Question 1

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

Question 2

At what rate per annum will ₹8,000 amount to ₹9,261 in 3 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 9261 = 8000(1 + r/100)^3. Step 3: (1 + r/100)^3 = 9261/8000 = 1.157625. Step 4: Taking cube root: 1 + r/100 = 1.05. Step 5: r/100 = 0.05, so r = 5% per annum.

Question 3

A principal amounts to ₹12,100 in 2 years at 10% per annum compound interest. What is the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 12100 = P(1 + 10/100)^2 = P(1.1)^2 = P × 1.21. Step 3: P = 12100/1.21 = ₹10,000. Therefore, the principal is ₹10,000.

Question 4

What is the compound interest on ₹6,400 for 2 years at 12.5% per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: A = 6400(1 + 12.5/100)^2 = 6400(1.125)^2 = 6400 × 1.265625 = ₹8,100. Step 3: Compound Interest = A - P = 8100 - 6400 = ₹1,700.

Question 5

The difference between compound interest and simple interest on ₹4,000 for 2 years at 5% per annum is:

Accepted Answer

Step 1: Simple Interest = (P × R × T)/100 = (4000 × 5 × 2)/100 = ₹400. Step 2: Amount at CI = 4000(1 + 5/100)^2 = 4000(1.05)^2 = 4000 × 1.1025 = ₹4,410. Step 3: Compound Interest = 4410 - 4000 = ₹410. Step 4: Difference = CI - SI = 410 - 400 = ₹10.

Question 6

A sum of ₹5,000 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 = 5000(1 + 10/100)^2 = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050. Therefore, the amount after 2 years is ₹6,050.

Question 7

The compound interest on ₹5,000 for 2 years at a certain rate per annum is ₹1,050. What is the rate of interest per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: Amount A = 5000 + 1050 = 6050. Step 3: 6050 = 5000(1 + r/100)^2. Step 4: (1 + r/100)^2 = 6050 ÷ 5000 = 1.21. Step 5: 1 + r/100 = √1.21 = 1.1. Step 6: r/100 = 0.1, so r = 10% per annum.

Question 8

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 the amount to become 8P: 8P = P(1 + r/100)^n, so (1 + r/100)^n = 8. Step 3: Since (1 + r/100)^5 = 2, we have [(1 + r/100)^5]^3 = 2^3 = 8. Step 4: Therefore, (1 + r/100)^15 = 8. Step 5: n = 15 years.

Question 9

A sum of ₹12,000 is invested at 8% per annum compound interest. What will be the amount after 3 years?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: A = 12000(1 + 8/100)^3 = 12000(1.08)^3. Step 3: Calculate (1.08)^3 = 1.08 × 1.08 × 1.08 = 1.259712. Step 4: A = 12000 × 1.259712 = 15,116.544 ≈ ₹15,116.54. Rounding to nearest rupee: ₹15,117.

Question 10

The difference between compound interest and simple interest on a sum for 2 years at 5% per annum is ₹50. What is the principal?

Accepted Answer

Step 1: For 2 years, CI - SI = P × r^2 / 100^2 (standard formula for 2-year difference). Step 2: 50 = P × 5^2 / 10000 = P × 25 / 10000. Step 3: 50 = P / 400. Step 4: P = 50 × 400 = ₹20,000.

Question 11

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

Accepted Answer

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

Question 12

A sum of ₹8,000 is invested at 10% per annum compound interest for 2 years. What is the compound interest earned?

Accepted Answer

Step 1: Use CI formula: A = P(1 + r/100)^n = 8000 × (1 + 10/100)² = 8000 × (1.1)² = 8000 × 1.21 = ₹9,680. Step 2: CI = A − P = 9680 − 8000 = ₹1,680. Therefore, the compound interest is ₹1,680.

Question 13

The difference between compound interest and simple interest on a sum for 3 years at 5% per annum is ₹61.25. What is the principal?

Accepted Answer

Step 1: For 3 years at 5% p.a., CI - SI = P × r² × (300 + 3r) / (100)³. Step 2: Alternatively, calculate directly: SI = P×5×3/100 = 0.15P. Step 3: Amount under CI = P(1.05)³ = P(1.157625). Step 4: CI = P(1.157625 - 1) = 0.157625P. Step 5: Difference = 0.157625P - 0.15P = 0.007625P = 61.25. Step 6: P = 61.25 / 0.007625 = 8,000.

Question 14

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

Accepted Answer

Step 1: If principal doubles in 5 years, then 2P = P(1 + r/100)^5, so (1 + r/100)^5 = 2. Step 2: For amount to become 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 15

A sum becomes ₹6,000 in 2 years and ₹6,600 in 3 years at compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Let principal = P and rate = r% p.a. Step 2: After 2 years: P(1 + r/100)² = 6000. Step 3: After 3 years: P(1 + r/100)³ = 6600. Step 4: Divide equation 3 by equation 2: [P(1 + r/100)³] / [P(1 + r/100)²] = 6600/6000. Step 5: (1 + r/100) = 1.1, so r/100 = 0.1, thus r = 10% p.a.

Question 16

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 values: 9680 = P(1 + 10/100)^2 = P(1.1)^2 = P(1.21). Step 3: Solve for P: P = 9680 ÷ 1.21 = 8000. Therefore, the principal is ₹8,000.

Question 17

A man invests ₹50,000 at 8% per annum compound interest for 2 years. If the interest is compounded half-yearly, what is the final amount?

Accepted Answer

Step 1: When compounded half-yearly, rate per half-year = 8/2 = 4% and number of periods = 2×2 = 4. Step 2: Amount = P(1 + r/100)^n = 50000(1 + 4/100)^4 = 50000(1.04)^4. Step 3: Calculate (1.04)^4: (1.04)² = 1.0816, then (1.0816)² = 1.16985856 ≈ 1.1699. Step 4: Amount = 50000 × 1.1699 = ₹58,495.

Question 18

A sum becomes ₹2,420 in 2 years at 10% per annum compound interest. What will it become in 3 years at the same rate?

Accepted Answer

Step 1: First find principal using A = P(1 + r/100)^n. Step 2: 2420 = P(1.1)^2 = P × 1.21, so P = 2420/1.21 = ₹2,000. Step 3: Amount after 3 years = 2000(1.1)^3 = 2000 × 1.331 = ₹2,662.

Question 19

The compound interest on ₹4,000 for 2 years at 5% per annum is:

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 4000(1 + 5/100)^2 = 4000(1.05)^2. Step 2: (1.05)^2 = 1.1025, so A = 4000 × 1.1025 = 4,410. Step 3: Compound Interest = A - P = 4410 - 4000 = ₹410.

Question 20

If ₹3,000 is invested at 20% per annum compound interest, how much interest will be earned in 1.5 years (compounded half-yearly)?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 20/2 = 10% and number of periods = 1.5 × 2 = 3. Step 2: A = P(1 + r/100)^n = 3000(1 + 10/100)^3 = 3000(1.1)^3 = 3000 × 1.331 = ₹3,993. Step 3: Compound Interest = 3993 - 3000 = ₹993.

Question 21

A sum of ₹5,000 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 = 5000(1 + 10/100)^2 = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050. Therefore, the amount after 2 years is ₹6,050.

Question 22

The compound interest on ₹6,400 at 12.5% per annum for 2 years is:

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: A = 6400(1 + 12.5/100)^2 = 6400(1.125)^2 = 6400 × 1.265625 = ₹8,100. Step 3: Compound Interest = A - P = 8100 - 6400 = ₹1,700.

Question 23

A principal amounts to ₹12,100 in 2 years at 10% per annum compound interest. What is the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 12100 = P(1 + 10/100)^2 = P(1.1)^2 = P × 1.21. Step 3: P = 12100/1.21 = ₹10,000. Therefore, the principal is ₹10,000.

Question 24

At what rate per annum will ₹8,000 amount to ₹9,680 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 9680 = 8000(1 + r/100)^2. Step 3: (1 + r/100)^2 = 9680/8000 = 1.21. Step 4: 1 + r/100 = √1.21 = 1.1. Step 5: r/100 = 0.1, so r = 10% per annum.

Question 25

At what rate per annum will ₹5,000 amount to ₹6,050 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, where A = 6050, P = 5000, n = 2. 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 26

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: Substitute P = 8000, r = 10, n = 2. Step 3: 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 27

₹5,000 is invested at 20% per annum compound interest. If the interest is compounded half-yearly, what will be the amount after 1.5 years?

Accepted Answer

Step 1: When compounded half-yearly, the rate becomes 20/2 = 10% per half-year. Step 2: Number of half-years in 1.5 years = 1.5 × 2 = 3. Step 3: Use A = P(1 + r/100)^n: A = 5000(1 + 10/100)^3 = 5000(1.1)^3. Step 4: Calculate (1.1)^3 = 1.331. Step 5: A = 5000 × 1.331 = ₹6,655. Therefore, the amount is ₹6,655.

Question 28

A sum of money becomes ₹9,680 after 2 years at 10% per annum compound interest. What is 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 29

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 P becomes 2P in 5 years, then (1 + r/100)^5 = 2. Step 2: We need to find n such that (1 + r/100)^n = 8. Step 3: Note that 8 = 2³, so (1 + r/100)^n = [(1 + r/100)^5]^3. Step 4: Therefore, n = 5 × 3 = 15 years.

Question 30

A sum of ₹12,000 is invested at 8% per annum compound interest. What will be the amount after 3 years?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: A = 12000(1 + 8/100)^3 = 12000(1.08)^3. Step 3: Calculate (1.08)^3 = 1.08 × 1.08 × 1.08 = 1.259712. Step 4: A = 12000 × 1.259712 = 15,116.544 ≈ ₹15,116.54. Rounding to nearest rupee: ₹15,117.

Question 31

A certain sum becomes ₹1,44,000 after 2 years and ₹1,72,800 after 3 years at compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: The amount after 2 years is ₹1,44,000 and after 3 years is ₹1,72,800. Step 2: The interest earned in the 3rd year = 1,72,800 - 1,44,000 = ₹28,800. Step 3: This interest is earned on the principal of ₹1,44,000 (the amount at the end of year 2). Step 4: Rate = (28,800 / 1,44,000) × 100 = 20% per annum.

Question 32

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 values: 9680 = P(1 + 10/100)^2 = P(1.1)^2 = P(1.21). Step 3: Solve for P: P = 9680 ÷ 1.21 = 8000. Therefore, the principal is ₹8,000.

Question 33

The difference between compound interest and simple interest on a sum for 2 years at 5% per annum is ₹50. What is the principal?

Accepted Answer

Step 1: For 2 years, CI - SI = P × (r/100)² = P × (5/100)² = P × 0.0025. Step 2: Given CI - SI = 50, so P × 0.0025 = 50. Step 3: P = 50 ÷ 0.0025 = 20,000. Therefore, the principal is ₹20,000.

Question 34

The compound interest on a certain sum for 2 years at 5% per annum is ₹1,025. What is the principal?

Accepted Answer

Step 1: Compound Interest (CI) = A - P, where A = P(1 + r/100)^n. Step 2: So, 1025 = P(1.05)^2 - P = P[(1.05)^2 - 1]. Step 3: Calculate (1.05)^2 = 1.1025. Step 4: 1025 = P[1.1025 - 1] = P(0.1025). Step 5: P = 1025 ÷ 0.1025 = 10,000. Therefore, the principal is ₹10,000.

Question 35

A principal amount doubles in 5 years at a certain rate of compound interest per annum. 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 after 5 years. Step 2: Using A = P(1 + r/100)^n: 2P = P(1 + r/100)^5, so (1 + r/100)^5 = 2. Step 3: For the amount to become 8 times: 8P = P(1 + r/100)^n, so (1 + r/100)^n = 8. Step 4: Since (1 + r/100)^5 = 2, we have [(1 + r/100)^5]^3 = 2^3 = 8. Step 5: Therefore, (1 + r/100)^15 = 8, which means n = 15 years.

Question 36

A sum of money becomes ₹9,680 after 2 years at a certain rate of compound interest per annum. If the same sum becomes ₹10,648 after 3 years at the same rate, find the principal amount.

Accepted Answer

Step 1: Let the principal be P and rate be R% per annum. After 2 years: P(1 + R/100)² = 9,680. After 3 years: P(1 + R/100)³ = 10,648. Step 2: Divide the second equation by the first: [P(1 + R/100)³] / [P(1 + R/100)²] = 10,648 / 9,680. This gives (1 + R/100) = 10,648 / 9,680 = 1.10. So R = 10%. Step 3: Substitute back: P(1.10)² = 9,680, so P × 1.21 = 9,680, therefore P = 8,000.

Question 37

A principal amount doubles in 5 years under compound interest. In how many years will it become 8 times 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: We need to find n such that 8P = P(1 + R/100)^n, which means (1 + R/100)^n = 8. Step 3: Note that 8 = 2³, so (1 + R/100)^n = [(1 + R/100)^5]³ = (1 + R/100)^15. Step 4: Therefore, n = 15 years.

RRB NTPC Compound Interest

RRB NTPC Compound Interest — Past Exam Questions

Compound Interest— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Compound Interest — Practice Questions

60-Second Revision — Compound Interest