Compound Interest Practice Questions (Hard)

Last Updated : 23 Jul, 2025

Compound interest is the interest you earn on both the money you originally invested and the interest that has already been added.

This means you make money on the interest itself, which causes your money to grow faster over time. Unlike simple interest, which is only calculated on the original amount, compound interest keeps building on itself, making it grow more quickly.

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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Hard Difficulty Solved Examples of Compound Interest (C.I.)

Question 1: A person invests ₹5,000 in a bank at an annual interest rate of 5%, compounded yearly. Additionally, the person deposits ₹1,000 at the beginning of each year for 5 years. Calculate the total interest earned and the final amount in the account at the end of 5 years.

Solution:

Given: Intial investement: ₹5000,
Rate: 5% = 0.05,
Time: 5years,
Additional investment of ₹1000 at the begining of each year.

At the start of the first year, deposit ₹1,000. The new principal becomes ₹5,000 + ₹1,000 = ₹6,000.

  • Year-by-Year Breakdown:
    • Year 1:
      Interest on ₹6,000: 6,000 × 0.05 = 300
      Total after interest: 6,000 + 300 = 6,300
      Add ₹1,000 at the beginning of the next year: 6,300 + 1,000 = 7,300.
    • Year 2:
      Interest on ₹7,300: 7,300 × 0.05 = 365
      Total after interest: 7,300 + 365 = 7,665.
      Add ₹1,000 at the beginning of the next year: 7,665 + 1,000 = 8,6657.
    • Year 3:
      Interest on ₹8,665: 8,665 × 0.05 = 433.25
      Total after interest: 8,665 + 433.25 = 9,098.25.
      Add ₹1,000 at the beginning of the next year: 9,098.25 + 1,000 = 10,098.25.
    • Year 4:
      Interest on ₹10,098.25: 10,098.25 × 0.05 = 504.91
      Total after interest: 10,098.25 + 504.91 = 10,603.16.
      Add ₹1,000 at the beginning of the next year: 10,603.16 + 1,000 = 11,603.16
    • Year 5:
      Interest on ₹11,603.16: 11,603.16 × 0.05 = 580.16
      Total after interest: 11,603.16 + 580.16 = 12,183.32.

Total Interest = 300 + 365 + 433.25 + 504.91 + 580.16 = 2183.32
Total Amount = 12,183.32

Question 2: There is a 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 10,000 after 4 years at the same rate?

Solution:

Given: P = ₹10,000
T = 5 years
We are told that there is a 50% increase in the amount, which means the simple interest is 50% of Rs. 10,000:
SI = 50/100 × 10000 = 5000

Now Substitute this value in the formula: SI = (P × R × T)/100​

5000 = (10000 × R × 5 )/100
R = 500000/50000
R = 10%

Now, let's calculate the compound interest for Rs. 10,000 at a rate of 10% per annum for 4 years using the compound interest formula: A = P(1 + R/100​)T
A = 10000 × (1 + 10/100)4
⇒ A = 10000 × (1.1)4
⇒ A = 10000 × 1.4641
⇒ A = 14641

CI = A -P = 14641 - 10000 = 4641
The compound interest after 4 years is Rs. 4641.

Question 3: The difference between simple interest and compound interest compounded annually on a certain sum of money for 2 years at 5% per annum is ₹1.25. What is the principal amount?

Solution:

Given:

  • Difference between compound interest (CI) and simple interest (SI) = ₹1.25
  • Time (t) = 2 years
  • Rate (r) = 5% = 5/100 = 0.05
  • Let the principal (sum) be P.

Formula for the difference between CI and SI for 2 years: Difference = P × (r/100)2

Substitute the values:
1.25 = P × 1.25/(0.05)2
⇒ 1.25 = P × 0.0025
⇒ P = 1.25/0.0025 = 500

The Principal amount is ₹500.

Question 4: At what rate of compound interest per annum will a sum of Rs. 1500 become Rs. 1650 in 2 years?

Solution:

Using the Compound interest formula: A = P(1 + r/100)t

Where:

  • A = 1650,
  • P = 1500,
  • r is the rate of interest per annum,
  • t = 2 years.

Substitute the given values into the formula:

1650 = 1500(1 + r/100​)2
⇒ (1 + r/100​)2 = 1650/1500​ = 1.1
⇒ 1 + r/100​ = √1.1 ​≈ 1.0488
⇒ r/100 ​= 1.0488 − 1 = 0.0488
⇒ r = 0.0488 × 100 = 4.88

The rate ofd compound interest is approximately 4.88% per annum.

Question 5: What is the difference between the compound interests on ₹10,000 for 2 years at 6% per annum compounded yearly and half-yearly?

Solution:

Given:

  • Principal (P): ₹10,000
  • Rate (r): 6% = 0.06
  • Time (t): 2 years

Compound Interest Compounded Yearly

Formula: A = P × (1 + r/1)t

Substitute values:
Ayearly = 10,000 × (1 + 0.06)2
⇒ Ayearly = 10,000 × 1.1236
⇒ Ayearly = 11,236

Compound Interest:
CIyearly = Ayearly − P = 11,236 − 10,000 = 1,236

Compound Interest Compounded Half-Yearly

Formula: A = P × (1 + r/2)2t

Substitute values:
Ahalf-yearly = 10,000 × (1 + 0.03)4
⇒ Ahalf-yearly = 10,000 × 1.1255 = 11,255.

Compound Interest: CI half - yearly = A half - yearly − P = 11,255 − 10,000 = 1,255

Difference Between Compound Interests

Difference = CI half - yearly − CI yearly
⇒ Difference = 1,255 − 1,236
⇒ Difference = 19

Question 6: On a certain sum of money lent out at 10% p.a., the difference between the compound interest for 2 years, payable yearly, and the simple interest for 2 years is ₹50. What is the principal amount?

Solution:

Given:

  • Rate (r): 10% = 0.10
  • Time (t): 2 years
  • Difference between compound interest (CI) and simple interest (SI): ₹50
  • Let the principal amount (P) be unknown.

Simple Interest Formula( SI): PRT/100
Compoound Interest Formula (CI): P(1 + R/100)T - P

  • SI = P × 0.10 × 2 = 0.2P
  • CI = P × (1 + 0.10)2 − P = P × (1.1)2 − P
    • CI = P × 1.21 − P = 0.21P

Given that the difference between CI and SI is ₹50, we can set up the equation: CI - SI = 50

50 = 0.21P − 0.2P
⇒ 50 = 0.01P
⇒ 50 = 0.01P
⇒ 50 = 0.01P
⇒ P = 5000

The principal amount is ₹5000.

Question 7: A person invests ₹40,000 in a bank at an annual interest rate of 8%, compounded annually, for 2 years. Additionally, they deposit ₹10,000 at the beginning of each year and withdraw ₹2,000 annually. Calculate the total amount the person will have at the end of 2 years.

Solution:

Given Data:

  • Initial investment: ₹40,000
  • Annual interest rate: 8% (compounded annually)
  • Time period: 2 years
  • Annual deposit: ₹10,000 (beginning of each year)
  • Annual withdrawal: ₹2,000

Year 1:

  1. At the beginning of Year 1:
    Deposit ₹10,000 → Total principal = ₹40,000 + ₹10,000 = ₹50,000
  2. Interest at the end of Year 1:
    Interest = 50,000 × 0.08 = 4,000
    Total after interest = ₹50,000 + ₹4,000 = ₹54,000
  3. Withdraw ₹2,000:
    Total after withdrawal = ₹54,000 − ₹2,000 = ₹52,000

Year 2:

  1. At the beginning of Year 2:
    Deposit ₹10,000 → Total principal = ₹52,000 + ₹10,000 = ₹62,000
  2. Interest at the end of Year 2:
    Interest = 62,000 × 0.08 = 4,960
    Total after interest = ₹62,000 + ₹4,960 = ₹66,960
  3. Withdraw ₹2,000:
    Total after withdrawal = ₹66,960 − ₹2,000 = ₹64,960

Total amount after 2 years = ₹64,960

Question 8: Person A and Person B each invest ₹12,000 in a bank at an annual interest rate of 8%, compounded yearly, for 3 years.

  • Person A deposits an additional ₹2,000 at the beginning of each year.
  • Person B deposits an additional ₹2,000 at the end of each year.

Find the difference in the interest earned between Person A and Person B.

Solution:

Given:

  • Initial investment (P): ₹12,000
  • Interest rate (r): 8% per annum (compounded yearly)
  • Time (n): 3 years
  • Annual deposit: ₹2,000
  1. Interest earned by Person A (Deposits ₹2,000 at the beginning of each year):
    Total interest earned: ₹4,130.94
  2. Interest earned by Person B (Deposits ₹2,000 at the end of each year):
    Total interest earned: ₹3,611.52
  3. Difference in interest earned:
    ₹4,130.94 − ₹3,611.52 = ₹519.42

The difference in interest is ₹510.42.

Practice Questions on Compound Interest (Hard)

Question 1: A person invests ₹6,000 in a bank at an annual interest rate of 4%, compounded yearly. Additionally, the person deposits ₹1,500 at the beginning of each year for 4 years. Calculate the total interest earned and the final amount in the account at the end of 4 years.

Question 2: A sum of ₹15,000 grows to ₹18,000 in 3 years at simple interest. What will be the compound interest on ₹15,000 for 2 years at the same rate?

Question 3: The difference between simple interest and compound interest compounded annually on ₹8,000 for 2 years at 4% per annum is ₹64. What is the principal amount?

Question 4: At what rate of compound interest per annum will ₹2,000 become ₹2,400 in 2 years?

Question 5: Find the difference between the compound interest on ₹5,000 for 3 years at 8% per annum compounded yearly and half-yearly.

Question 6: On a certain sum of money lent out at 10% p.a., the difference between the compound interest for 2 years, payable yearly, and the simple interest for 2 years is ₹50. What is the principal amount?

Question 7: A person invests ₹40,000 in a bank at an annual interest rate of 8%, compounded annually, for 2 years. Additionally, they deposit ₹10,000 at the beginning of each year and withdraw ₹2,000 annually. Calculate the total amount the person will have at the end of 2 years.

Question 8: Person A and Person B each invest ₹12,000 in a bank at an annual interest rate of 8%, compounded yearly, for 3 years. Person A deposits an additional ₹2,000 at the beginning of each year. Person B deposits an additional ₹2,000 at the end of each year. Find the difference in the interest earned between Person A and Person B.

Answer Key

  1. Total Interest: ₹1,643.64
    Final Amount: ₹13,643.64
  2. Compound Interest: ₹2,067
  3. Principal Amount: ₹40,000
  4. Rate of Interest: 9.54%
  5. Difference in CI: ₹28.60
  6. Principal Amount: ₹5,000
  7. Total Amount: ₹64,960
  8. Difference in Interest: ₹519.42
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