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- Question
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
- Correct Answer
- Rs. 3972
ExplanationLet 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.
Compound Interest problems
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- 1. 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.
- 2. 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. - 3. 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= 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
- 4. 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%
- 5. 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 - 6. 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.
- 7. 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%.
- 8. 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. = Rs. [ 4000 x ❨ 1 + 10 ❩ 2 - 4000 ] 100 = Rs. ❨ 4000 x 11 x 11 - 4000 ❩ 10 10 = Rs. 840. ∴ Sum = Rs. ❨ 420 x 100 ❩ = Rs. 1750. 3 x 8 - 9. 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 Discuss
Correct Answer: 625
Explanation:
Let the sum be Rs. x. Then,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.
- 10. A, B and C enter into a partnership in the ratio 7⁄2 : 4⁄3 : 6⁄5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:
Options- A. Rs. 2100
- B. Rs. 2400
- C. Rs. 3600
- D. Rs. 4000 Discuss
Correct Answer: Rs. 4000
Explanation:
Ratio of initial investments = ❨ 7 : 4 : 6 ❩ = 105 : 40 : 36. 2 3 5 Let the initial investments be 105x, 40x and 36x.
∴ A : B : C = ❨ 105x x 4 + 150 x 105x x 8 ❩ : (40x x 12) : (36x x 12) 100 = 1680x : 480x : 432x = 35 : 10 : 9.
Hence, B's share = Rs. ❨ 21600 x 10 ❩ = Rs. 4000. 54
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