Compound Interest Aptitude

Compound Interest problems are a key aspect of financial aptitude tests, focusing on calculating the interest on an initial principal balance, where the interest from previous periods is added to the principal. Understanding Compound Interest is essential for assessing investments, savings, loans, and other financial products.

1. What will be the compound interest on $2000 after 3 years at the rate of 10% per annum?

Compound Interest = Principal × (1 + Rate/100)^Time - Principal
= $2000 × (1 + 10/100)^3 - $2000
= $2000 × 1.331 - $2000
= $662.

2. Find the compound interest on $5000 for 2 years at 4% per annum compounded annually.

Compound Interest = $5000 × (1 + 4/100)^2 - $5000
= $5000 × 1.0816 - $5000
= $408.

3. A sum of money becomes double in 5 years at compound interest. What is the rate of interest?

Let the principal be P. Then, amount = 2P.
2P = P × (1 + R/100)^5
(1 + R/100)^5 = 2
R ≈ 14.4%.

4. The compound interest on a certain sum for 2 years at 10% per annum is $210. Find the sum.

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$210 = P × (1 + 10/100)^2 - P
P = $2000.

5. If the compound interest on a sum for two years at 12% per annum is $144, what is the simple interest on the same sum at the same rate and for the same time?

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$144 = P × (1 + 12/100)^2 - P
P = $1000.
Simple Interest = P × R × T / 100
= $1000 × 12 × 2 / 100
= $240.

6. The compound interest on $1500 at 10% per annum for 2 years compounded semi-annually is:

Rate = 10/2 = 5% per half-year, Time = 2 × 2 = 4 half-years.
Compound Interest = $1500 × (1 + 5/100)^4 - $1500
= $1500 × 1.21550625 - $1500
= $330.

7. A sum becomes $1296 in 3 years and $1728 in 4 years at compound interest. The sum is:

$1296 × (1 + R/100) = $1728
(1 + R/100) = 1.333
R ≈ 33.3%
Principal = $1296 / (1 + 33.3/100)^3
≈ $900.

8. The difference between the compound interest and simple interest on $8000 for 2 years at 5% per annum is:

Simple Interest = P × R × T / 100
= $8000 × 5 × 2 / 100
= $800.
Compound Interest = $8000 × (1 + 5/100)^2 - $8000
= $8000 × 1.1025 - $8000
= $820.
Difference = $820 - $800 = $20.

9. The compound interest on a certain sum for 2 years at 10% per annum is $1050. Find the sum.

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$1050 = P × (1 + 10/100)^2 - P
P = $5000.

10. A sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it become 9 times itself?

Amount = P × (1 + R/100)^T
3P = P × (1 + R/100)^3
(1 + R/100)^3 = 3
For 9 times, 9P = P × (1 + R/100)^T
(1 + R/100)^T = 9
T = 2 × 3 = 6 years.

11. If the compound interest on a certain sum for 2 years at 10% per annum is $2100, find the principal.

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$2100 = P × (1 + 10/100)^2 - P
P = $20000.

12. The compound interest on $10000 for 3 years at 5% per annum, compounded annually, is:

Compound Interest = Principal × (1 + Rate/100)^Time - Principal
= $10000 × (1 + 5/100)^3 - $10000
= $10000 × 1.157625 - $10000
= $1576.25.

13. A sum of $5000 amounts to $6050 in 2 years at a certain rate of compound interest. Find the rate of interest.

Amount = Principal × (1 + Rate/100)^Time
$6050 = $5000 × (1 + R/100)^2
(1 + R/100)^2 = 1.21
R ≈ 10%.

14. The difference between the compound interest and the simple interest on a certain sum of money for 2 years at 8% per annum is $64. The sum is:

Let the principal be P.
Difference = P × (R/100)^2
$64 = P × (8/100)^2
P = $9000.

15. The compound interest on $15000 for 2 years at 8% per annum, compounded annually, is:

Compound Interest = Principal × (1 + Rate/100)^Time - Principal
= $15000 × (1 + 8/100)^2 - $15000
= $15000 × 1.1664 - $15000
= $2464.

16. If the compound interest on a sum for 3 years at 10% per annum is $3310, find the sum.

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$3310 = P × (1 + 10/100)^3 - P
P = $10000.

17. A sum of money becomes $1064.78 in 2 years and $1157.63 in 3 years on compound interest. Find the rate of interest.

Amount for 3rd year / Amount for 2nd year = (1 + R/100)
$1157.63 / $1064.78 = 1 + R/100
R ≈ 8%.

18. If the compound interest on a certain sum for 2 years at 15% per annum is $1230, find the principal.

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$1230 = P × (1 + 15/100)^2 - P
P = $4000.

19. The compound interest on $2500 for 1 year at 20% per annum, compounded semi-annually, is:

Rate = 20/2 = 10% per half-year, Time = 2 half-years.
Compound Interest = $2500 × (1 + 10/100)^2 - $2500
= $2500 × 1.21 - $2500
= $510.

20. A sum of $8000 amounts to $9261 in 3 years at a certain rate of compound interest. Find the rate of interest.

Amount = Principal × (1 + Rate/100)^Time
$9261 = $8000 × (1 + R/100)^3
(1 + R/100)^3 = 1.157625
R ≈ 5%.

21. The difference between the compound interest and the simple interest on a certain sum of money for 2 years at 7% per annum is $49. The sum is:

Let the principal be P.
Difference = P × (R/100)^2
$49 = P × (7/100)^2
P = $7500.

22. The compound interest on $6000 for 2 years at 10% per annum, compounded annually, is:

Compound Interest = Principal × (1 + Rate/100)^Time - Principal
= $6000 × (1 + 10/100)^2 - $6000
= $6000 × 1.21 - $6000
= $1260.

23. If the compound interest on a sum for 2 years at 12% per annum is $1440, find the sum.

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$1440 = P × (1 + 12/100)^2 - P
P = $6000.

24. A sum of money at compound interest amounts to $2500 in 2 years and to $3000 in 3 years. Find the rate of interest.

Amount for 3rd year / Amount for 2nd year = (1 + R/100)
$3000 / $2500 = 1 + R/100
R ≈ 10%.

25. The compound interest on a certain sum for 3 years at 10% per annum is $993. What is the principal?

Let the principal be P.
Compound Interest = P × (1 + R/100)^T - P
$993 = P × (1 + 10/100)^3 - P
P = $3000.