Compound Interest problems
- 1. If Rs. 7500 are borrowed at compound interest at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options- A. Rs. 8082
- B. Rs. 7800
- C. Rs. 8100
- D. Rs. 8112 Discuss
Correct Answer: Rs. 8112
Explanation:
Amount = Rs. 7500(1 + 4/100)2
= Rs. 7500 x 26/25 x 26/25
= Rs .8112
- 2. A sum amounts to Rs. 3149.29 in 3 years at compound interest. The sum is?
Options- A. Rs. 1500
- B. Rs. 2000
- C. Rs. 2500
- D. Rs. 3000 Discuss
Correct Answer: Rs. 2500
Explanation:
Let P be the principle and R% per annum be rate
Then, P(1 +R/100)3 = 3149.28 .....(i)
and P(1 + R/100)2 = 2916 .....(ii)
on dividing(i) and (ii) we get
? (1 + R/100) = 3149.28/2916
? R/100 = 233.28/2916
? R = 233.28/2916 x 100 = 8%
Now, P(1 + 8/100)2 = 2916
? P x 27/25 x 27/25 = 2916
? P = (2916 x 25 x 25)/(27 x 27)
= Rs. 2500
- 3. A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times itself in?
Options- A. 15 years
- B. 20 years
- C. 12 years
- D. 10 years Discuss
Correct Answer: 15 years
Explanation:
Let the principal be P and rate be r%.Then
2P = P(1 + r/100)5
? (1 + r/100)5 = 2
Let it be 8 times in t years, then
? 8P = P(1 + r/100)t
? (1 + r/100)t = 8
? (2)3 ? (1 + r/100)15
? t =15 year.
- 4. The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 420. The simple interest on the same sum at the same rate and for the same time will be?
Options- A. Rs. 350
- B. Rs. 375
- C. Rs. 380
- D. Rs. 400 Discuss
Correct Answer: Rs. 400
Explanation:
Let the principal be P. Then,
? P(1 +10/100)2 - P =420
? P(121 - 100/100) =420
? P = Rs. 2000
? Requared S.I.= Rs.(2000 x 2 x 10)/100
= Rs. 400
- 5. Rs. 1600 at 10% per annum compounded half yearly amount to Rs. 1944.81 in?
Options- A. 2 years
- B. 3 years
- C. 11/2 years
- D. 21/2 Discuss
Correct Answer: 2 years
Explanation:
1600(1 +5/100)t = 1944.81
? (21/20)t =194481/160000 =(441/400)2 = (21/20)4
? T = 4( half years)
? Required time =2 years
- 6. What will be the approximate compound interest on Rs. 101005 at 10% p.a. for 3 years?
Options- A. Rs. 4500
- B. Rs. 3000
- C. Rs. 3300
- D. Rs. 3600 Discuss
Correct Answer: Rs. 3300
Explanation:
Compound interest = P {(1 + r/100)t - 1}
= 10105 { (1 +10/100)3 - 1}
=10105 {(11/10)3 - 1}
=10105 {1331/1000 - 1}
=10105(331/1000)
= 3344.755
= Rs. 3300(app.)
- 7. If the compound interest of a certain sum of money for two successive years be Rs, 225 and Rs. 238.50. What is the rate of interest per annum?
Options- A. 5%
- B. 6%
- C. 71/2
- D. 10% Discuss
Correct Answer: 6%
Explanation:
From question it is clear that the simple interest of rupees 225 for one year is 238.50 - 225.
So Rate = (simple interest x 100 )/( time x principle)
= {(238.50 - 225) x 100}/(225 x 1) % = 6%
- 8. A moneylender lends Rs. 2000 for 6 months at 20% per annum whereas the interest is compounded quarterly. After the given period he will get the amount of?
Options- A. Rs. 2205
- B. Rs. 2200
- C. Rs. 2160
- D. Rs. 2040 Discuss
Correct Answer: Rs. 2205
Explanation:
For the quarterly interest,
Time = (6/12) year x 4 = 2 quarterly
Rate = 20/4 = 5%
(? On quarterly interest time is multiplied by 4 and rate is divided by 4)
Hence,required amount = Principal (1 + Rate/100)Time
= 2000(1 +5/10)2
= 2000(21/20)2
= Rs. 2205
- 9. In what time will Rs. 6250 amount to Rs. 6632.55 at 4% compound interest payable half yearly?
Options- A. 3 years
- B. 3/2 years
- C. 1 years
- D. 5/2 years Discuss
Correct Answer: 3/2 years
Explanation:
Since Interest accumulates half yearly so effective rate = R/2 = 4/2 = 2.
And effective time is 2t.
? 6250 [1 + 2/100]2t = 6632.55
? (1 +2/100)2t = 663255/625000 = 132651/125000 = (51/50)3
? (51/50)2t = (51/50)3
? 2t =3
? t = 3/2 years
- 10. Find the effective annual rate of 4 per cent per annum compound interest paid quarterly.?
Options- A. 4.0604%
- B. 4.604%
- C. 5.0605%
- D. 5.605% Discuss
Correct Answer: 4.0604%
Explanation:
Effective annual rate = 100(1 + {(4/4) /100})4 - 100
= (101/100)4 x 100 - 100
= 104.0604 - 100
= 4.0604%
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