Difference Between Simple Interest and Compound Interest Questions with Answers and Solutions

In the previous chapters, we practiced Simple Interest Questions and Compound Interest Questions separately. Now it’s time to bring both concepts together and understand how they differ in real-world situations.

This chapter focuses on Difference Between Simple Interest and Compound Interest Questions, one of the most important topics for SSC, RRB, Banking, Defence, Police, and other competitive examinations. The questions are arranged from easy to exam level, helping you gradually build confidence and improve your problem-solving skills.

Before attempting these questions, we recommend revising the important formulas from our Simple Interest & Compound Interest Formula page. A strong understanding of both concepts will help you solve these questions quickly and accurately.

To strengthen your Quantitative Aptitude preparation, you can also explore our:

• Maths Notes for detailed concept explanations
• Maths Formula Section for quick revision
• Practice Questions for every Quantitative Aptitude chapter
• Previous Year Questions (PYQs) from SSC, RRB, Banking, Defence, Police, and other competitive examinations
• Quantitative Aptitude Syllabus to understand the topics covered in different competitive exams
• Math Calculators to verify your answers and improve your understanding

Now, challenge yourself by solving each question without looking at the solution first. Once you’ve attempted the question, compare your approach with the detailed solution to identify mistakes and improve your speed and accuracy.

Quick Note: SI & CI Difference Formulas

Question 1: During a financial awareness camp at Parade, Kanpur, two friends each deposited ₹25,000 for 2 years at 10% per annum.

• Aman chose Simple Interest.
• Bharat chose Compound Interest, compounded annually.

Calculate:

1. Simple Interest earned by Aman.
2. Compound Interest earned by Bharat.
3. By how much did Bharat earn more than Aman?

Solution

Given

Principal Amount (P) = ₹25,000

Rate of Interest (R) = 10% per annum

Time (T) = 2 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)²

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (25,000 × 10 × 2) ÷ 100

= ₹5,000

Step 2: Calculate the Compound Interest

Amount

= 25,000 × (1 + 10/100)²

= 25,000 × (1.10)²

= 25,000 × 1.21

= ₹30,250

Compound Interest

= ₹30,250 − ₹25,000

= ₹5,250

Step 3: Compare the Two

Difference

= Compound Interest − Simple Interest

= ₹5,250 − ₹5,000

= ₹250

Answer

• Simple Interest earned by Aman = ₹5,000
• Compound Interest earned by Bharat = ₹5,250
• Bharat earned ₹250 more than Aman.

So,

Exam Tip (SSC, RRB, Banking, Defence & Police Exams)

For 2-year questions, you can quickly find the difference between Compound Interest and Simple Interest using the shortcut:

Difference (CI − SI) = (P × R²) ÷ 100²

Applying the formula:

= (25,000 × 10²) ÷ 100²

= (25,000 × 100) ÷ 10,000

= ₹250

Note: This shortcut is applicable only for 2-year questions.

Question 2: A family planning a vacation to Puri Beach invested ₹40,000 for 3 years at 8% per annum.

Calculate:

1. Simple Interest
2. Compound Interest
3. Difference between the two interest amounts.

Solution

Given

Principal Amount (P) = ₹40,000

Rate of Interest (R) = 8% per annum

Time (T) = 3 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)³

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (40,000 × 8 × 3) ÷ 100

= ₹9,600

Step 2: Calculate the Compound Interest

Amount

= 40,000 × (1 + 8/100)³

= 40,000 × (1.08)³

= 40,000 × 1.259712

= ₹50,388.48

Compound Interest

= ₹50,388.48 − ₹40,000

= ₹10,388.48

Step 3: Calculate the Difference

Difference

= Compound Interest − Simple Interest

= ₹10,388.48 − ₹9,600

= ₹788.48

Answer

• Simple Interest = ₹9,600
• Compound Interest = ₹10,388.48
• Difference = ₹788.48

So, 

Question 3: A Pharmacist in Indian Railways invested ₹60,000 for 2 years at 12% per annum.

Calculate:

1. Amount under Simple Interest
2. Amount under Compound Interest
3. Difference between the maturity amounts.

Solution

Given

Principal Amount (P) = ₹60,000

Rate of Interest (R) = 12% per annum

Time (T) = 2 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)²

Compound Interest = Amount − Principal

Step 1: Calculate the Amount under Simple Interest

Simple Interest

= (60,000 × 12 × 2) ÷ 100

= ₹14,400

Amount

= Principal + Simple Interest

= ₹60,000 + ₹14,400

= ₹74,400

Step 2: Calculate the Amount under Compound Interest

Amount

= 60,000 × (1 + 12/100)²

= 60,000 × (1.12)²

= 60,000 × 1.2544

= ₹75,264

Step 3: Calculate the Difference

Difference

= Compound Interest Amount − Simple Interest Amount

= ₹75,264 − ₹74,400

= ₹864

Answer

• Amount under Simple Interest = ₹74,400
• Amount under Compound Interest = ₹75,264
• Difference between the maturity amounts = ₹864

So,

Exam Tip (SSC, RRB, Banking, Defence & Police Exams)

Since this is a 2-year question, you can directly calculate the difference between the maturity amounts using the shortcut:

Difference (CI − SI) = (P × R²) ÷ 100²

= (60,000 × 12²) ÷ 100²

= (60,000 × 144) ÷ 10,000

= ₹864

Question 4: A spare-parts dealer in the Auto Market, Hisar borrowed ₹80,000 for 3 years at 10% per annum.

How much extra interest would he pay if the loan used Compound Interest instead of Simple Interest?

Solution

Given

Principal Amount (P) = ₹80,000

Rate of Interest (R) = 10% per annum

Time (T) = 3 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)³

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (80,000 × 10 × 3) ÷ 100

= ₹24,000

Step 2: Calculate the Compound Interest

Amount

= 80,000 × (1 + 10/100)³

= 80,000 × (1.10)³

= 80,000 × 1.331

= ₹1,06,480

Compound Interest

= ₹1,06,480 − ₹80,000

= ₹26,480

Step 3: Calculate the Extra Interest

Extra Interest

= Compound Interest − Simple Interest

= ₹26,480 − ₹24,000

= ₹2,480

Answer

The spare-parts dealer would pay ₹2,480 more if the loan used Compound Interest instead of Simple Interest.

So,

Exam Tip (SSC, RRB, Banking, Defence & Police Exams)

Whether the money is invested or borrowed, the calculation method remains the same.

• Investment: Higher Compound Interest means more earnings.
• Loan: Higher Compound Interest means more interest payable.

Always read the question carefully to understand whether the difference represents an additional gain or an additional cost.

Question 5:A trader earned a 20% profit on selling motorcycle accessories in Auto Market, Hisar and invested the entire profit of ₹48,000 at 10% per annum for 2 years.

Find the difference between Compound Interest and Simple Interest earned on this investment.

(Students who are unsure how the ₹48,000 profit was determined can revise the Profit, Loss & Discount chapter.)

Solution

Given

Principal Amount (P) = ₹48,000

Rate of Interest (R) = 10% per annum

Time (T) = 2 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)²

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (48,000 × 10 × 2) ÷ 100

= ₹9,600

Step 2: Calculate the Compound Interest

Amount

= 48,000 × (1 + 10/100)²

= 48,000 × (1.10)²

= 48,000 × 1.21

= ₹58,080

Compound Interest

= ₹58,080 − ₹48,000

= ₹10,080

Step 3: Calculate the Difference

Difference

= Compound Interest − Simple Interest

= ₹10,080 − ₹9,600

= ₹480

Answer

The difference between the Compound Interest and Simple Interest earned is ₹480.

So, 

Question 6: An engineer working at Jindal Steel, Jajpur invested ₹1,00,000 at 8% compound interest for 3 years.

Another engineer at Tata Steel invested the same amount for the same period at 8% simple interest.

Who earns more interest and by how much?

Solution

Given

Principal Amount (P) = ₹1,00,000

Rate of Interest (R) = 8% per annum

Time (T) = 3 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)³

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (1,00,000 × 8 × 3) ÷ 100

= ₹24,000

Step 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

Step 3: Compare the Interest Earned

Difference

= Compound Interest − Simple Interest

= ₹25,971.20 − ₹24,000

= ₹1,971.20

Answer

The engineer who invested at Compound Interest earns ₹1,971.20 more than the engineer who invested at Simple Interest.

So,

Exam Tip (SSC, RRB, Banking, Defence & Police Exams)

When the principal, rate, and time are the same, Compound Interest always earns more than Simple Interest for periods greater than one year because interest is earned on the accumulated interest every year.

Question 7: A resident of Unnao invested ₹50,000 at 12% per annum for 2 years.

Calculate the percentage by which the Compound Interest exceeds the Simple Interest.

(Related topic: Percentage.)

Solution

Given

Principal Amount (P) = ₹50,000

Rate of Interest (R) = 12% per annum

Time (T) = 2 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)²

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (50,000 × 12 × 2) ÷ 100

= ₹12,000

Step 2: Calculate the Compound Interest

Amount

= 50,000 × (1 + 12/100)²

= 50,000 × (1.12)²

= 50,000 × 1.2544

= ₹62,720

Compound Interest

= ₹62,720 − ₹50,000

= ₹12,720

Step 3: Calculate the Difference

Difference

= Compound Interest − Simple Interest

= ₹12,720 − ₹12,000

= ₹720

Step 4: Calculate the Percentage by which Compound Interest Exceeds Simple Interest

Percentage Difference

= (Difference ÷ Simple Interest) × 100

= (720 ÷ 12,000) × 100

= 6%

Answer

The Compound Interest exceeds the Simple Interest by 6%.

So,

Question 8: The elder brother invested under Simple Interest, while the younger brother invested under Compound Interest.

Both invested for 2 years at 10% per annum.

If the elder brother invested ₹45,000, calculate the difference between their interest earnings.

(Related topic: Ratio & Proportion.)

Solution

Given

Principal Amount (P) = ₹45,000

Rate of Interest (R) = 10% per annum

Time (T) = 2 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)²

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (45,000 × 10 × 2) ÷ 100

= ₹9,000

Step 2: Calculate the Compound Interest

Amount

= 45,000 × (1 + 10/100)²

= 45,000 × (1.10)²

= 45,000 × 1.21

= ₹54,450

Compound Interest

= ₹54,450 − ₹45,000

= ₹9,450

Step 3: Calculate the Difference

Difference

= Compound Interest − Simple Interest

= ₹9,450 − ₹9,000

= ₹450

Answer

The younger brother earns ₹450 more in interest than the elder brother.

So,

Question 9:A person invested money at 10% per annum for 2 years.The Compound Interest exceeded the Simple Interest by ₹500.

Find the Principal Amount.

Solution

Given

Difference between Compound Interest and Simple Interest = ₹500

Rate of Interest (R) = 10% per annum

Time (T) = 2 years

Principal Amount (P) = ?

Formula Used

For 2 years,

Difference (CI − SI) = (P × R²) ÷ 100²

Step 1: Substitute the Given Values

500 = (P × 10²) ÷ 100²

Step 2: Simplify the Equation

500 = (P × 100) ÷ 10,000

500 = P ÷ 100

Step 3: Calculate the Principal

P = 500 × 100

= ₹50,000

Answer

The Principal Amount is ₹50,000.

So,

Exam Tip (SSC, RRB, Banking, Defence & Police Exams)

If the difference between Compound Interest and Simple Interest is given for 2 years, use the shortcut:

Principal = (Difference × 100²) ÷ R²

For this question,

Principal

= (500 × 100²) ÷ 10²

= (500 × 10,000) ÷ 100

= ₹50,000

Question 10: A Bank Manager introduced two investment plans.

• Plan A: Simple Interest at 10% per annum
• Plan B: Compound Interest at 10% per annum, compounded annually.

After 3 years, a customer found that Plan B earned ₹1,155 more interest than Plan A.

Find the Principal Amount.

Solution

Given

Difference between Compound Interest and Simple Interest = ₹1,155

Rate of Interest (R) = 10% per annum

Time (T) = 3 years

Principal Amount (P) = ?

Formula Used

For 3 years,

Difference (CI − SI) = P × R² × (300 + R) ÷ 100³

Step 1: Substitute the Given Values

1,155 = P × 10² × (300 + 10) ÷ 100³

Step 2: Simplify the Equation

1,155 = P × 100 × 310 ÷ 10,00,000

1,155 = 31P ÷ 1,000

Step 3: Calculate the Principal

31P = 1,155 × 1,000

31P = 11,55,000

P = 11,55,000 ÷ 31

= ₹37,258.06 (Approx.)

Answer

The Principal Amount is approximately ₹37,258.06.

So,

Question 11: A resident of Parade, Kanpur purchased a laptop after receiving a 20% discount and saved ₹18,000.

He invested the entire savings for 2 years at 10% per annum.

Calculate the difference between Compound Interest and Simple Interest.

(Students can revise the Discount questions to understand how the savings were calculated.)

Solution

Given

Savings after discount (Principal Amount) = ₹18,000

Rate of Interest (R) = 10% per annum

Time (T) = 2 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)²

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (18,000 × 10 × 2) ÷ 100

= ₹3,600

Step 2: Calculate the Compound Interest

Amount

= 18,000 × (1 + 10/100)²

= 18,000 × (1.10)²

= 18,000 × 1.21

= ₹21,780

Compound Interest

= ₹21,780 − ₹18,000

= ₹3,780

Step 3: Calculate the Difference

Difference

= Compound Interest − Simple Interest

= ₹3,780 − ₹3,600

= ₹180

Answer

The Compound Interest exceeds the Simple Interest by ₹180.

So,

Exam Tip (SSC, RRB, Banking, Defence & Police Exams)

Don’t get distracted by the 20% discount mentioned in the question. Since the saved amount (₹18,000) is already given, it directly becomes the principal for the interest calculation.

For 2-year questions, you can use the shortcut:

Difference (CI − SI) = (P × R²) ÷ 100²

= (18,000 × 10²) ÷ 100²

= (18,000 × 100) ÷ 10,000

= ₹180

Question 12: A Pharmacist in Indian Railways and a Station Master each invested ₹75,000 for 3 years.

• The Pharmacist chose Simple Interest at 9% per annum.
• The Station Master chose Compound Interest at 9% per annum, compounded annually.

Calculate:

1. Simple Interest earned by the Pharmacist.
2. Compound Interest earned by the Station Master.
3. Difference in interest earned.
4. Difference in maturity amounts.
5. By what percentage did the Compound Interest exceed the Simple Interest?

Solution

Given

Principal Amount (P) = ₹75,000

Rate of Interest (R) = 9% per annum

Time (T) = 3 years

Formula Used

Simple Interest

SI = (P × R × T) ÷ 100

Compound Interest

Amount = Principal × (1 + R/100)³

Compound Interest = Amount − Principal

Step 1: Calculate the Simple Interest

Simple Interest

= (75,000 × 9 × 3) ÷ 100

= ₹20,250

Simple Interest Amount

= ₹75,000 + ₹20,250

= ₹95,250

Step 2: Calculate the Compound Interest

Amount

= 75,000 × (1 + 9/100)³

= 75,000 × (1.09)³

= 75,000 × 1.295029

= ₹97,127.18 (Approx.)

Compound Interest

= ₹97,127.18 − ₹75,000

= ₹22,127.18 (Approx.)

Step 3: Calculate the Difference in Interest

Difference

= ₹22,127.18 − ₹20,250

= ₹1,877.18 (Approx.)

Step 4: Calculate the Difference in Maturity Amounts

Difference

= ₹97,127.18 − ₹95,250

= ₹1,877.18 (Approx.)

Step 5: Calculate the Percentage by which Compound Interest Exceeds Simple Interest

Percentage Difference

= (Difference ÷ Simple Interest) × 100

= (1,877.18 ÷ 20,250) × 100

≈ 9.27%

Answer

• Simple Interest earned: ₹20,250
• Compound Interest earned: ₹22,127.18 (Approx.)
• Difference in interest earned: ₹1,877.18 (Approx.)
• Difference in maturity amounts: ₹1,877.18 (Approx.)
• Compound Interest exceeds Simple Interest by: 9.27% (Approx.)

So,

Exam Tip (SSC, RRB, Banking, Defence & Police Exams)

When the principal is the same, remember these facts:

• Difference in Interest = Difference in Maturity Amount
• This is because both investments start with the same principal.
• If asked for the percentage by which Compound Interest exceeds Simple Interest, use:

Percentage Difference = (Difference ÷ Simple Interest) × 100

What We Learned in This Section

In this section, we learned how to calculate Simple Interest, Compound Interest, Maturity Amount, and the difference between SI and CI. We also practiced shortcut methods, reverse questions, percentage comparisons, and exam-oriented word problems involving investments and loans.

Related Topics

To strengthen your understanding, you should also learn:

• Percentage – The foundation of interest calculations.
• Ratio and Proportion – Useful for solving investment and finance problems.
• Profit, Loss and Discount – Frequently combined with Simple Interest and Compound Interest in competitive exams.

FAQ

1. Why is Compound Interest always greater than Simple Interest?

Compound Interest is usually greater than Simple Interest for periods longer than one year because interest is earned on both the principal and the accumulated interest, whereas Simple Interest is calculated only on the principal.

2. What is the shortcut formula for the difference between SI and CI?

• For 2 years: Difference = (P × R²) ÷ 100²
• For 3 years: Difference = P × R² × (300 + R) ÷ 100³

3. Can we use the 2-year shortcut for 3-year questions?

No. The 2-year shortcut is valid only for 2-year questions. For 3-year questions, use the dedicated 3-year shortcut formula or calculate SI and CI separately.

4. Which exams ask Difference Between SI and CI questions?

These questions are commonly asked in SSC, RRB, Banking, Defence, Police, State PSC, and other competitive examinations.

5. Is the difference between maturity amounts equal to the difference between interest amounts?

Yes. When the principal amount is the same, the difference between the maturity amounts is equal to the difference between the interest amounts

Important Resources Related to Difference Between Simple Interest and Compound Interest Questions with Answers and Solutions

1. Simple Interest & Compound Interest
2. Simple Interest Questions with Answers and Solutions
3. Simple Interest & Compound Interest Formula with Examples and Explanations
4. Compound Interest Questions with Answers and Solutions (15 Solved)
5. Compound Growth Questions with Answers and Solutions
6. Depreciation Questions with Answers and Solutions
7. Simple Interest & Compound Interest Practice Questions
8. Simple Interest & Compound Interest PYQs SSC, RRB, Banking & Defence Exams With Solution.