x | = 1 |
| 625 | 25 |
⟹ x = 625.
- 6. The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is Rs. 1.50. The sum is?
Options- A. Rs. 600
- B. Rs. 500
- C. Rs. 400
- D. Rs. 300 Discuss
Correct Answer: Rs. 600
Explanation:
Let the sum be Rs . 100 then
S.I. = Rs.(100 x 5 x 2/100)= Rs. 10
C.I = Rs. [{100 x (1 + 5/100)2} - 100] = Rs. 41/4
? Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25
? 0.25 : 150 : : 100 : P
? P = (1.50 x 100) / 0.25 = Rs. 600
- 7. If the compound interest on a certain sum for 2 years at 12.5% per annum is 170, the simple interest is?
Options- A. Rs. 150
- B. Rs. 152.50
- C. Rs. 160
- D. Rs. 162.50 Discuss
Correct Answer: Rs. 160
Explanation:
Let the principle is P
so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170
? p x (112.5/100) x (112.5/100) - p = 170
? P [ 12656.25 - 10000 ] = 170 x 10000
? p = (170 x 10000) / 2656.25
Simple interest SI = (P x T x R )/100
= [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100
= 160
- 8. A sum amounts to Rs. 1352 in 2 years at 4% compound interest.The sum is?
Options- A. Rs. 1300
- B. Rs. 1250
- C. Rs. 1260
- D. Rs. 1200 Discuss
Correct Answer: Rs. 1250
Explanation:
Let the sum be P.
Then, 1352 = P(1 +4/100)2
? 1352 = P x 26/25 x 26/25
? P = (1352 x 25 x 25) / (26 x 26) = 1250
? Principal = Rs. 1250
- 9. Rs. 800 at 5% per annum compound interest will amount to Rs. 882 in?
Options- A. 1 years
- B. 2 years
- C. 3 years
- D. 4 years Discuss
Correct Answer: 2 years
Explanation:
Let time be t years
? 882 = 800( 1 +5/1000)t
? 882/800 = (21/20)t
? (21/20)2 = (21/20)t
? t =2
? Time = 2years
- 10. The compound interest on Rs. 2800 for 1 1/ 2 years at 10% per annum is?
Options- A. Rs. 441.35
- B. Rs. 436.75
- C. Rs. 434
- D. Rs. 420 Discuss
Correct Answer: Rs. 434
Explanation:
? Final Amount = Rs.[2800 x (1 + 10/100) x (1 +5/100)]
= Rs. [ 2800 x 11/10 x 21/20 ]
= Rs. 3234
? Required C.I. = Rs.(3234 - 2800) = Rs .434
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