In the previous chapter, we solved Simple Interest Questions with Answers and Solutions, where you learned how to calculate simple interest, principal amount, rate of interest, time period, and total amount using the simple interest formula. If you’ve practiced those questions, you’ve already built a strong foundation.
Now it’s time to move one step ahead and learn Compound Interest, one of the most important topics in Quantitative Aptitude for competitive exams.
Unlike simple interest, compound interest is calculated not only on the original principal but also on the interest earned in previous years. Once you understand this concept, solving compound interest questions becomes much easier.
To help you learn systematically, we have arranged these Compound Interest Questions in increasing order of difficulty—from easy to medium, tough, and finally exam-level questions.
Don’t worry if some questions look lengthy at first. If your concepts are clear, you will be able to solve every question step by step.
We recommend attempting every question on your own before checking the answer and solution. Even if your answer is incorrect, understanding the solution will help you avoid similar mistakes in future competitive exams.
If you want to strengthen your Quantitative Aptitude preparation further, you can also explore our:
- Maths Notes for detailed concept explanations
- Formula Section for quick revision before exams
- Practice Questions covering every important aptitude topic
- Previous Year Questions (PYQs) from SSC, RRB, Banking, Defence, Police, and other competitive examinations
- Competitive Exam Syllabus to understand the topics asked in different exams
- Math Calculators to verify your answers, understand calculations, and strengthen your concepts
Now, start solving the Compound Interest questions below and challenge yourself to complete each question before looking at the solution.
Compound Interest Questions Practice Overview
| Feature | Details |
| Number of Questions | 15 Solved Questions |
| Difficulty Level | Basic → Intermediate → Advanced |
| Suitable For | SSC, RRB, Banking, Defence, Police, State PSC & Other Competitive Exams |
| Concepts Covered | Amount, Compound Interest, Principal, Rate, Time, Half-Yearly, Quarterly, Reinvestment & Changing Interest Rate |
| Estimated Time | 30–40 Minutes |
Quick Note: Compound Interest Formulas
| Formula | Expression |
| Amount (CI) | A = P(1 + R/100)ⁿ |
| Compound Interest | CI = A − P |
| Compound Interest | CI = P[(1 + R/100)ⁿ − 1] |
| Principal (CI) | P = A ÷ (1 + R/100)ⁿ |
| Principal (using CI) | P = CI ÷ [(1 + R/100)ⁿ − 1] |
Question 1: A Bank Manager invests ₹20,000 at 10% compound interest per annum, compounded annually, for 2 years. Find the Compound Interest earned.
Solution
Given
- Principal Amount (P) = ₹20,000
- Rate of Interest (R) = 10% per annum
- Time (T) = 2 years
- Number of Compounding Periods (n) = 2 (Compounded annually)
Formula Used
Amount (A) = P × (1 + R/100)ⁿ
Compound Interest (CI) = Amount − Principal
Substitute the Values
Amount
= 20,000 × (1 + 10/100)²
= 20,000 × (1.10)²
= 20,000 × 1.21
= ₹24,200
Compound Interest
= ₹24,200 − ₹20,000
= ₹4,200
Answer
The Compound Interest earned is ₹4,200.
Exam Tip (SSC, RRB, Banking, Defence & Police Exams)
For 2 years with annual compounding, you can calculate the amount year by year instead of using the formula.
After Year 1
= ₹20,000 + 10% of ₹20,000
= ₹20,000 + ₹2,000
= ₹22,000
After Year 2
= ₹22,000 + 10% of ₹22,000
= ₹22,000 + ₹2,200
= ₹24,200
Compound Interest
= ₹24,200 − ₹20,000
= ₹4,200
Question 2: A Railway Employee at Lucknow Junction deposits ₹50,000 at 8% compound interest per annum for 3 years. Calculate the Total Amount received at maturity.
Solution
Given
- Principal Amount (P) = ₹50,000
- Rate of Interest (R) = 8% per annum
- Time (T) = 3 years
- Compounding = Annually
- Number of Compounding Periods (n) = 3 (Since interest is compounded once every year for 3 years.)
Formula Used
Amount (A) = P × (1 + R/100)ⁿ
Substitute the Values
Amount
= 50,000 × (1 + 8/100)³
= 50,000 × (1.08)³
= 50,000 × 1.259712
= ₹62,985.60
Answer
The Total Amount received at maturity is ₹62,985.60.
Exam Tip (SSC, RRB, Banking, Defence & Police Exams)
For annual compounding, you can calculate the amount year by year without using the formula.
After Year 1
= ₹50,000 + 8% of ₹50,000
= ₹50,000 + ₹4,000
= ₹54,000
After Year 2
= ₹54,000 + 8% of ₹54,000
= ₹54,000 + ₹4,320
= ₹58,320
After Year 3
= ₹58,320 + 8% of ₹58,320
= ₹58,320 + ₹4,665.60
= ₹62,985.60
Question 3: An employee of Visa Steel invests ₹40,000 at 12% compound interest per annum for 3 years. Find the Compound Interest earned.
Solution
Given
- Principal Amount (P) = ₹40,000
- Rate of Interest (R) = 12% per annum
- Time (T) = 3 years
- Compounding = Annually
- Number of Compounding Periods (n) = 3 (Since interest is compounded once every year for 3 years.)
Substitute the Values
Amount
= 40,000 × (1 + 12/100)³
= 40,000 × (1.12)³
= 40,000 × 1.404928
= ₹56,197.12
Compound Interest
= ₹56,197.12 − ₹40,000
= ₹16,197.12
Answer
The Compound Interest earned is ₹16,197.12.
Question 4: A resident of Kaithal received ₹72,900 after investing money for 2 years at 8% compound interest per annum. Find the Principal Amount invested.
Solution
Given
- Amount (A) = ₹72,900
- Rate of Interest (R) = 8% per annum
- Time (T) = 2 years
- Compounding = Annually
- Number of Compounding Periods (n) = 2 (Since interest is compounded once every year for 2 years.)
Formula Used
Principal (CI) P = A ÷ (1 + R/100)ⁿ
Substitute the Values
Principal
= 72,900 ÷ (1 + 8/100)²
= 72,900 ÷ (1.08)²
= 72,900 ÷ 1.1664
= ₹62,500
Answer
The Principal Amount invested is ₹62,500.
Question 5: An Assistant Section Officer (ASO) invested ₹25,000 at 10% compound interest per annum. If the amount became ₹30,250, find the Time Period.
Solution
Given
- Principal Amount (P) = ₹25,000
- Amount (A) = ₹30,250
- Rate of Interest (R) = 10% per annum
- Time (T) = ?
Formula Used
Amount = Principal × (1 + R/100)ⁿ
Substitute the Values
30,250 = 25,000 × (1 + 10/100)ⁿ
30,250 = 25,000 × (1.10)ⁿ
Divide both sides by 25,000.
30,250 ÷ 25,000 = (1.10)ⁿ
1.21 = (1.10)ⁿ
Since,
(1.10)² = 1.21
Therefore,
n = 2 years
Answer
The Time Period is 2 years.
Exam Tip (SSC, RRB, Banking, Defence & Police Exams)
When the Amount and Principal are given, first divide the amount by the principal.
Amount ÷ Principal
= 30,250 ÷ 25,000
= 1.21
Now compare it with common compound values:
- (1.10)¹ = 1.10
- (1.10)² = 1.21
- (1.10)³ = 1.331
Since 1.21 = (1.10)², the time period is 2 years
Question 6: A Captain in the Indian Army invested ₹50,000. After 2 years, the investment grew to ₹60,500 under annual compound interest. Find the Rate of Interest per annum.
Solution
Given
- Principal Amount (P) = ₹50,000
- Amount (A) = ₹60,500
- Time (T) = 2 years
- Compounding = Annually
- Number of Compounding Periods = 2
- Rate of Interest (R) = ?
Formula Used
Amount = Principal × (1 + R/100)ⁿ
Substitute the Values
60,500 = 50,000 × (1 + R/100)²
Divide both sides by 50,000.
60,500 ÷ 50,000 = (1 + R/100)²
1.21 = (1 + R/100)²
Since,
1.21 = (1.10)²
Therefore,
1 + R/100 = 1.10
R/100 = 0.10
R = 10%
Answer
The Rate of Interest is 10% per annum.
Exam Tip (SSC, RRB, Banking, Defence & Police Exams)
For questions involving 2 years, first calculate:
Amount ÷ Principal
= 60,500 ÷ 50,000
= 1.21
Now identify its square root.
√1.21 = 1.10
Therefore,
1 + R/100 = 1.10
So,
R = 10%
Question 7: A Bank Employee invests ₹80,000 at 10% compound interest per annum, compounded half-yearly, for 2 years. Calculate the Compound Interest.
Solution
Given
- Principal Amount (P) = ₹80,000
- Rate of Interest = 10% per annum
- Time = 2 years
- Compounding = Half-Yearly
- Rate per Half-Year = 10% ÷ 2 = 5%
- Number of Compounding Periods = 2 × 2 = 4
Formula Used
Amount = Principal × (1 + R/100)ⁿ
Substitute the Values
Amount
= 80,000 × (1 + 5/100)⁴
= 80,000 × (1.05)⁴
= 80,000 × 1.21550625
= ₹97,240.50
Compound Interest
= ₹97,240.50 − ₹80,000
= ₹17,240.50
Answer
The Compound Interest is ₹17,240.50.
Question 8: An employee of Banaras Locomotive Works (BLW) invests ₹60,000 at 12% compound interest per annum, compounded quarterly, for 1 year. Find the Amount received at maturity.
Solution
Given
- Principal Amount (P) = ₹60,000
- Rate of Interest = 12% per annum
- Time = 1 year
- Compounding = Quarterly
- Rate per Quarter = 12% ÷ 4 = 3%
- Number of Compounding Periods = 1 × 4 = 4
Substitute the Values
Amount
= 60,000 × (1 + 3/100)⁴
= 60,000 × (1.03)⁴
= 60,000 × 1.12550881
= ₹67,530.53
Answer
The Amount received at maturity is ₹67,530.53.
Question 9: A resident of Unnao invests ₹30,000 at 10% per annum for 2 years.
Calculate:
- The Simple Interest
- The Compound Interest
- The Difference between Compound Interest and Simple Interest
Solution
Given
- Principal Amount (P) = ₹30,000
- Rate of Interest (R) = 10% per annum
- Time (T) = 2 years
1. Simple Interest
Simple Interest
= (P × R × T) ÷ 100
= (30,000 × 10 × 2) ÷ 100
= ₹6,000
2. Compound Interest
Amount
= 30,000 × (1 + 10/100)²
= 30,000 × (1.10)²
= 30,000 × 1.21
= ₹36,300
Compound Interest
= ₹36,300 − ₹30,000
= ₹6,300
3. Difference between Compound Interest and Simple Interest
Difference
= ₹6,300 − ₹6,000
= ₹300
Answer
- Simple Interest = ₹6,000
- Compound Interest = ₹6,300
- Difference (CI − SI) = ₹300
Question 10: A Section Controller invests ₹1,00,000 at 8% per annum for 3 years.Calculate the additional interest earned under Compound Interest compared to Simple Interest.
Solution
Given
- Principal Amount (P) = ₹1,00,000
- Rate of Interest (R) = 8% per annum
- Time (T) = 3 years
1. Calculate the Simple Interest
Simple Interest
= (P × R × T) ÷ 100
= (1,00,000 × 8 × 3) ÷ 100
= ₹24,000
2. Calculate the Compound Interest
Amount
= 1,00,000 × (1 + 8/100)³
= 1,00,000 × (1.08)³
= 1,00,000 × 1.259712
= ₹1,25,971.20
Compound Interest
= ₹1,25,971.20 − ₹1,00,000
= ₹25,971.20
3. Calculate the Additional Interest
Additional Interest
= Compound Interest − Simple Interest
= ₹25,971.20 − ₹24,000
= ₹1,971.20
Answer
The additional interest earned under Compound Interest compared to Simple Interest is ₹1,971.20.
Question 11: A Tata Steel engineer invested a certain amount at 10% compound interest per annum. After 3 years, the amount became ₹1,33,100.
Find:
- The Principal Amount
- The Compound Interest earned.
Solution
Given
- Amount (A) = ₹1,33,100
- Rate of Interest (R) = 10% per annum
- Time (T) = 3 years
- Principal Amount (P) = ?
Substitute the Values
Principal
= ₹1,33,100 ÷ (1 + 10/100)³
= ₹1,33,100 ÷ (1.10)³
= ₹1,33,100 ÷ 1.331
= ₹1,00,000
Compound Interest
= Amount − Principal
= ₹1,33,100 − ₹1,00,000
= ₹33,100
Answer
- Principal Amount = ₹1,00,000
- Compound Interest Earned = ₹33,100
Question 12: A Bank Manager and a Station Master at Lucknow Junction each invest ₹50,000.
- The Bank Manager invests at 10% compound interest per annum for 3 years.
- The Station Master invests at 8% compound interest per annum for 4 years.
Who receives the higher maturity amount, and by how much?
Solution
Given
Bank Manager
- Principal Amount = ₹50,000
- Rate = 10% per annum
- Time = 3 years
Station Master
- Principal Amount = ₹50,000
- Rate = 8% per annum
- Time = 4 years
Step 1: Calculate the Bank Manager’s Maturity Amount
Amount
= 50,000 × (1 + 10/100)³
= 50,000 × (1.10)³
= 50,000 × 1.331
= ₹66,550
Step 2: Calculate the Station Master’s Maturity Amount
Amount
= 50,000 × (1 + 8/100)⁴
= 50,000 × (1.08)⁴
= 50,000 × 1.36048896
= ₹68,024.45
Step 3: Compare the Two Amounts
Difference
= ₹68,024.45 − ₹66,550
= ₹1,474.45
Answer
- Bank Manager’s Maturity Amount = ₹66,550
- Station Master’s Maturity Amount = ₹68,024.45
The Station Master receives the higher maturity amount by ₹1,474.45.
Question 13: A Subedar in the Indian Army invests ₹80,000 at 10% compound interest per annum, compounded annually.
After 2 years, he withdraws the entire amount and immediately reinvests it for another 2 years at 8% compound interest per annum.
Find:
- Amount after the first investment
- Final Amount after 4 years
- Total Compound Interest earned
Solution
Given
First Investment
- Principal Amount = ₹80,000
- Rate = 10% per annum
- Time = 2 years
Second Investment
- Principal = Amount received after the first investment
- Rate = 8% per annum
- Time = 2 years
Step 1: Calculate the Amount after the First Investment
Amount
= 80,000 × (1 + 10/100)²
= 80,000 × (1.10)²
= 80,000 × 1.21
= ₹96,800
Step 2: Reinvest ₹96,800 for Another 2 Years at 8%
Amount
= 96,800 × (1 + 8/100)²
= 96,800 × (1.08)²
= 96,800 × 1.1664
= ₹1,12,907.52
Step 3: Calculate the Total Compound Interest
Compound Interest
= Final Amount − Original Principal
= ₹1,12,907.52 − ₹80,000
= ₹32,907.52
Answer
- Amount after the First Investment = ₹96,800
- Final Amount after 4 Years = ₹1,12,907.52
- Total Compound Interest Earned = ₹32,907.52
Question 14: A resident of Barabanki invests ₹1,20,000 at 12% compound interest per annum, compounded annually.
After 2 years, the rate is reduced to 10% per annum for the next 2 years.
Find:
- Amount after the first 2 years
- Final Amount after 4 years
- Total Compound Interest earned
Solution
Given
First 2 Years
- Principal Amount = ₹1,20,000
- Rate = 12% per annum
- Time = 2 years
Next 2 Years
- Principal = Amount after the first 2 years
- Rate = 10% per annum
- Time = 2 years
Step 1: Calculate the Amount after the First 2 Years
Amount
= 1,20,000 × (1 + 12/100)²
= 1,20,000 × (1.12)²
= 1,20,000 × 1.2544
= ₹1,50,528
Step 2: Calculate the Final Amount after the Next 2 Years
Amount
= 1,50,528 × (1 + 10/100)²
= 1,50,528 × (1.10)²
= 1,50,528 × 1.21
= ₹1,82,138.88
Step 3: Calculate the Total Compound Interest
Compound Interest
= Final Amount − Original Principal
= ₹1,82,138.88 − ₹1,20,000
= ₹62,138.88
Answer
- Amount after the First 2 Years = ₹1,50,528
- Final Amount after 4 Years = ₹1,82,138.88
- Total Compound Interest Earned = ₹62,138.88
Question 15: An ASO and an employee of Chittaranjan Locomotive Works (CLW) each invest ₹75,000 for 3 years.
- The ASO earns Simple Interest at 10% per annum.
- The CLW employee earns Compound Interest at 10% per annum, compounded annually.
Calculate:
- Simple Interest earned by the ASO
- Compound Interest earned by the CLW employee
- Difference in interest earned
- Difference in the maturity amounts
Solution
Given
- Principal Amount = ₹75,000
- Rate of Interest = 10% per annum
- Time = 3 years
Step 1: Calculate the Simple Interest Earned by the ASO
Simple Interest
= (75,000 × 10 × 3) ÷ 100
= ₹22,500
Maturity Amount
= ₹75,000 + ₹22,500
= ₹97,500
Step 2: Calculate the Compound Interest Earned by the CLW Employee
Amount
= 75,000 × (1 + 10/100)³
= 75,000 × (1.10)³
= 75,000 × 1.331
= ₹99,825
Compound Interest
= ₹99,825 − ₹75,000
= ₹24,825
Step 3: Calculate the Difference in Interest Earned
Difference in Interest
= ₹24,825 − ₹22,500
= ₹2,325
Step 4: Calculate the Difference in the Maturity Amounts
Difference in Maturity Amounts
= ₹99,825 − ₹97,500
= ₹2,325
Answer
- Simple Interest Earned = ₹22,500
- Compound Interest Earned = ₹24,825
- Difference in Interest Earned = ₹2,325
- Difference in the Maturity Amounts = ₹2,325
Common Mistakes Students Make While Solving Compound Interest Questions
- Forgetting to subtract the principal while calculating Compound Interest.
- Using the annual rate directly in half-yearly or quarterly questions.
- Not converting the number of compounding periods correctly.
- Using Simple Interest formulas in Compound Interest questions.
- Comparing investments without calculating the final maturity amount.
What You Learned in This Compound Interest Questions Section
In this section, you learned how to:
- Calculate the Amount and Compound Interest.
- Find the Principal Amount, Rate of Interest, and Time Period.
- Solve annual, half-yearly, and quarterly compounding questions.
- Solve questions involving changing interest rates and reinvestment.
- Compare different compound interest investments.
Exam Tip: Before solving any Compound Interest question, identify what the question is asking. Many students know the formulas but lose marks by applying the wrong method. Understand the concept first, then solve the calculation.
Learn More Quantitative Aptitude Topics
Continue your preparation with these important topics:
FAQ:
1. How do you calculate Compound Interest?
Compound Interest is calculated by subtracting the Principal Amount from the Total Amount.
Compound Interest = Amount − Principal
or
CI = A − P
2. What is the formula to calculate the Total Amount in Compound Interest?
The Total Amount under Compound Interest is calculated using the formula:
A = P × (1 + R/100)ⁿ
where:
- A = Amount (Maturity Value)
- P = Principal Amount
- R = Rate of Interest (per annum)
- n = Time (in years)
3. What is the formula to calculate the Principal Amount in Compound Interest?
If the Amount, Rate of Interest, and Time are known, the Principal Amount is calculated using:
P = A ÷ (1 + R/100)ⁿ
4. How do you calculate the Rate of Interest in Compound Interest?
If the Principal Amount, Amount, and Time are known, first use the Compound Interest formula:
A = P × (1 + R/100)ⁿ
Then solve for the Rate of Interest.
For two years, you can often find the rate by taking the square root of A ÷ P.
5. How do you calculate the Time Period in Compound Interest?
If the Principal Amount, Amount, and Rate of Interest are known, use:
A = P × (1 + R/100)ⁿ
Then solve for n.
6. How do you calculate Compound Interest when interest is compounded half-yearly?
For half-yearly compounding:
- Divide the annual rate by 2.
- Multiply the time by 2.
- Then use the Compound Interest formula.
7. How do you calculate Compound Interest when interest is compounded quarterly?
For quarterly compounding:
- Divide the annual rate by 4.
- Multiply the time by 4.
- Then use the Compound Interest formula.
Important Links Related to Simple Interest and Compound Interest
- Simple Interest & Compound Interest
- Simple Interest Questions with Answers and Solutions
- Simple Interest & Compound Interest Formula with Examples and Explanations
- Difference Between Simple Interest and Compound Interest Questions with Answers and Solutions
- Compound Growth Questions with Answers and Solutions
- Depreciation Questions with Answers and Solutions
- Simple Interest & Compound Interest Practice Questions
- Simple Interest & Compound Interest PYQs SSC, RRB, Banking & Defence Exams With Solution.