Question 1

A sum of ₹8,000 is invested at 10% per annum compound interest. What will be the amount after 2 years?

Accepted Answer

Step 1: Use the compound interest formula A = P(1 + r/100)^n. Step 2: A = 8000(1 + 10/100)^2 = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680. Therefore, the amount after 2 years is ₹9,680.

Question 2

₹5,000 becomes ₹6,050 in 2 years at compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 6050 = 5000(1 + r/100)^2. Step 3: (1 + r/100)^2 = 6050/5000 = 1.21. Step 4: 1 + r/100 = √1.21 = 1.1. Step 5: r/100 = 0.1, so r = 10% per annum.

Question 3

A principal amount doubles itself in 5 years at compound interest. In how many years will it become 8 times at the same rate?

Accepted Answer

Step 1: If principal doubles in 5 years, then A = 2P when n = 5. Step 2: For amount to become 8 times: 8P = P(1 + r/100)^n. Step 3: Since 2P = P(1 + r/100)^5, we have (1 + r/100)^5 = 2. Step 4: For 8P: (1 + r/100)^n = 8 = 2^3 = [(1 + r/100)^5]^3 = (1 + r/100)^15. Step 5: Therefore, n = 15 years.

Question 4

₹10,000 is invested at 5% per annum compound interest compounded half-yearly. What is the amount after 1 year?

Accepted Answer

Step 1: When interest is compounded half-yearly, the rate per half-year = 5/2 = 2.5% and number of periods = 2. Step 2: A = P(1 + r/100)^n = 10000(1 + 2.5/100)^2 = 10000(1.025)^2. Step 3: (1.025)^2 = 1.050625. Step 4: A = 10000 × 1.050625 = ₹10,506.25.

Question 5

The difference between compound interest and simple interest on a sum for 2 years at 10% per annum is ₹100. What is the principal?

Accepted Answer

Step 1: For 2 years, CI - SI = P × (r/100)^2 / 100 × (100 + r). Alternatively, CI - SI = P × r^2 / (100)^2 for 2 years. Step 2: Using the formula: 100 = P × (10)^2 / (100)^2 = P × 100 / 10000 = P / 100. Step 3: P = 100 × 100 = ₹10,000.

Question 6

A sum of ₹4,000 is invested at 12% per annum compound interest. What will be the compound interest earned in 2 years?

Accepted Answer

Step 1: Calculate the amount using A = P(1 + r/100)^n = 4000(1 + 12/100)^2 = 4000(1.12)^2. Step 2: (1.12)^2 = 1.2544. Step 3: A = 4000 × 1.2544 = ₹5,017.60. Step 4: Compound Interest = A - P = 5017.60 - 4000 = ₹1,017.60.

Question 7

A sum of ₹8,000 is invested at 10% per annum compound interest. What will be the amount after 3 years?

Accepted Answer

Step 1: Use the compound interest formula A = P(1 + r/100)^n. Step 2: A = 8000(1 + 10/100)^3 = 8000(1.1)^3. Step 3: (1.1)^3 = 1.331. Step 4: A = 8000 × 1.331 = ₹10,648. Therefore, the amount after 3 years is ₹10,648.

Question 8

The compound interest on ₹5,000 at 8% per annum for 2 years is how much more than the simple interest for the same period?

Accepted Answer

Step 1: Calculate CI: A = 5000(1 + 8/100)^2 = 5000(1.08)^2 = 5000 × 1.1664 = ₹5,832. CI = 5832 - 5000 = ₹832. Step 2: Calculate SI: SI = (5000 × 8 × 2)/100 = ₹800. Step 3: Difference = 832 - 800 = ₹32. Therefore, CI is ₹32 more than SI.

Question 9

At what rate per annum will ₹6,000 amount to ₹7,986 in 3 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 7986 = 6000(1 + r/100)^3. Step 3: (1 + r/100)^3 = 7986/6000 = 1.331. Step 4: Take cube root: 1 + r/100 = 1.1. Step 5: r/100 = 0.1, so r = 10%. Therefore, the rate is 10% per annum.

Question 10

The difference between compound interest and simple interest on ₹10,000 at 5% per annum for 3 years is:

Accepted Answer

Step 1: Calculate CI: A = 10000(1 + 5/100)^3 = 10000(1.05)^3. Step 2: (1.05)^3 = 1.157625. Step 3: A = 10000 × 1.157625 = ₹11,576.25. CI = 11576.25 - 10000 = ₹1,576.25. Step 4: Calculate SI: SI = (10000 × 5 × 3)/100 = ₹1,500. Step 5: Difference = 1576.25 - 1500 = ₹76.25. Therefore, the difference is ₹76.25.

Question 11

A sum of money doubles itself in 5 years at compound interest. In how many years will it become 8 times at the same rate?

Accepted Answer

Step 1: If principal P doubles in 5 years, then 2P = P(1 + r/100)^5, so (1 + r/100)^5 = 2. Step 2: We need to find n such that 8P = P(1 + r/100)^n, so (1 + r/100)^n = 8. Step 3: Note that 8 = 2^3, so (1 + r/100)^n = [(1 + r/100)^5]^3 = 2^3. Step 4: This means (1 + r/100)^n = (1 + r/100)^(5×3), so n = 15 years. Therefore, the sum will become 8 times in 15 years.

Question 12

A principal amount doubles itself in 5 years at compound interest. In how many years will it become 8 times itself at the same rate?

Accepted Answer

Step 1: If P doubles in 5 years, then 2P = P(1 + r/100)^5, so (1 + r/100)^5 = 2. Step 2: For amount to be 8P: 8P = P(1 + r/100)^n, so (1 + r/100)^n = 8. Step 3: Since 8 = 2³, we have [(1 + r/100)^5]^3 = (1 + r/100)^15. Step 4: Therefore n = 15 years.

Question 13

A principal amount invested at 20% per annum compound interest becomes ₹17,280 after 2 years. If the same principal is invested at 10% per annum simple interest, what will be the amount after 3 years?

Accepted Answer

Step 1: Find principal using compound interest formula: 17280 = P(1 + 20/100)² = P(1.2)² = P(1.44). Step 2: P = 17280 ÷ 1.44 = 12,000. Step 3: Using simple interest formula for 3 years at 10%: A = P + (P × r × t)/100 = 12000 + (12000 × 10 × 3)/100 = 12000 + 3600 = 15,600. Therefore, the amount is ₹15,600.

Question 14

A sum of money becomes ₹9,680 after 2 years at 10% per annum compound interest. What was the principal amount?

Accepted Answer

Step 1: Use the compound interest formula A = P(1 + r/100)^n. Step 2: Substitute: 9680 = P(1 + 10/100)^2 = P(1.1)^2 = P(1.21). Step 3: P = 9680 ÷ 1.21 = 8000. Therefore, the principal is ₹8,000.

Question 15

The difference between compound interest and simple interest on a sum for 3 years at 5% per annum is ₹244. What is the principal?

Accepted Answer

Step 1: For 3 years at 5% p.a., CI = P[(1.05)³ - 1] = P[1.157625 - 1] = 0.157625P. Step 2: SI = (P × 5 × 3)/100 = 0.15P. Step 3: Difference = 0.157625P - 0.15P = 0.007625P = 244. Step 4: P = 244 ÷ 0.007625 = 32,000. Therefore, principal is ₹32,000.

Question 16

A certain sum becomes ₹6,050 in 2 years and ₹6,655 in 3 years at compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Amount after 2 years = ₹6,050. Amount after 3 years = ₹6,655. Step 2: The interest earned in the 3rd year = 6655 - 6050 = ₹605. Step 3: This ₹605 is the interest on ₹6,050 for 1 year. Step 4: Rate = (605/6050) × 100 = 10% per annum.

Question 17

A sum of ₹12,000 is invested at compound interest. If the amount becomes ₹13,200 in 1 year and ₹14,520 in 2 years, what is the rate of interest, and how much interest is earned in the 2nd year?

Accepted Answer

Step 1: Interest in 1st year = 13200 - 12000 = ₹1,200. Rate = (1200/12000) × 100 = 10% p.a. Step 2: Interest in 2nd year = 14520 - 13200 = ₹1,320. Verification: Interest on ₹13,200 at 10% = (13200 × 10)/100 = ₹1,320. ✓ Therefore, rate is 10% p.a. and interest in 2nd year is ₹1,320.

SSC CPO Compound Interest

Compound Interest— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Compound Interest — Practice Questions

60-Second Revision — Compound Interest