Compound Interest Practice Questions (Medium)

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.

This means that interest is earned on interest, leading to exponential growth over time. 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

Where,

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.

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Medium Difficulty Solved Examples on Compound Interest (C.I.)

Question 1: What is the compound interest on 10000 for one year at the rate of 20% per annum, if the interest is compounded quarterly?
Solution:

Given,
Principal (P) = Rs 10000
Rate (R) = 20%
Time (T) = 1 year
n = 4
By Formula,
A = P (1 + r/n)^nt
⇒ A = 10000 (1 + 0.2/4)⁴
⇒ A = 10000 (1.05)⁴
⇒ A = 12155.06

Compound Interest = A - P = 12155.06 - 10000 = 2155.06

Question 2: What will be the amount needed to pay for the amount of 10,000 if it is taken as a loan for 5 years at a 2 percent rate compounding quarterly?.

Solution:

Amount = P (1 + r/n)^nt
Principal = 10,000
Rate of Interest = 2
n = 4
Time= 5 years
Amount = 10,000(1 + 0.02/4)^{5 · 4}
⇒ A = 11,048.9557
Thus, the amount paid at the end of 5 years is ₹ 11,048.9557

Question 3: If the borrower returns 10,000 in interest compounded annually after 5 years at 6 percent interest calculate the principal amount.

Solution:

A = 10,000
t = 5 years
r = 6%
n = 1
P = ?
10000 = P(1 + (0.06/1)^{1 ⋅ 5}
⇒ 10000 = P ⋅ (1.06)⁵
⇒ 10000 = P ⋅ 1.338
⇒ P = 10000/1.338
⇒ P = 7473

Question 4: If you deposit $20000 into an account paying 6% annual interest compounded monthly. Find the amount and interest after 3 months. for the

Solution:

P = $20000 , r = 6% , 3 months = 3/12 years = 0.25 =years, n =12
A = 20000(1 + (0.06/12))^12⋅3/12
⇒ A = 20000 ⋅ (1.005)³
⇒ A = 20000 ⋅ 1.015
⇒ A = 20300
Compound Interest = A - P = 20300 - 10000 = 300

Question 5: The compound interest on a certain sum of money at a certain rate for 2 years is Rs. 80.80 and the simple interest on the same sum is Rs. 70 at the same rate and for the same time. The rate of interest is?

Solution:

To find the rate of interest, we can use the relationship between simple interest (SI) and compound interest (CI) for small time periods.
Given: Compound Interest (CI) for 2 years = Rs. 80.80
Simple Interest (SI) for 2 years = Rs. 70
The difference between CI and SI is the interest on the interest:
Difference = 80.80 - 70 = 10.80
This difference represents the interest on the interest for the first year.
The simple interest for one year is : 70/2 = 35
The interest on Rs. 35 for the second year at the same rate will be the difference, Rs. 10.80. Set up the equation:
(35 × r)/100 = 10.80
⇒ r = (10.80 × 100)/35
⇒ r ≅ 30.8

Question 6: The simple interest and compound interest (compounded annually) on a certain sum of money with a given rate for a period of 2 years are Rs. 1,200 and Rs. 1,260, respectively. What is the principal sum of money?

Solution:

Given: Simple Interest (SI) for 2 years = Rs. 1,200
Compound Interest (CI) for 2 years = Rs. 1,260
The difference between CI and SI is the interest on the interest:
Difference = CI - SI} = 1,260 - 1,200 = 60
The simple interest for one year is half of Rs. 1,200, which is Rs. 600.
The interest on Rs. 600 for the second year at the same rate will be Rs. 60. Solve for the rate r:
600 × r /100 = 60
⇒ r = 10%
Substitute these values into the formula:
1,200 = (P × 10 × 2)/100
⇒ P = 6,000

Question 7: A sum of Rs. 2,500 amounts to Rs. 5,000 in three years at compound interest. What is the interest for six years?

Solution:

Given: Principal (P) = Rs. 2,500
Amount after 3 years (A₃) = Rs. 5,000
Time (n) = 3 years
The formula for compound interest is:
A = P × (1 + r)ⁿ
Substitute the given values into the formula:
5,000 =2,500 × (1 + r)³
⇒ 5,000/2,500 = (1 + r)³
⇒ 2 = (1 + r)³
⇒ 1 + r = ³√2
⇒ r = ³√2 − 1 ≈ 0.2599 or 25.99% per annum.
Use the compound interest formula:
A₆= P × (1 + r)⁶
⇒ A₆= 2,500 × ( ³√2)⁶
Since ( ³√2)⁶ = 4:
A₆= 2,500 ×4 = 10,000
Compound interest (CI) is:
CI = A₆− P
⇒ CI = 10,000 − 2,500 = 7,500
The compound interest for six years is Rs. 7,500.

Question 8: If the rate of interest is 4% per annum for the first year, 5% per annum for the second year, and 6% per annum for the third year, then the compound interest of 10,000 for 3 years will be?

Solution:

Given:
Principal (P) = ₹10,000
Rate for the 1st year = 4% = 0.04
Rate for the 2nd year = 5% = 0.05
Rate for the 3rd year = 6% = 0.06
Time = 3 years
Year 1: A₁ = P × (1 + r₁)
A₁ = 10,000 × (1 + 0.04) = 10,000 × 1.04 = 10,400
Year 2: A₂ = A₁× (1 + r₂)
A₂= 10,400 × (1 + 0.05) = 10,400 × 1.05 = 10,920
Year 3: A₃ = A2× (1 + r₃)
A₃= 10,920 × (1 + 0.06) = 10,920 × 1.06 = 11,575.20
Compound interest (CI) is:
⇒ CI = A₃ − P
⇒ CI = 11,575.20 − 10,000 = 1,575.20
The compound interest for 3 years is ₹1,575.20.

Practice Questions of C.I. Compound Interest (Medium)

Question 1: What is the compound interest on ₹15,000 for 2 years at a rate of 10% per annum, compounded annually.

Question 2: A sum of ₹5,000 becomes ₹7,000 in 2 years at compound interest. What is the rate of interest per annum?

Question 3: What will ₹20,000 amount to in 3 years at 8% per annum compounded quarterly?

Question 4: A sum of ₹4,000 becomes ₹6,480 in 4 years at compound interest compounded annually. Find the rate of interest.

Question 5: If the rate of interest is 5% for the first year, 6% for the second year, and 7% for the third year, find the compound interest on ₹12,000 for 3 years.

Question 6: Find the compound interest on ₹8,000 for 2 years at a rate of 10% compounded half-yearly.

Question 7: A sum of ₹10,000 amounts to ₹15,625 in 4 years at compound interest compounded annually. Find the rate of interest.

Question 8: Find the compound interest on ₹5,000 for 1.5 years at 12% compounded half-yearly.

Answer Key

₹3,150
18.32%
₹25,364.84
12.82%
₹2,290.92
₹1,724.05
11.80%
₹955.08

Compound Interest Practice Questions (Medium)

Medium Difficulty Solved Examples on Compound Interest (C.I.)

Year 1: A₁ = P × (1 + r₁)
A₁ = 10,000 × (1 + 0.04) = 10,000 × 1.04 = 10,400

Year 2: A₂ = A₁× (1 + r₂)
A₂= 10,400 × (1 + 0.05) = 10,400 × 1.05 = 10,920

Year 3: A₃ = A2× (1 + r₃)
A₃= 10,920 × (1 + 0.06) = 10,920 × 1.06 = 11,575.20

Practice Questions of C.I. Compound Interest (Medium)

Answer Key

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Compound Interest Practice Questions (Medium)

Medium Difficulty Solved Examples on Compound Interest (C.I.)

Year 1: A1 = P × (1 + r1)A1​ = 10,000 × (1 + 0.04) = 10,000 × 1.04 = 10,400

Year 2: A2 = A1 × (1 + r2)A2 ​= 10,400 × (1 + 0.05) = 10,400 × 1.05 = 10,920

Year 3: A3 = A2 × (1 + r3)A3 ​= 10,920 × (1 + 0.06) = 10,920 × 1.06 = 11,575.20

Practice Questions of C.I. Compound Interest (Medium)

Answer Key

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Year 1: A₁ = P × (1 + r₁)
A₁ = 10,000 × (1 + 0.04) = 10,000 × 1.04 = 10,400

Year 2: A₂ = A₁× (1 + r₂)
A₂= 10,400 × (1 + 0.05) = 10,400 × 1.05 = 10,920

Year 3: A₃ = A2× (1 + r₃)
A₃= 10,920 × (1 + 0.06) = 10,920 × 1.06 = 11,575.20