Compound Interest problems
- 1. Vandana invested an amount of ? 8000 in a fixed deposit scheme for 2 yr at the rate of 5% pa compound interest. How much amount will Vandana get on maturity of the fixed deposit?
Options- A. ? 8000
- B. ? 8890
- C. ? 8888
- D. ? 8820 Discuss
Correct Answer: ? 8820
Explanation:
Given, P = ? 8000, R = 5% and n = 2 Yr
According to the formula,
Amount = p ( 1 + R / 100 )n
= 8000 ( 1 + 5/100 )2
= 8000 x (105/100)2
=8000 x (21/20) x (21/20)
= 20 x 21 x 21
= ? 8820
- 2. Raja invested ? 15000 at the rate of 10 % pa for 1 yr. If the interest is compound half-yearly, then find the amount received by Raja at the end of the year.
Options- A. ? 16537.50
- B. ? 18000
- C. ? 19000.50
- D. ? 20000 Discuss
Correct Answer: ? 16537.50
Explanation:
Given P = ? 15000 , R = 10 %
and n = 1 yr
Accounting to the formula,
Amount = P(1 + R/(2 x 100))2n
= 15000 x (1 + 5/100 )2
= 15000 x (105/100 )2
= 15000 x (21/20) x (21/20)
= ? 16537.50
- 3. What amount will be received on a sum of Rs 15000 in 1 1/ 4 yr at 12% pa, if interest is compounded quarterly?
Options- A. Rs 16596.88
- B. Rs 16789.08
- C. Rs 17630.77
- D. Rs 17389.12 Discuss
Correct Answer: Rs 17389.12
Explanation:
Given, P = Rs 15000, R = 12 %
and n = 11/4 = 5/4 Yr
According to the formula,
Amount = p [1 + R/(100 x 4)]4n
= 15000 x [1 + 12/(100 x 4)]4 x 5/4
= 15000(412/400)5
= 15000 (103/100)5
= 15000 x (103/100) x (103/100) x (103/100) x (103/100) x (103/100)
= (15 x 103 x 103 x 103 x 103 x 103) / 10000000
= Rs 17389.111
= Rs 17389.12 (approx )
- 4. The compound interest on ? 30000 at 7% pa for a certain time is ?4347. The time is
Options- A. 2 yr
- B. 2.5 yr
- C. 3 yr
- D. 4 yr Discuss
Correct Answer: 2 yr
Explanation:
Given, CI = ? 4347, P = ? 30000 and R = 7%
By formula, CI = P[(1 + R/100)n - 1 ]
? 4347 = 30000 [(1+7/100)n - 1]
? (107/100)n = (4347/30000) + 1
? (107/100)n = 34347/30000 = 11449/10000
? (107/100)n = (107/100)2
? n = 2
- 5. What is the difference between compound interest and simple interest for 2 yr on the sum of ? 1250 at 4% pa?
Options- A. ? 3
- B. ? 4
- C. ? 2
- D. ? 8 Discuss
Correct Answer: ? 2
Explanation:
Given, P = ? 1250, n = 2 yr and R = 4%
According to the formula,
Difference between compound interest and simple interest = PR2/1002
? Required difference = (1250 x 4 x 4)/(100 x 100) = ? 2
- 6. The difference between compound and simple rates of interest on ? 10000 for 3 yr at 5% per annum is
Options- A. ? 76.25
- B. ? 76.75
- C. ? 76.50
- D. ? 76 Discuss
Correct Answer: ? 76.25
Explanation:
Required difference = P(R/100)2 x [(300 + R)/100]
= 10000(5/100)2 (305/100)
= 76.25
- 7. A borrowed sum was paid in the two annual installments of ? 121 each. If the rate of compound interest is 10% pa, what sum was borrowed?
Options- A. ? 217.80
- B. ? 210
- C. ? 220
- D. ? 200 Discuss
Correct Answer: ? 210
Explanation:
According to the question,
Borrowed sum = [121/{1/(1 + 10/100)}] + 121/(1 + 10/100)2
= 121/(11/10) + 121/{(11/10) x (11/10)]
=110 + 100
= ? 210
- 8. If ? 3000 amounts to ?4329 at compound interest in a certain time , then ? 3000 amounts to what inhalf of the time?
Options- A. ? 3400
- B. ? 3600
- C. ? 38000
- D. ? 3520 Discuss
Correct Answer: ? 3600
Explanation:
Let rate = R% and time = n yr
Then, 4320 = 3000(1+R/100)n
? (1+R/100)n = 4320/3000 = 1.44
? (1 + R/100)n/2 = ?1.44 = 1.2
? Required amount for n/2 yr
= 3000(1+ R/100)n/2
= 3000 x 1.2 = ? 3600
- 9. The population of a city increases at the rate of 5% pa. If the present population of the city is 185220, then what was its population 3 yr ago?
Options- A. 181500
- B. 183433
- C. 160000
- D. 127783 Discuss
Correct Answer: 160000
Explanation:
Given, P = 185220 R = 5% (increases) and n = 3 yr
According to the formula,
Population n yr ago = P/(1 + R/100)n
= 185220/(1 + 5/100)3
= 185220/[(21/20) x (21/20) x (21/20)]
= [185220 x 20 x 20 x 20] / [21 x 21 x 21]
= 20 x 20 x 20 x 20
= 160000
- 10. A sum of ? 400 amounts to ? 441 in 2 yr. What will be its amount, if the rate of interest is increased by 5%?
Options- A. ? 484
- B. ? 560
- C. ? 512
- D. ? 600 Discuss
Correct Answer: ? 484
Explanation:
According to the given condition.
441 = 400 (1 + R/100)2
? 441/400 = (1 + R/100)2
? (21/20)2 = (1 + R/100)2
? 21/20 = 1 + R/100
? (21/20) - 1 = R/100
? R/100 = 1/20
? R = 5%
? new rate = 5 + 5 = 10%
? Amount = 400 (1 + 10/100)2
= 400 x (11/10) x (11/10)
= ? 484
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