Compound Interest problems
- 1. A sum of Rs. 550 was taken as a loan. This is to be repaid in two equal annual instalments. if the rate of interested be 20% compound annually then the value of each instalment is?
Options- A. Rs. 421
- B. Rs. 396
- C. Rs. 360
- D. Rs. 350 Discuss
Correct Answer: Rs. 360
Explanation:
Let the value of each instalment be Rs. x
Then, {x/(1 + 20/100) + x/(1 + 20/100)2} = 550
? 5x / 6 + 25x / 36 =550
? 55x / 36 = 550
? x = 360
- 2. If the simple interest on certain sum of money be Rs. 40 for 2 years and the compound interest on the same sum at the same rate and for the same time be Rs. 45. What is the principle?
Options- A. Rs. 70
- B. Rs. 90
- C. Rs. 85
- D. Rs. 80 Discuss
Correct Answer: Rs. 80
Explanation:
S.I. for 2 year = Rs. 40
S.I. for 1 year = Rs. 20
Rate = {(C.I. for 2 year - S.I. for 2 year) / (S.I. for 1 year)} x 100
= {(45 - 40) / 20} x 100 = 25%
? Principal = (S.I. x 100)/(Rate x Time)
= (40 x 100)/(25 x 2)
= Rs. 80
- 3. Neeraj saves Rs. 400 at the end of each year and lends this saving at 5% p.a. compound interest, How much will it worth at the end of 3 years?
Options- A. Rs. 1312. 50
- B. Rs. 1284
- C. Rs. 1315
- D. Rs. 1324.05 Discuss
Correct Answer: Rs. 1324.05
Explanation:
Amount after 3 years = 400(1 + 5/100)3 + 400(1 + 5/100)2 + 400(1 + 5/100)
= 400(1+ 5/100) {1+ 5/100)2 + (1 + 5/100) + 1 }
= 400(105/100) {(105/100)2 + (105/100) + 1}
= 400(21/20) {(21/20)2 + 21/20 + 1}
= 400(441/400 + 21/20 + 1)
= 400(441 + 420 + 400/400)
= 420(1261/400)
= Rs.1324.05
- 4. If a sum of money placed at compound interest becomes 3 times of itself in 3 years. In how many years will it be 9 times at the same rate of interest?
Options- A. 6 years
- B. 9 years
- C. 12 years
- D. 5 years Discuss
Correct Answer: 6 years
Explanation:
Let the principle be P then amount be 3P
? 3P =P(1 + r/100)3
? 3 = (1 + r/100)3
On squaring on both the sides,
? (3)2 = {(1 + r/100)3}2
? 9 = (1 + r/100)6
Hence,it will become 9 times in 6 years.
- 5. A person invested a certain amount at simple interest at the rate of 6 percent annum earning Rs. 900 as an interest at the end of three years. Had the interest been compounded every year. How much more interest would he have earned on the same amount with the same interest after three years?
Options- A. Rs. 38.13
- B. Rs. 25.33
- C. Rs. 55.08
- D. Rs. 35.30 Discuss
Correct Answer: Rs. 55.08
Explanation:
Certain sum for the person = (900 x 100)/(6 x 3) =Rs. 5000
? Interest on Rs. 5000 by C.I. = 5000(1 +6/100)3 - 5000 = Rs. 955.08
? More interest =Rs. (955.08 - 900) = Rs. 55.08
- 6. The difference between the simple and the compound interest compounded every six months at the rate of 10 percent per annum at the end of two years is Rs. 124.05. What is the sum?
Options- A. Rs. 10000
- B. Rs. 6000
- C. Rs. 12000
- D. Rs. 8000 Discuss
Correct Answer: Rs. 8000
Explanation:
Let the sum be Rs. P, then
? [ P(1 +5/100)4 - P] - [(P x 10 x 2)/100 ] = 124.05
Solving the above equation,we get P = Rs. 8000.
- 7. The cash price of a refrigerator is Rs. 7044. A customer paid Rs. 2000 in case and promised to pay the remaining money in 3 yearly equal instalments at the rate of 5% per annum compound interest. What is the value of each instalment?
Options- A. Rs. 1865
- B. Rs. 1868.28
- C. Rs. 1752
- D. Rs. 1852.20 Discuss
Correct Answer: Rs. 1852.20
Explanation:
Remaining money = 7044 - 2000 = Rs. 5044
If each installment is of Rs. P
When the amount is Rs. P at the end of first, second and third year at the rate of 5% then principal will be - P/(1 + 5/100), P/(1 +5/100)2 and P/(1 +5/100)3
? P/(1 +5/100) + P/(1 + 5/100)2 + P/(1 +5/100)3 = 5044
? P(20/21) + P(20/21)2 + P(20/21)3 = 5044
? P(20/21) { 1 +(20/21) + (20/21)2} = 5044
? P(20/21) {1 +20/21 +400/441} = 5044
? P(20/21) {441 + 420 + 400/441} =5044
? P(20/21) (1261/441) =5044
? P = (5044 x 21 x 441)/ (20 x 1261) = Rs. 1852.20
- 8. Vijay obtains a loan of 64000 against his fixed deposits. If the rate of interest be 2.5 paise per rupee per annum. Calculate the compound interest payable after 3 years?
Options- A. Rs. 4921
- B. Rs. 5020
- C. Rs. 4821
- D. Rs. 4920 Discuss
Correct Answer: Rs. 4921
Explanation:
P = Rs. 64000
r = 2.5 paise per rupee per annum (given)
= 0.025 rupee per rupee per annum
= 0.025 x 100 rupee per hundred rupee per annum
= 0.025 x 100 per cent per annum
= 2.5 per cent per annum
t = 3 years
C.I. = 6400[(1 + 2.5/100)3 - 1]
= 64000[(1.025)3 - 1]
= 64000[1.0769 - 1]
= 64000 x 0.0769
= 4921.6
= Rs. 4921
? The compound interest payable is Rs. 4921.
- 9. Divided Rs. 3903 between A and B, so that A's share at the end of 7 years may equal to B's share at the end of 9 years, compound interest being at 4 per cent?
Options- A. Rs. 2028, Rs. 1875
- B. Rs. 2018, Rs. 1885
- C. Rs. 2008, Rs. 1895
- D. Rs. 2038, Rs. 1865 Discuss
Correct Answer: Rs. 2028, Rs. 1875
Explanation:
We have (A's present share) (1 + 4/100)7 = (B's present share) (1 + 4/100)9
? A's present share/B's present share = (1 + 4/100)2 = (26/25)2 = 676/625
Dividing Rs. 3903 in the ratio of 676 : 625
? A's present share = 676/(676 + 625) of Rs .3903 = Rs. 2028
B's present share = Rs. 3903 - Rs. 2028 = Rs. 1875
- 10. Akash borrows ? 65000 at 10% per annum simple interest for 3 yr and lends it at 10% per annum compound interest for 3 yr , Find his gain after three years.?
Options- A. ? 2015
- B. ? 1330
- C. ? 1300
- D. None of these Discuss
Correct Answer: ? 2015
Explanation:
SI on ? 65000 at the rate of 10% for 3 yr
= (65000 x 10 x 3)/100 = ? 19500
CI on ? 65000 at the rate of 10% for 3 yr
= 65000(1 + 10/100)2 - 65000
= 65000(11 x 11 x 11 - 10 x 10 x 10)/1000 = ? 21515
? Required gain = 21515 - 19500 = ? 2015
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