Aquileo | Compound Interest Practice Questions (Easy)

Compound interest is the interest on a loan or investment that is calculated based on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, where the interest is calculated only on the initial principal, compound interest grows faster because it is applied to the new balance after each compounding period.

The formula to calculate compound interest is:

A = P(1 + r/n)^nt
C.I. = A - P
A represents the total amount of money after compounding,
P represents the initial amount,
r is the annual rate of interest,
n represents the number of times interest is compounded in a year, and
t represents the number of years.
C.I. is Compound Interest

Solved Examples on (C.I.)Compound Interest (Easy)

Question 1: Find the compound interest on Rs 30000 at 7% interest compounded annually for two years.
Solution:

Principal P = Rs 30000
Rate R = 7%
Time = 2 year
By formula:
A = 30000 (1 + 7/100)²
A = 30000 (107/100)²
A = 34347
Compound Interest = A - P = 34347 - 30000 = 4347
Answer: Interest = ₹4347

Question 2: If you deposit $15000 into an account paying 8% annual interest compounded yearly. Find the amount and interest after 6 years.
Solution:

In this example we have P = $15000 , r = 8% , n = 1 and t = 6 years
Put the values in the Formula: A = P(1 + n/r)ⁿ^⋅^t
A = 15000(1 + (0.08/1))^{1 ⋅ 6}
A = 15000 ⋅ (1.08)⁶
A = 15000 ⋅ 1.5869
A = 23803
To find interest we use formula C.I. = A - P, since A = $23803 and P = $15000 we have:
C.I. = 23803 − 15000
C.I. = 8803
Answer:
Interest = $8803
Amount = $23803

Question 3: Calculate the compound interest on $3,000 at an annual interest rate of 10%, compounded half-yearly, over a period of 2 years.
Solution:

P = $3000, r = 10%, n = 2 and t = 2 years
After plugging the given information we have:
A = 3000 (1 + (0.1/2))^{2 ⋅ 2}
A = 3000 ⋅ (1.05)⁴
A = 3000 ⋅ 1.2155
A = 3646.5
To find interest we use formula C.I. = A - P, since A = $3646.5 and P = $3000 we have:
C.I. = 3646.5 − 3000
C.I. = 646.5
Answer:
Interest = $646.5
Amount = $3646.5

Question 4: If you deposit $5000 into an account paying 5% annual interest compounded yearly. Find the amount and interest after 2 years.
Solution:

In this example we have P = $5000 , r = 5% , n = 1 and t = 2 years
Put the values in the Formula: A = P(1 + n/r)ⁿ^⋅^t
A = 5000(1 + (0.05/1))^1⋅2
A = 5000 ⋅ (1.05)²
A = 5000 ⋅ 1.1025
A = 5512.5
To find interest we use formula C.I. = A - P, since A = $5512.5 and P = $5000 we have:
C.I. = 5512.5 − 5000
C.I. = 512.5
Answer:
Interest = $512.5

Question 5: How much money would you need to deposit today at 6% annual interest compounded yearly to have $5000 in the account after 4 years?
Solution:

A = $5000 , r = 6% , n = 1 and t = 4 years
After plugging the given information we have
5000 = P(1 + (0.06/1))^{1 ⋅ 4}
5000 = P ⋅ (1.06)⁴
5000 = P ⋅ 1.2625
P = 5000/1.2625
P = 3960
Answer: $3960 must be invested to make 5000 in 4 years at the rate of 6% per anum.

Question 6: You invest $1,000 for 2 years at an annual interest rate of 5%, compounded annually. What will be the amount at the end of 2 years?
Solution:

P = $1,000), r = (5% or 0.05), t = 2 years
Substitute the known values into the formula:
A = 1000(1 + 0.05)²
Calculate (1.05)²:
A = 1000 × 1.1025
A = 1102.50
Answer: The amount after 2 years will be $1,102.50.

Question 7: You invest Rs 15,000 at an interest rate of 8% compounded annually. How many years will it take for your investment to double?
Solution:

We can use the Rule of 72 to estimate how long it will take for the investment to double.
The formula is: N = 72/r
Where:
N = Number of years
r = Interest rate (in percentage)
Here, r = 8%:
N = 72/8 = 9 years
Answer: It will take approziamtely 9 years for your Rs 15,000 to double to Rs 30,000 at an 8% annual interest rate compounded annually.

Question 8: You invest $4,000 for 2 years, and the amount grows to $4,800 with compound interest. What is the annual interest rate (compounded yearly)?
Solution:

A = $4,800, P = $4,000, t = Time in years (2 years), R = ?
Substitute the known values into the formula: 4800 = 4000(1 + r)²
Divide both sides by 4000:
4800/4000 = (1 + r)²
1.2 = (1 + r)²
Take the square root of both sides to solve for 1 + r:
√1.2 = 1 + r
r = 1.0954 −1
r = 0.0954 ≈ 0.10
Answer: The annual interest rate is approximately 10%.

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Practice Questions on (C.I.)Compound Interest (Easy)

Question 1: Find the compound interest on Rs 50,000 at 6% interest compounded annually for 3 years.

Question 2: If you deposit $10,000 into an account paying 4% annual interest compounded yearly, find the amount and interest after 5 years.

Question 3: Calculate the compound interest on $2,000 at an annual interest rate of 6%, compounded quarterly, over a period of 3 years.

Question 4: You deposit Rs 12,000 at 8% annual interest, compounded annually. Find the amount and interest after 4 years.

Question 5: How much money would you need to deposit today at 10% annual interest compounded yearly to have $6,000 in the account after 3 years?

Question 6: You invest Rs 8,000 for 2 years at an annual interest rate of 9%, compounded annually. What will be the amount at the end of 2 years?

Question 7: How many years will it take for an investment of $2,500 at an annual interest rate of 5% to double in value if compounded yearly?

Question 8: You invest Rs 5,000 for 3 years, and the amount grows to Rs 6,000 with compound interest. What is the annual interest rate (compounded yearly)?

Answer Key
Compound Interest = Rs 9,550.80
Amount = $12,166.53, Compound Interest = $2,166.53
Compound Interest = $382.38
Amount = Rs 16,326, Compound Interest = Rs 4,326
Deposit (Principal) = $4,508
Amount = Rs 9,504
Time = 14.21 years
Annual Interest Rate = 6.27%

Compound Interest Practice Questions (Easy)

Solved Examples on (C.I.)Compound Interest (Easy)

Practice Questions on (C.I.)Compound Interest (Easy)

Answer Key

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