Question 1

₹5,000 is invested at 20% per annum compound interest. What is the compound interest earned in 2 years?

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 5000(1 + 20/100)^2 = 5000(1.2)^2 = 5000 × 1.44 = ₹7,200. Step 2: Compound Interest = A − P = 7,200 − 5,000 = ₹2,200. Therefore, the compound interest is ₹2,200.

Question 2

A sum of money becomes ₹4,840 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 known values: 4840 = P(1 + 10/100)^2. Step 3: Simplify: 4840 = P(1.1)^2 = P(1.21). Step 4: Solve for P: P = 4840 ÷ 1.21 = 4000. Therefore, the principal is ₹4,000.

Question 3

The compound interest on ₹4,000 at 50% per annum for 2 years is:

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 4,000(1 + 50/100)^2 = 4,000(1.5)^2 = 4,000 × 2.25 = ₹9,000. Step 2: Compound Interest = A − P = 9,000 − 4,000 = ₹5,000. Therefore, the compound interest is ₹5,000.

Question 4

The compound interest on ₹4,000 at 5% per annum for 2 years is how much more than the simple interest for the same period?

Accepted Answer

Step 1: Calculate compound interest. A = 4000(1 + 5/100)^2 = 4000(1.05)^2 = 4000 × 1.1025 = ₹4,410. CI = 4410 - 4000 = ₹410. Step 2: Calculate simple interest. SI = (4000 × 5 × 2)/100 = ₹400. Step 3: Difference = CI - SI = 410 - 400 = ₹10. Therefore, CI is ₹10 more than SI.

Question 5

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 6

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 7

Find the compound interest on ₹8,000 at 10% per annum for 2 years, compounded annually.

Accepted Answer

Step 1: Use CI formula: A = P(1 + r/100)^n. Step 2: A = 8000 × (1 + 10/100)² = 8000 × (1.1)² = 8000 × 1.21 = ₹9,680. Step 3: CI = A − P = 9680 − 8000 = ₹1,680. Therefore, the answer is ₹1,680.

Question 8

A principal becomes ₹10,800 in 2 years at 20% per annum compound interest. What is the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 10,800 = P(1 + 20/100)^2. Step 2: 10,800 = P(1.2)^2 = P × 1.44. Step 3: P = 10,800 ÷ 1.44 = ₹7,500. Therefore, the principal is ₹7,500.

Question 9

₹12,000 is invested at 25% per annum compound interest. What will be the amount after 1 year?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n = 12,000(1 + 25/100)^1 = 12,000(1.25) = ₹15,000. Step 2: After 1 year, the amount is ₹15,000. Therefore, the answer is ₹15,000.

Question 10

At what rate per annum will ₹6,000 become ₹7,260 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 7,260 = 6,000(1 + r/100)^2. Step 2: 7,260 ÷ 6,000 = (1 + r/100)^2, which gives 1.21 = (1 + r/100)^2. Step 3: Taking square root: 1.1 = 1 + r/100, so r/100 = 0.1, thus r = 10%. Therefore, the rate is 10% per annum.

Question 11

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 A = 2P. So 2P = P(1 + r/100)^5, which means (1 + r/100)^5 = 2. Step 2: For the amount to become 8P: 8P = P(1 + r/100)^n → (1 + r/100)^n = 8. Step 3: Note that 8 = 2^3, so (1 + r/100)^n = [(1 + r/100)^5]^3 = (1 + r/100)^15. Step 4: Therefore n = 15 years.

Question 12

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 becomes 2P in 5 years, then A = P(1 + r/100)^5 = 2P, so (1 + r/100)^5 = 2. Step 2: We need to find n such that P(1 + r/100)^n = 8P, 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: So n = 15 years. Therefore, the sum will become 8 times in 15 years.

Question 13

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: Amount A = P + CI = 5000 + 1050 = ₹6,050. Step 2: Use A = P(1 + r/100)^n: 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 14

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 15

At what rate per annum will ₹12,000 amount to ₹14,520 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 14520 = 12000(1 + r/100)^2. Step 3: (1 + r/100)^2 = 14520/12000 = 1.21. Step 4: 1 + r/100 = √1.21 = 1.1. Step 5: r/100 = 0.1, so r = 10% per annum. Therefore, the rate is 10% per annum.

Question 16

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. Here A = 9680, r = 10%, n = 2. 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 17

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% p.a. 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. Therefore R = 10% p.a. Step 3: Substitute back: P(1.10)² = 9,680, so P × 1.21 = 9,680, thus P = 8,000. Verification: 8,000 × 1.10³ = 8,000 × 1.331 = 10,648 ✓

Question 18

A sum of ₹8,000 is invested at compound interest at 10% per annum 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. Common mistake: Simple Interest = 8000 × 10 × 2/100 = ₹1,600 (distractor). Therefore, answer is ₹1,680.

Question 19

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, SI = (P × 5 × 2) ÷ 100 = 0.1P. Step 2: For CI, A = P(1 + 5/100)^2 = P(1.05)^2 = 1.1025P, so CI = 0.1025P. Step 3: Difference = CI − SI = 0.1025P − 0.1P = 0.0025P. Step 4: Given difference = ₹50, so 0.0025P = 50 → P = 50 ÷ 0.0025 = ₹20,000.

Question 20

A principal becomes ₹2,420 after 2 years at 10% per annum compound interest. What was the original principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 2420 = P(1 + 10/100)^2 = P(1.1)^2 = P × 1.21. Step 3: P = 2420/1.21 = ₹2,000. Therefore, the original principal was ₹2,000.

Question 21

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 22

A man invests ₹50,000 at 10% p.a. compound interest for 3 years, but the interest is compounded half-yearly. He then invests the entire amount (principal + interest) at 8% p.a. simple interest for 2 years. What is his total gain?

Accepted Answer

Step 1: For compound interest (half-yearly): Rate per half-year = 10/2 = 5%, Number of half-years = 3 × 2 = 6. Amount = 50,000(1.05)⁶. Step 2: Calculate (1.05)⁶ = 1.340096 ≈ 1.3401. Amount after 3 years = 50,000 × 1.3401 = 67,005. Step 3: This amount is now invested at 8% SI for 2 years. SI = (67,005 × 8 × 2)/100 = 10,721.60 ≈ 10,722. Step 4: Final amount = 67,005 + 10,722 = 77,727. Step 5: Total gain = 77,727 − 50,000 = ₹27,727.

Question 23

A sum of money becomes ₹9,680 after 2 years and ₹10,648 after 3 years when invested at compound interest. What is the principal amount?

Accepted Answer

Step 1: Let rate = R% p.a. and principal = P. 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: (1 + R/100) = 10,648 ÷ 9,680 = 1.10, so R = 10%. Step 3: Substitute back: P(1.10)² = 9,680 → P × 1.21 = 9,680 → P = 8,000. Therefore, the principal is ₹8,000.

Question 24

A certain sum becomes 4 times itself in 8 years at compound interest. In how many years will it become 8 times itself at the same rate?

Accepted Answer

Step 1: Let principal = P and rate = r% p.a. After 8 years: 4P = P(1 + r/100)⁸, so (1 + r/100)⁸ = 4. Step 2: Let (1 + r/100) = x. Then x⁸ = 4. Step 3: We need to find n such that x^n = 8. Since x⁸ = 4, we have x = 4^(1/8). Step 4: For x^n = 8: (4^(1/8))^n = 8, so 4^(n/8) = 8. Taking log: (n/8)log(4) = log(8). Step 5: (n/8) × log(2²) = log(2³), so (n/8) × 2log(2) = 3log(2). Step 6: n/8 = 3/2, so n = 12 years.

Question 25

A principal amount is invested at 20% per annum compound interest. If the compound interest earned in the 2nd year is ₹2,400, what is the compound interest earned in the 3rd year?

Accepted Answer

Step 1: Let principal = P. Amount after 1 year = P(1.20). Amount after 2 years = P(1.20)². Step 2: Compound interest in 2nd year = P(1.20)² − P(1.20) = P(1.20)[(1.20) − 1] = P(1.20)(0.20) = 0.24P. Given: 0.24P = 2,400, so P = 10,000. Step 3: Amount after 2 years = 10,000 × 1.44 = 14,400. Amount after 3 years = 10,000 × 1.728 = 17,280. Step 4: Compound interest in 3rd year = 17,280 − 14,400 = ₹2,880.

Question 26

A sum of money becomes ₹9,680 after 2 years and ₹10,648 after 3 years when invested at compound interest. Find the principal amount.

Accepted Answer

Step 1: The difference between amounts after 3 years and 2 years gives us one year's interest on ₹9,680. Interest for year 3 = ₹10,648 − ₹9,680 = ₹968. Step 2: Rate of interest = (968/9680) × 100 = 10% per annum. Step 3: Using A = P(1 + r/100)^n, we have 9,680 = P(1.10)^2 = P × 1.21. Step 4: P = 9,680 ÷ 1.21 = ₹8,000.

Question 27

A sum of ₹12,000 is invested at compound interest. If the amount becomes ₹13,200 after 1 year and ₹14,520 after 2 years, what is the rate of interest per annum?

Accepted Answer

Step 1: Principal = ₹12,000, Amount after 1 year = ₹13,200. Step 2: Interest earned in 1st year = 13,200 - 12,000 = ₹1,200. Step 3: Rate for 1st year = (1,200/12,000) × 100 = 10% p.a. Step 4: Verify with 2nd year: Amount after 2 years should be 13,200 × (1 + 10/100) = 13,200 × 1.10 = ₹14,520. ✓ Confirmed. Therefore, the rate is 10% p.a.

Question 28

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

Accepted Answer

Step 1: Let principal = P. Simple Interest for 2 years = (P × 10 × 2)/100 = 0.2P. Step 2: Compound Interest for 2 years = P(1.10)² - P = P(1.21 - 1) = 0.21P. Step 3: Difference = CI - SI = 0.21P - 0.2P = 0.01P. Step 4: Given difference = ₹100, so 0.01P = 100 → P = 10,000. Therefore, the principal is ₹10,000.

Question 29

₹5,000 is invested at 20% p.a. compound interest, compounded half-yearly. What is the amount after 1.5 years?

Accepted Answer

Step 1: Principal = ₹5,000, Rate = 20% p.a., Time = 1.5 years = 3 half-years. Step 2: Half-yearly rate = 20/2 = 10% per half-year. Step 3: Amount = P(1 + R/100)ⁿ = 5,000(1 + 10/100)³ = 5,000(1.10)³. Step 4: (1.10)³ = 1.331. Step 5: Amount = 5,000 × 1.331 = ₹6,655. Therefore, the amount is ₹6,655.

Question 30

A sum of money becomes ₹9,680 after 2 years and ₹10,648 after 3 years when invested at compound interest compounded annually. What is 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. Therefore R = 10%. Step 3: Substitute back: P(1.10)² = 9,680, so P × 1.21 = 9,680, thus P = 8,000. Verification: 8,000 × 1.10 × 1.10 × 1.10 = 10,648 ✓

Question 31

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

Accepted Answer

Step 1: Let principal = P, rate = R% p.a. Given: P(1 + R/100)⁵ = 2P. Step 2: (1 + R/100)⁵ = 2, so (1 + R/100) = 2^(1/5). Step 3: For amount to be 8P: P(1 + R/100)ⁿ = 8P → (1 + R/100)ⁿ = 8. Step 4: (2^(1/5))ⁿ = 8 = 2³ → 2^(n/5) = 2³ → n/5 = 3 → n = 15 years. Therefore, it takes 15 years.

Question 32

What is the compound interest earned on ₹5,000 at 20% per annum for 1.5 years, compounded half-yearly?

Accepted Answer

Step 1: When compounded half-yearly, rate becomes 20/2 = 10% per half-year. Step 2: Time = 1.5 years = 3 half-years. Step 3: A = 5000(1 + 10/100)^3 = 5000(1.1)^3 = 5000 × 1.331 = 6,655. Step 4: Compound Interest = 6,655 - 5,000 = ₹1,655.

Question 33

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 34

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. Step 2: For amount to become 8 times, A = 8P = 2^3 × P. Step 3: Since the amount doubles every 5 years, to get 2^3, we need 3 doubling periods. Step 4: Time = 3 × 5 = 15 years.

Question 35

A sum of money becomes ₹4,840 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 known values: 4840 = P(1 + 10/100)^2. Step 3: Simplify: 4840 = P(1.1)^2 = P(1.21). Step 4: Solve for P: P = 4840 ÷ 1.21 = 4000. Therefore, the principal is ₹4,000.

Question 36

At what rate per annum will ₹6,250 become ₹7,290 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, where A = 7,290, P = 6,250, n = 2. Step 2: 7,290 = 6,250(1 + r/100)^2. Step 3: (1 + r/100)^2 = 7,290 ÷ 6,250 = 1.1664. Step 4: 1 + r/100 = √1.1664 = 1.08. Step 5: r/100 = 0.08, so r = 8% per annum.

Question 37

₹10,000 is invested at 5% per annum compound interest compounded annually. What is the compound interest earned in the 3rd year only?

Accepted Answer

Step 1: Amount after 2 years: A₂ = 10000(1.05)^2 = 10000 × 1.1025 = ₹11,025. Step 2: Amount after 3 years: A₃ = 10000(1.05)^3 = 10000 × 1.157625 = ₹11,576.25. Step 3: Compound interest in 3rd year = A₃ - A₂ = 11,576.25 - 11,025 = ₹551.25.

Question 38

₹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 39

A sum of money becomes ₹4,320 in 2 years and ₹5,184 in 3 years at compound interest. What is the principal amount?

Accepted Answer

Step 1: Let principal = P and rate = r% p.a. Step 2: After 2 years: P(1 + r/100)^2 = 4,320. Step 3: After 3 years: P(1 + r/100)^3 = 5,184. Step 4: Divide equation 3 by equation 2: (1 + r/100) = 5,184/4,320 = 1.2. Step 5: So r = 20%. Step 6: P(1.2)^2 = 4,320, so P × 1.44 = 4,320, thus P = ₹3,000.

Question 40

₹12,000 is invested at 8% per annum compound interest. What will be the difference between the compound interest and simple interest for 2 years?

Accepted Answer

Step 1: Compound Interest: A = 12000(1.08)^2 = 12000 × 1.1664 = ₹13,996.80. CI = 13,996.80 - 12,000 = ₹1,996.80. Step 2: Simple Interest: SI = (12000 × 8 × 2)/100 = ₹1,920. Step 3: Difference = CI - SI = 1,996.80 - 1,920 = ₹76.80.

Question 41

A sum of money becomes ₹6,480 in 2 years and ₹7,776 in 3 years at compound interest. What is the principal and rate of interest?

Accepted Answer

Step 1: Let principal = P and rate = r% p.a. Step 2: After 2 years: 6480 = P(1 + r/100)^2. Step 3: After 3 years: 7776 = P(1 + r/100)^3. Step 4: Divide equation 3 by equation 2: 7776/6480 = (1 + r/100). Step 5: 1.2 = 1 + r/100, so r = 20% p.a. Step 6: Substitute back: 6480 = P(1.2)^2 = P × 1.44. Step 7: P = 6480/1.44 = ₹4,500.

Question 42

A sum of ₹12,000 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 = 12000(1 + 10/100)^2 = 12000(1.1)^2 = 12000 × 1.21 = ₹14,520. Therefore, the amount after 2 years is ₹14,520.

Question 43

The difference between compound interest and simple interest on a certain principal for 2 years at 12% per annum is ₹144. 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: Substitute: 144 = P × 12^2 / 100^2 = P × 144 / 10000. Step 3: Solve for P: P = 144 × 10000 / 144 = 10,000. Therefore, the principal is ₹10,000.

Question 44

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 A = 2P when n = 5. Using A = P(1 + r/100)^n: 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 = (1 + r/100)^15. Therefore, n = 15 years.

Question 45

₹5,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the amount after 1 year?

Accepted Answer

Step 1: When compounded half-yearly, rate per half-year = 12/2 = 6% and number of periods = 2. Step 2: A = P(1 + r/100)^n = 5000(1 + 6/100)^2 = 5000(1.06)^2. Step 3: (1.06)^2 = 1.1236. Step 4: A = 5000 × 1.1236 = ₹5,618.

Question 46

The difference between compound interest and simple interest on a sum for 2 years at 8% per annum is ₹64. 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: 64 = P × 8^2 / 10000 = P × 64 / 10000. Step 3: 64 = 64P / 10000. Step 4: P = 64 × 10000 / 64 = ₹10,000.

Question 47

₹8,000 becomes ₹9,261 in 3 years at a certain rate of compound interest per annum. What is the rate of 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 48

The compound interest on ₹12,000 at 8% per annum for 3 years is how much more than the simple interest for the same period?

Accepted Answer

Step 1: Calculate CI: A = 12000(1.08)^3. Calculate (1.08)^3 = 1.08 × 1.08 × 1.08 = 1.259712. So A = 12000 × 1.259712 = 15,116.544. CI = 15,116.544 − 12,000 = 3,116.544. Step 2: Calculate SI = (12000 × 8 × 3)/100 = 2,880. Step 3: Difference = 3,116.544 − 2,880 = 236.544 ≈ ₹237.

Question 49

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 50

A certain sum is invested at compound interest. It becomes ₹2,400 after 1 year and ₹2,880 after 2 years. If the same sum were invested at simple interest at the same rate, what would be the amount after 2 years?

Accepted Answer

Step 1: From the given data, interest earned in the first year = 2,400 − P. Interest earned in the second year = 2,880 − 2,400 = ₹480. Step 2: In compound interest, the second year's interest is earned on (P + first year's interest). So, 480 = (2,400) × (r/100), giving r = 20% p.a. Step 3: From 2,400 = P(1.20), we get P = 2,000. Step 4: At simple interest for 2 years: A = P + (P × r × t)/100 = 2,000 + (2,000 × 20 × 2)/100 = 2,000 + 800 = ₹2,800.

Question 51

A sum of money becomes ₹9,680 after 2 years and ₹10,648 after 3 years when invested at compound interest. Find the principal and rate of interest per annum.

Accepted Answer

Step 1: The difference between amounts at year 3 and year 2 gives us one year's interest on ₹9,680. So, interest for 1 year = ₹10,648 − ₹9,680 = ₹968. Step 2: Rate of interest = (968/9680) × 100 = 10% per annum. Step 3: Using A = P(1 + r/100)^n, we have 9,680 = P(1.10)^2. Step 4: P = 9,680 / 1.21 = ₹8,000. Therefore, Principal = ₹8,000 and Rate = 10% p.a.

NDA Compound Interest

NDA Compound Interest — Past Exam Questions

Compound Interest — Practice Questions