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- Question
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
- Correct Answer
- Rs. 2.04
ExplanationC.I. when interest
compounded yearly= Rs. [ 5000 x ❨ 1 + 4 ❩ x ❨ 1 + ½ x 4 ❩ ] 100 100 = Rs. ❨ 5000 x 26 x 51 ❩ 25 50 = Rs. 5304. C.I. when interest is
compounded half-yearly= Rs. [ 5000 x ❨ 1 + 2 ❩ 3 ] 100 = Rs. ❨ 5000 x 51 x 51 x 51 ❩ 50 50 50 = Rs. 5306.04 ∴ Difference = Rs. (5306.04 - 5304) = Rs. 2.04
Compound Interest problems
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- 1. 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%
- 2. 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 - 3. 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 = Rs. [ 25000 x ❨ 1 + 12 ❩ 3 ] 100 = Rs. ❨ 25000 x 28 x 28 x 28 ❩ 25 25 25 = Rs. 35123.20 ∴ C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20
- 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% Discuss
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. 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 = Rs. [ 8000 x ❨ 1 + 5 ❩ 2 ] 100 = Rs. ❨ 8000 x 21 x 21 ❩ 20 20 = Rs. 8820. - 6. 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:
∴ C.I. = Rs. (3321 - 3200) = Rs. 121Amount = Rs. [ 1600 x ❨ 1 + 5 ❩ 2 + 1600 x ❨ 1 + 5 ❩ ] 2 x 100 2 x 100 = Rs. [ 1600 x 41 x 41 + 1600 x 41 ] 40 40 40 = Rs. [ 1600 x 41 ❨ 41 + 1 ❩ ] 40 40 = Rs. [ 1600 x 41 x 81 ] 40 x 40 = Rs. 3321. - 7. 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 Discuss
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.
- 8. 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:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.∴ R = ❨ 100 x 60 ❩ = 10% p.a. 100 x 6 Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
∴ C.I. = Rs. [ 12000 x { ❨ 1 + 10 ❩ 3 - 1 ] ] 100 = Rs. ❨ 12000 x 331 ❩ 1000 = 3972. - 9. 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:
Amount = Rs. (30000 + 4347) = Rs. 34347.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.
- 10. 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%.
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