Compound Interest problems
- 1. The population of a country is 100 crore and it is the possibility that the population will become 13.31 crore in 3 yr. What will be the annual rate percent on this growth?
Options- A. 8%
- B. 12.7%
- C. 10%
- D. 15% Discuss
Correct Answer: 10%
Explanation:
Given, P = 10 crore
and population after 3 yr = 13.31 crore
According to the formula,
Population after n yr = P (1 + R/100 )n
? 13.31 = 10 (1 + R/100 )3
? 1331/1000 = (1 + R/100 )3
? (11/10)3 = (1 + R/100 )3
? 1 + R/100 = 11/10
? R/100 = 11/10 - 1 = 1/10
? R = 10%
- 2. If the different between the compound interest and the simple interest on a certain sum for 2 yr at 8% per annum is ? 32, then the sum is
Options- A. ? 5000
- B. ? 5550
- C. ? 6000
- D. ? 5250 Discuss
Correct Answer: ? 5000
Explanation:
Given, R = 8%, D = ? 32 and P = ?
By formula, D = P(R/100)2
? 32 = P(8/100)2
? P = 32 x [(100 x 100)/(8 x 8)]
= ? 5000
- 3. What will be the principle, if the rate of 5% per annum can yield ? 410 as compound interest in 2 yr?
Options- A. ? 4000
- B. ? 42000
- C. ? 8000
- D. ? 21000 Discuss
Correct Answer: ? 4000
Explanation:
Let the amount be ? P
R = 5%, n = 2 yr and CI ? 410
By formula, CI = P [ (1 + R/100)n - 1 ]
? 410 = P [ (1 + 5/100)2 - 1]
? 410 = P [ (1 + 1/20)2 - 1]
? 410 = P [ (21/20)2 - 1]
? 410 = P [ 441/400 - 1 ]
? 410 = P [(441 - 400) /400] = P x 41/400
? P = (410 x 400)/41
? P = ? 4000
- 4. At what per cent annual compound interest, rate, a certain sum amounts to its 27 times in 3 yr?
Options- A. 100%
- B. 150%
- C. 75%
- D. 200% Discuss
Correct Answer: 200%
Explanation:
Let sum = P
and given that n = 3 yr
According to the question,
Amount = 27 P
According to the formula,
Amount = P (1 + R/100)n
? 27 P = P (1 + R/100)3
? 27 = (1 + R/100)3
? (1 + R/100)3 = (3)3
? 1 + R/100 = 3
? R/100 = 3 - 1 = 2
? R = 200%
- 5. The compound interest on Rs. 30000 at 7% per annum for a
certain time is Rs. 4347. The time is?
Options- A. 2 years
- B. 21/2 years
- C. 3 years
- D. 4 years Discuss
Correct Answer: 2 years
Explanation:
? 30000 x (1 +7/100)t = 30000 + 4347
? (107/100)t = 34347/30000
?11449/10000 = (107/100)2
? Time = 2 years
- 6. The difference of compound interest on Rs.800 for 1 year at 20% per annum when compound half yearly and quarterly is?
Options- A. Nil
- B. Rs. 2.50
- C. Rs. 4.40
- D. Rs. 6.60 Discuss
Correct Answer: Rs. 4.40
Explanation:
C.I. when reckoned half yearly
= Rs.[800 x (1 + 10/100)2 - 800]
= Rs. 168
C.I.when reckoned quarterly
= Rs.800[(1 + 5/100)4 - 1]
= 800[(194481 - 160000)/160000]
= 34481/200
= Rs.172.40
? Required difference =Rs.(172.40 - 168)
= Rs.4.40
- 7. The compound interest of Rs. 20480 at 6 1/ 4% per annum for 2 years 73
days is?
Options- A. Rs. 3000
- B. Rs. 3131
- C. Rs. 2929
- D. Rs. 3636 Discuss
Correct Answer: Rs. 2929
Explanation:
C.I. = Rs[20480 x(1 +25/4 x 100)2 (1 + 1/5 x 25/4 x 100) - 20480 ]
= Rs.[(20480 x 17/16 x 17/16 x 81/80) - 20480]
= 20480[23409 - 20480/20480]
= Rs .2929
- 8. The difference in compound interest and simple interest for 2 years on a sum of money is Rs. 160. If the simple interest for 2 years be Rs. 2880, the rate per cent is?
Options- A. 55/9%
- B. 121/2%
- C. 111/9%
- D. 9% Discuss
Correct Answer: 111/9%
Explanation:
? S.I. for 1 year =Rs. 1440
? S.I. on Rs.1440 for 1 year = Rs.160
Hence, ? Rate per cent = (100 x 160) / (1440 x 1) %
= 100/9%
= 111/9%
- 9. The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound and simple interest for 3 years will be?
Options- A. Rs .48
- B. Rs. 66.56
- C. Rs. 98.56
- D. None of these Discuss
Correct Answer: Rs. 98.56
Explanation:
S.I. for first year = Rs. 400
S.I. on Rs .400 for 1 year =Rs. 32
? Rate = (interest x 100)/(principle x time) = (100 x 32)/(400 x 1) = 8%
Hence, the difference for 3rd year is S.I.on Rs. 832
= Rs.(832 x 8/100)
= Rs. 66.56
? Total difference = Rs.(32 + 66.56)
= Rs. 98.56
- 10. A man borrows Rs. 4000 from a bank at 7 1/ 2% compound interest. At the end of every he pays Rs. 1500 as part repayment of loan and interest. How much does he still owe to the bank after there such installments?
Options- A. Rs. 123.25
- B. Rs. 125
- C. Rs. 400
- D. Rs. 469.18 Discuss
Correct Answer: Rs. 123.25
Explanation:
Balance = Rs.[{4000 x (1 x 15/2 x 100)3} - {1500 x (1 + 15/2 x 100)2 + 1500 x (1 + 15/2 x 100) + 1500}]
= Rs. 123.25
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