Compound Interest problems
- 1. 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.l.= Rs.[100 x (1 +5/100)2] =Rs.41/4
? difference between C.I. and S.I. = Rs. (41/4-10) = Re.0.25
? 0.25 : 1.50 : : 100 : P
? P = (1.50 x 100) / 0.25 = Rs. 600
- 2. The simple interest on a certain sum for 2 years at 10% per annum is Rs.90. The corresponding compound interest is?
Options- A. Rs. 99
- B. Rs. 95.60
- C. Rs. 94.50
- D. Rs. 108 Discuss
Correct Answer: Rs. 94.50
Explanation:
Principle = (100 x interest) / (time x rate)
? Sum = (100 x 90) / (2 x 10) = Rs. 450
C.I. =Rs.[ 450 x (1 + 10/100)2 - 450] = Rs. 94.50
- 3. What is the principle amount which earns Rs. 132 as compound interest for the second years at 10% per annum?
Options- A. Rs. 1000
- B. Rs. 1200
- C. Rs. 1320
- D. None of these Discuss
Correct Answer: Rs. 1200
Explanation:
Let P the principle at the end of first year.
Then (P x 10 x 1)/100 =132
? P =1320
Let Q be the original principle
Then, Q + (Q x 10 x 1)/100 =1320
? Q =1200
- 4. Simple interest on a sum at 4% per annum for 2 years is Rs.80. The compound interest on the same sum for the same period is?
Options- A. Rs. 81.60
- B. Rs. 160
- C. Rs. 1081.60
- D. None of these Discuss
Correct Answer: Rs. 81.60
Explanation:
principle = (interest x 100) / (time x rate)
= Rs. (100 x 80)/(4 x 2) = Rs. 1000
? C.I. =Rs.[{1000 x (1 + 4/100)2 - 1000}]
= Rs. 81.60
- 5. 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 years
- B. 4 years
- C. 5 years
- D. 6 years Discuss
Correct Answer: 4 years
Explanation:
? P x (1 + 20/100)t > 2P
? (6/5)n > 2
Now, (6/5) x (6/5) x (6/5) x (6/5) > 2
? 1296/615 > 2
? t = 4 years
- 6. A sum of money amounts to Rs. 10648 in 3 years and Rs. 9680 in 2 years. The rate of interest is?
Options- A. 5%
- B. 10%
- C. 15%
- D. 20% Discuss
Correct Answer: 10%
Explanation:
Let P be the principle and R% per annum be the rate. Then,
P(1 + R/100)3 = 10648 ....(i)
and P(1 + R/100)2 = 9680 .....(ii)
on dividing (i) by (ii), we have
? (1 + R/100) = 10648/9680
? R/100 =968/9680 = 1/10
? R =100/10 = 10%
- 7. A sum is invested at compound interest payable annually. The interest in two successive years was Rs. 500 and Rs. 540. The sum is?
Options- A. Rs. 3750
- B. Rs. 5000
- C. Rs. 5600
- D. Rs. 6250 Discuss
Correct Answer: Rs. 6250
Explanation:
S.I. on Rs. 500 for 1 year = 540 - 500 = Rs. 40
? Rate = (100 x 40)/(500 x 1) = 8%
and Sum = Rs.(100 x 500)/(8 x 1) = Rs. 6250
- 8. The difference between simple interest and compound interest at the same rate for Rs. 5000 for 2 years is Rs. 72.The rate of interest is?
Options- A. 10%
- B. 12%
- C. 6%
- D. 8% Discuss
Correct Answer: 12%
Explanation:
? [5000 x (1 +R/100)2 - 5000] - (5000 x 2 x R)/100 =72
? 5000[(1 +R/100)2 - 1 - R/50] = 72
? 1 + R2/10000 + 2R/100 - 1 - R/5 = 72/5000
? R2 = (72/5000 x 10000) = 144
? R = 12%
- 9. A sum of money becomes Rs. 6690 after three years and Rs. 10035 after six years on compound interest. The sum is?
Options- A. Rs. 4400
- B. Rs. 4445
- C. Rs. 4460
- D. Rs. 4520 Discuss
Correct Answer: Rs. 4460
Explanation:
Let the principal be P,then
P(1 + R/100)3 = 6690
And P(1 + R/100)6 = 10,035
Now, dividing (ii)by (i),we get
? (1 + R/100)3 = 10035/6690 = 3/2
? P x 3/2 = 6690
? P = (6690 x 2/3 ) = Rs. 4460
- 10. What will be the compound interest of Rs. 8000 at 10% p.a. for 1 1/ 2 years. When compound interest is payable half yearly?
Options- A. Rs. 1261
- B. Rs. 1385
- C. Rs. 1480
- D. Rs. 1255 Discuss
Correct Answer: Rs. 1261
Explanation:
Yearly interest = 10%
Half yearly = 5%
Time = 11/2 = (3/2) x 2 half yearly = 3 half yearly
Amount = 8000(1 + 5/100)3
= 8000 x (21/20)3
= 8000 x 21/20 x 21/20 x 21/20
= Rs. 9261
Compound interest = Amount - Principal = 9261 - 8000
= Rs. 1261
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