Compound Interest Questions

Introduction to Compound Interest Questions

The topic of compound interest in mathematics and daily life is very important. Compound interest means that you earn interest not only on the money you first invested (called the principal), but also on the interest already added. In simple words, in compound interest, your money increases rapidly because you gain "interest in interest".

For example, if you deposit ₹100 in the bank with a 10% interest rate, after one year, you earn ₹10 interest and have ₹110. In the second year, the interest is calculated on ₹110 (not just 100), so you get ₹11. In this way, the amount increases.

In this article, we will learn the formula for compound interest, how to solve problems step-by-step, and practice with solved examples. By the end, you will clearly understand how compound interest works and how to answer the questions correctly.

 

Table of Contents

• Compound Interest Definition
• Compound Interest Questions and Answers
• Modified Formulas Based on Compounding Frequency
• Practice Questions
• Conclusion
• FAQs on Compound Interest Questions

 

Compound Interest Definition 

Composite interest is extra money that we earn not only on the main money we kept (called the principal), but also on the interest that gets added to it over time. In simple words, it means "interest in interest". This makes money grow faster than simple interest.

For example, if you keep the ₹1000 in the bank at 10% interest after the first year, you earn ₹100 interest (so total = ₹1100). In the second year, you do not earn interest only on ₹1000, but on ₹1100. That's why you get ₹110 interest rates, and now the total is  ₹1210. In this way, the money increases every year as interest rates are also counted in the next calculation.

The formula for compound interest is : 

A = P * ( 1 + (R / 100))^T  

Where:

• A = Total amount after interest

• P = Privnil (the main money)

• R = Rate of interest 

• T = Time (in years)

 Compound Interest ( CI ) - A - P

 

Compound Interest Questions and Answers

1. CI with Annual Compounding 

Q. Find the amount and compound interest on ₹15000 for 3 years at 8% p.a., compounded annually.
Formula:

 A = P * ( 1 + (R / 100))ⁿ , ( CI ) - A - P

Work:

P = 15000, R = 8 , n =3

A = 15000 (1 + (8/100))³  = 15000 (1.08)³ = ₹18,895.68

CI = 18895.68 − 1500 = ₹3895.68

Answer: Amound =  ₹18895.68 , CI = ₹3895.68.

2. Find the rate (R) from given P, A, n

Q. A sum becomes ₹ 6050 in 2 years at compound interest. The principal is ₹5000. Find the rate per annum.

Formula:

A = P * ( 1 + (R / 100))ⁿ  ⇒  ( 1 + (R / 100)) = n(√A/P)

Work:

( 1 + (R / 100))²  = 6050 / 5000 = 1.21

( 1 + (R / 100)) = √1.21 = 1.10

(R / 100) = 0.10

R = 10%

Answer: 10% p.a.

3. Half-yearly compounding

Q. Find the amount and CI on ₹24000 for 1 year at 12% p.a., compounded half-yearly.

Formula:

A = P ( 1 + (R / 200))²ⁿ

Work:

P = 24000, R =12, n = 1

A = 24000 ( 1 + (12 / 200))² = 24000 (1.06)² = 26966.40

A = ₹26,966.40

CI = 26966.40 – 24000 = 2966.40

CI = ₹2,966.40

Answer: Anomt = ₹26966.40, CI = ₹2966.40.

4. Quarterly compounding with 1.5 years

Q. Find the CI on ₹8000 for 1.5 years at 8% p.a., compounded quarterly.

Formula:

A = P ( 1 + (R / 400))⁴ⁿ

Work:

Time = 1.5 years = 6 quarters

P = 8000, R = 8

A = 8000 ( 1 + (8 / 400))⁶= 8000 (1.02)⁶ ≈ 9009.30  

 ^{CI ≈ ₹1009.30 – 8000 = 1009.30}

Answer: CI ≈ ₹1009.30

5. Deprstation 

Q. A phone costs ₹30000. Its value decreases by 10% each year. Find its value after 2 years.

Formula:

A = P ( 1 – (R / 100))ⁿ

Work:

P = 30000, R = 10, n=2

A = 30000 (0.09)² = 30000 * 0.81 = 24,300 

A = ₹24,300

Answer: Vale after 2 years = ₹24300 (loss = ₹5,700).

6. Population growth

Q. A town has 50000 people. The population grows at 4% per year. What will it be after 3 years?

Formula: 

A = P ( 1 + (R / 100))ⁿ

Work:

P = 50000, R= 4, n=3

A = 50000(1.04)³  ≈  50000 * 1.124864 = 56,243.20

Answer: About 56,243 people.

7. Find time(n) from P,A,R

Q. ₹2000 becomes ₹2315.25 at 5% p.a, compound interest. Find the time (years), annual compounding.

Formula: 

A = P( 1 + (R / 100))ⁿ → (1.05)ⁿ = (2315.25/2000) = 1.157625

Notice:

1.05³ = 1.157625  → n = 3years

Answer: 3 years

8. Different rates in different years

Q. ₹10000 is invested for 3 years: 10% in 1st year, 8% in 2nd, 12% in 3rd. Find the amount and CI.

Work: 

Year 1: 10000 → 10000 * 1.10 = 11000

Year 2: 11000 → 11000 * 1.08 = 11880

Year 3: 11880 → 11880 * 1.12 = 13305.60

CI = 13,305.60 − 10,000 = ₹3,305.60

Answer: Amount = ₹13,305.60, CI = ₹3,305.60

9. Find the principal (P) from the given amount 

Q. The amount is ₹24,200 after 2 years at 10% p.a. Find the principal.

Formula: 

A = P (1.10)²  → P = A / 1.21

P = 24200 / 1.21 = 20,000

Answer: Principal = ₹20,000.

10. Compare Simple Interest(SI) and Compund Interest (CI)

Q. For ₹5,000 at 10% p.a. for 2 years, find SI and CI, and the difference.

Formula: 

SI = (P * R * T / 100), CI = P  ( 1 + (R / 100))^T– P

Work:

SI:

SI = 5000 * 10 * 2 / (100) = 1,000

CI:

CI = 5000 (1.10)²– 5000 = 5000 * 1.21 – 5000 = 1,050

Difference: 1050 − 1000 = ₹50

Answer: SI = ₹1,000, CI = ₹1,050, CI is ₹50 more.

Modified Formulas Based on Compounding Frequency

Different compounding frequencies affect how the formula is applied. Here's a table for quick reference:

 

Practice Questions

1. What will be the compound interest on 8000 at the 15% rate per annum for 2 years and 4 months?

2. What is the compound interest on 8000 at 5% per annum for 2 years?

3. In what time will the amount of Rs 30000 amount to 34347 at 7% compound interest?

4. What is the amount and compound interest on Rs 10800 for 3 years at 12.5% per annum compound annually?

5. What is the compound interest on Rs 3500 at 6 per annum for 3 years, the interest being compounded half-yearly?

Conclusion

Compound interest means earning interest not only on the original money, but also on the interest already added. This is why money grows faster in compound interest. We learned the formulas, solved examples, and saw how it is used in banks, loans, savings, and investments. By practicing the sum, the topic becomes simple and very useful in real life.

 

FAQs on Compound Interest Questions

1. What is the compound interest on 8000 at 5% per annum for 2 years?

Ans: Formula:   

A = P  ( 1 + (R / 100))^T 

CI = A - P

Given:

P = ₹8000, R = 5%, T = 2 years

A = 8000 ( 1 + (5 / 100))² =  8000 * (1.05)²

A = 8000 × 1.1025 = ₹8820

CI = 8820 − 8000 = ₹820

2. What will be the compound interest on ₹25,000 after 3 years at 12 per annum?

Ans: A = 25000 (1 + 0.12)³

A = 25000 * (1.12)³

A = 25000×1.404928 = ₹35,123.20 

CI = 35123.20 − 25000 = ₹10,123.20

3. What is the compound interest on 6000 at 10% per annum for 2 years?

Ans: A = 6000 (1 + 0.10)² 

A = 6000 * (1.1)²

A = 6000 × 1.2

A = ₹7260

CI = 7260 − 6000

CI = ₹1260 CI

3. What is the simple interest on ₹5000 at 5% for 2 years?

Ans: Simple Interest Formula: SI = (P * R * T) / 100

SI = 5000 * 5 * 2 / 100

SI = 50000/100 = 500

4. What is the compound interest on ₹10,000 at 8% per annum for 2 years?

Ans: A = 10000 (1 + 0.08)²

            = 10000 × 1.1664

            = ₹11,664

CI = 11664 − 10000 = ₹1664