Compound Interest problems
- 1. In what time will Rs. 390625 amount to Rs. 456976 at 4 per cent compound interest?
Options- A. 2 years
- B. 4 years
- C. 3 years
- D. 5 years Discuss
Correct Answer: 4 years
Explanation:
? P(1 + r/100)t = A
? 390625(1 + 4/100)t = 456976
? (1 + 4/100)t = 456976/390625 =(26/25)4
? (26/25)t = (26/25)4
? t = 4
? The required time is 4 years.
- 2. Find the effective annual rate of 5 per cent per annum compound interest paid half yearly?
Options- A. 1.025%
- B. 6.0625%
- C. 5.062%
- D. None of these Discuss
Correct Answer: 5.062%
Explanation:
The amount of Rs. 100 in one year at compound interest at 5% per annum payable half yearly.
= Rs. 100(1 + 5/2 /100)2
=Rs. 100(102.5/100)2
=Rs. 100(1.025)2
=Rs. 105.0625
Thus, the nominal rate of 5% payable half yearly has the same effect as the rate of 5.0625 per cent would have, if payable yearly.
Hence 5.0625 per cent is called the effective annual rate 5% per annum payable half yearly.
- 3. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Options- A. 7%
- B. 7.5%
- C. 6%
- D. 6.5% Discuss
Correct Answer: 6%
Explanation:
Let the rate be R% per annum.
Then,
1200 x (1 + R/100)2 = 1348.32
? (1 + R/100)2 =1348.32/1200 = 1.1236 = (1.06)2
? (1 + R/100) =1.06
? R/100 = 0.06
? R = 6%
- 4. A sum of ? 2400 deposited at CI, Double after 5 yr. After 20 yr it will become?
Options- A. ? 24000
- B. ? 38400
- C. ? 19200
- D. Cannot be determined Discuss
Correct Answer: ? 38400
Explanation:
2P = P (1 + R/100) 5
? 24 P = P(1 + R/100)20
? The amount becomes 24 times
= 16 times and required amount = 2400 x 16 = ? 38400
- 5. Rohit earns an interest of ? 1656 for the third year and ? 1440 for the second year on the same sum. Find the rate of interest if it is lent at compound interest?
Options- A. 18%
- B. 12%
- C. 15%
- D. None of these Discuss
Correct Answer: 15%
Explanation:
Interest on ? 1440 = ? 216 for the third year
? Rate percentage = (216 x 100)/(1440 x 1) = 15 %
- 6. What will be the compound interest on a sum of ? 50000 after 3 yr at the rate of 12% pa?
Options- A. ? 80000
- B. ? 70246.40
- C. ? 20246.40
- D. ? 70000 Discuss
Correct Answer: ? 20246.40
Explanation:
Given, P = ? 50000, R = 12% and n = 3 Yr
According to the formula,
Amount = P (1 + R/100 )n
= 50000 (1 + 12/100 )3
= 50000 x (28/25) x (28/25) x (28/25)
= 16 x (28 x 28 x 28)/ 5 = 351232/5
= ? 70246.40
? CI = 702446.40 - 50000 = ? 20246.40
- 7. A sum amounts to ? 1352 in 2 yr at 4% compound interest. The sum is
Options- A. ? 1250
- B. ? 1200
- C. ? 1300
- D. ? 1260 Discuss
Correct Answer: ? 1250
Explanation:
Using the formula, A = p ( 1 + R/100 )n
? 1352 = p(1 + 4/100 )2
? 1352 = p(1.04 )2
? p = 1352/(1.04)2 = ? 1250
- 8. What will be the present worth of ? 169 due in 2 yr at 4 % pa compound interest?
Options- A. ? 156.25
- B. ? 160
- C. ? 150.50
- D. ? 154.75 Discuss
Correct Answer: ? 156.25
Explanation:
Given R = 4 %, n = 2 yr and A = ? 169.
P = ?
Amount = P(1 + R/100)n
? 169 = P(1 + 4/100 )2
? 169 = P(26/25)2
? P = 169 x (25 x 25)/(26 x 26)
? P = 105625 / 676
= ? 156.25
- 9. Find the compound interest on ? 31250 at 16 % pa compounded quaterly for 9 months.
Options- A. ? 4000
- B. ? 3902
- C. ? 3500
- D. ? 4200 Discuss
Correct Answer: ? 3902
Explanation:
Given, P = ? 31250,
n = 9 Month = 3 quarters and
R = 16% pa = 4% per quarter
According to the formula
Amount = P(1 + R/100 )n
= 31250(1 + 4/100 )3
= 31250 x (26/25) x (26/25) x (26/25)
= ? 35150
? CI = 35152 - 31250
= ? 3902
- 10. A sum amounts to ? 2916 in 2 yr and ? 3149.28 in 3 yr at compound interest. The sum is?
Options- A. ? 1500
- B. ? 2500
- C. ? 2000
- D. ? 3000 Discuss
Correct Answer: ? 2500
Explanation:
Let required amount be ? P.
According to the question,
2916 = P (1 + R/100)2 ... (i)
and 3149.28 = P(1 + R/100)3 ... (ii)
On dividing Eq. (ii) by Eq. (i), we get
1 + R/100 = 3149.28/2916
? R/100 = (3149.28/2916) - 1
? R = (233.28/2916) x 100 = 8%
From Eq. (i),
P = (2916 x 100 x 100)/(108 x 108)
= ? 2500
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