Question 1

A sum of ₹5,000 is invested at 10% per annum for 2 years. What is the difference between the compound interest and simple interest earned?

Accepted Answer

Step 1: Calculate Simple Interest: SI = (P × R × T) / 100 = (5000 × 10 × 2) / 100 = ₹1,000. Step 2: Calculate Compound Interest: A = P(1 + R/100)^T = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050. CI = 6050 - 5000 = ₹1,050. Step 3: Difference = CI - SI = 1050 - 1000 = ₹50.

Question 2

The difference between compound interest and simple interest on a principal of ₹8,000 at 5% per annum for 3 years is:

Accepted Answer

Step 1: Calculate SI = (8000 × 5 × 3) / 100 = ₹1,200. Step 2: Calculate CI: A = 8000(1.05)^3 = 8000 × 1.157625 = ₹9,261. CI = 9261 - 8000 = ₹1,261. Step 3: Difference = 1261 - 1200 = ₹61.

Question 3

A principal of ₹10,000 is invested at 8% per annum. The difference between CI and SI for 2 years is ₹64. Is this statement true or false?

Accepted Answer

Step 1: Calculate SI = (10000 × 8 × 2) / 100 = ₹1,600. Step 2: Calculate CI: A = 10000(1.08)^2 = 10000 × 1.1664 = ₹11,664. CI = 11664 - 10000 = ₹1,664. Step 3: Difference = 1664 - 1600 = ₹64. The statement is TRUE.

Question 4

On a sum of ₹6,000 at 12% per annum, the difference between CI and SI for 2 years is:

Accepted Answer

Step 1: Calculate SI = (6000 × 12 × 2) / 100 = ₹1,440. Step 2: Calculate CI: A = 6000(1.12)^2 = 6000 × 1.2544 = ₹7,526.40. CI = 7526.40 - 6000 = ₹1,526.40. Step 3: Difference = 1526.40 - 1440 = ₹86.40.

Question 5

A sum becomes ₹4,410 in 2 years at 5% per annum under compound interest. What would be the difference between CI and SI on this principal for 2 years?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T. 4410 = P(1.05)^2 = P × 1.1025. P = 4410 / 1.1025 = ₹4,000. Step 2: Calculate SI = (4000 × 5 × 2) / 100 = ₹400. Step 3: Calculate CI = 4410 - 4000 = ₹410. Step 4: Difference = 410 - 400 = ₹10.

Question 6

The difference between CI and SI on ₹9,000 at 20% per annum for 2 years is:

Accepted Answer

Step 1: Calculate SI = (9000 × 20 × 2) / 100 = ₹3,600. Step 2: Calculate CI: A = 9000(1.20)^2 = 9000 × 1.44 = ₹12,960. CI = 12960 - 9000 = ₹3,960. Step 3: Difference = 3960 - 3600 = ₹360.

Question 7

A sum of ₹8,000 is invested at 12% per annum. What is the difference between the compound interest and simple interest earned over 2 years?

Accepted Answer

Step 1: Calculate Simple Interest: SI = (P × R × T) / 100 = (8000 × 12 × 2) / 100 = ₹1,920. Step 2: Calculate Compound Interest: A = P(1 + R/100)^T = 8000(1.12)^2 = 8000 × 1.2544 = ₹10,035.20. CI = 10,035.20 - 8,000 = ₹2,035.20. Step 3: Difference = CI - SI = 2,035.20 - 1,920 = ₹115.20.

Question 8

At what rate per annum will the difference between compound interest and simple interest on ₹5,000 for 2 years be ₹50?

Accepted Answer

Step 1: Use the formula for 2 years: Difference = P × R² / (100)². Step 2: Substitute: 50 = 5000 × R² / 10000. Step 3: 50 = R² / 2. Step 4: R² = 100. Step 5: R = 10% per annum.

Question 9

A principal amount becomes ₹11,664 at 10% per annum compound interest in 2 years. What would be the simple interest on the same principal at the same rate for the same period?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T. 11,664 = P(1.10)^2 = P × 1.21. Step 2: P = 11,664 / 1.21 = ₹9,600. Step 3: Calculate SI: SI = (9600 × 10 × 2) / 100 = ₹1,920.

Question 10

A sum of ₹10,000 is invested at 8% per annum. The difference between compound interest for 2 years and simple interest for 2 years is what percentage of the principal?

Accepted Answer

Step 1: SI for 2 years = (10000 × 8 × 2) / 100 = ₹1,600. Step 2: CI for 2 years: A = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. CI = 11,664 - 10,000 = ₹1,664. Step 3: Difference = 1,664 - 1,600 = ₹64. Step 4: Percentage = (64 / 10,000) × 100 = 0.64%.

Question 11

If the difference between compound interest and simple interest on a principal for 2 years at 6% per annum is ₹43.20, what is the principal?

Accepted Answer

Step 1: For 2 years, Difference = P × R² / (100)². Step 2: 43.20 = P × 36 / 10000. Step 3: 43.20 = P × 0.0036. Step 4: P = 43.20 / 0.0036 = ₹12,000.

Question 12

The difference between CI and SI on a certain sum for 2 years at 10% per annum is ₹40. If the same sum is invested at 15% per annum for 2 years, what will be the difference between CI and SI?

Accepted Answer

Step 1: For 2 years, difference formula: CI - SI = P × (r/100)² = P × (10/100)² = 0.01P. Step 2: 0.01P = 40, so P = 4,000. Step 3: At 15% for 2 years: Difference = P × (15/100)² = 4,000 × 0.0225 = 90.

Question 13

A certain sum becomes ₹1,44,000 in 2 years and ₹1,72,800 in 3 years under compound interest. What is the difference between the compound interest of the 3rd year and the simple interest for 3 years on the original principal?

Accepted Answer

Step 1: CI earned in 3rd year = 1,72,800 - 1,44,000 = ₹28,800. Step 2: Rate = (28,800/1,44,000) × 100 = 20% p.a. Step 3: Principal = 1,44,000 / (1.2)² = 1,44,000 / 1.44 = ₹1,00,000. Step 4: SI for 3 years = (1,00,000 × 20 × 3)/100 = ₹60,000. Step 5: Difference = SI for 3 years - CI of 3rd year = 60,000 - 28,800 = ₹31,200.

Question 14

A principal of ₹5,000 is invested at 10% per annum. After how many years will the difference between compound interest and simple interest be ₹155?

Accepted Answer

Step 1: SI for n years = (5,000 × 10 × n)/100 = 500n. Step 2: CI for n years = 5,000[(1.1)ⁿ - 1]. Step 3: Difference = 5,000[(1.1)ⁿ - 1] - 500n = 155. Step 4: Simplify: 5,000(1.1)ⁿ - 5,000 - 500n = 155 → 5,000(1.1)ⁿ = 5,155 + 500n. Step 5: Test n = 3: LHS = 5,000(1.331) = 6,655, RHS = 5,155 + 1,500 = 6,655. ✓ Therefore, n = 3 years.

Question 15

₹8,000 is lent at 5% per annum for 3 years. What is the difference between the compound interest and simple interest earned?

Accepted Answer

Step 1: Simple Interest = (P × R × T) / 100 = (8000 × 5 × 3) / 100 = ₹1,200. Step 2: Amount under CI = P(1 + r/100)^n = 8000(1.05)³ = 8000 × 1.157625 = ₹9,261. Step 3: Compound Interest = 9261 − 8000 = ₹1,261. Step 4: Difference = 1261 − 1200 = ₹61.

Question 16

A principal amount earns ₹800 as simple interest in 2 years at 8% per annum. If the same principal is invested at 8% per annum for 2 years at compound interest, what will be the compound interest?

Accepted Answer

Step 1: Find Principal using SI = (P × R × T) / 100. So 800 = (P × 8 × 2) / 100, which gives P = 80000 / 16 = ₹5,000. Step 2: Calculate CI using A = P(1 + R/100)^T = 5000(1.08)^2 = 5000 × 1.1664 = ₹5,832. Step 3: CI = 5832 - 5000 = ₹832.

Question 17

A principal amounts to ₹11,025 in 2 years at 5% per annum under compound interest. What would be the simple interest on the same principal for the same period at the same rate?

Accepted Answer

Step 1: Find principal using A = P(1 + r/100)^n. Step 2: 11025 = P(1.05)² = P × 1.1025. Step 3: P = 11025/1.1025 = ₹10,000. Step 4: Simple Interest = (10000 × 5 × 2)/100 = ₹1,000.

Question 18

A sum of ₹5,000 is invested at 10% per annum for 2 years. What is the difference between the compound interest and simple interest earned?

Accepted Answer

Step 1: Calculate Simple Interest using SI = (P × R × T) / 100 = (5000 × 10 × 2) / 100 = ₹1,000. Step 2: Calculate Compound Interest using A = P(1 + R/100)^T = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050, so CI = 6050 - 5000 = ₹1,050. Step 3: Difference = CI - SI = 1050 - 1000 = ₹50.

Question 19

₹2,000 is invested at 5% per annum for 3 years. The difference between compound interest and simple interest is ₹15.25. Verify this and find the compound interest.

Accepted Answer

Step 1: Calculate SI = (2000 × 5 × 3) / 100 = ₹300. Step 2: Calculate CI using A = 2000(1.05)^3 = 2000 × 1.157625 = ₹2,315.25, so CI = 2315.25 - 2000 = ₹315.25. Step 3: Difference = 315.25 - 300 = ₹15.25 (verified). Therefore, CI = ₹315.25.

Question 20

The difference between compound interest and simple interest on a sum at 12% per annum for 2 years is ₹144. What is the principal?

Accepted Answer

Step 1: Let Principal = P. SI = (P × 12 × 2) / 100 = 0.24P. Step 2: CI = P(1.12)^2 - P = P(1.2544 - 1) = 0.2544P. Step 3: Difference = 0.2544P - 0.24P = 0.0144P = 144. Therefore, P = 144 / 0.0144 = ₹10,000.

Question 21

The difference between compound interest and simple interest on a principal for 2 years at 8% per annum is ₹64. What is the principal?

Accepted Answer

Step 1: For 2 years, CI − SI = P × (r/100)². Step 2: 64 = P × (8/100)². Step 3: 64 = P × (64/10000). Step 4: P = 64 × (10000/64) = ₹10,000.

Question 22

A sum becomes ₹6,050 in 2 years at 10% per annum under compound interest. What would be the simple interest on the same principal for the same period and rate?

Accepted Answer

Step 1: Find Principal using A = P(1 + R/100)^T. So 6050 = P(1.1)^2 = P × 1.21, which gives P = 6050 / 1.21 = ₹5,000. Step 2: Calculate SI = (5000 × 10 × 2) / 100 = ₹1,000.

Question 23

The simple interest on a sum for 2 years at 6% per annum is ₹480. What is the difference between compound interest and simple interest for the same principal, rate, and time period?

Accepted Answer

Step 1: Find Principal using SI = (P × R × T) / 100. So 480 = (P × 6 × 2) / 100, which gives P = 48000 / 12 = ₹4,000. Step 2: Calculate CI using A = 4000(1.06)^2 = 4000 × 1.1236 = ₹4,494.40, so CI = 4494.40 - 4000 = ₹494.40. Step 3: Difference = 494.40 - 480 = ₹14.40.

Question 24

At what rate per annum will the difference between simple interest and compound interest on ₹6,400 for 2 years be ₹64?

Accepted Answer

Step 1: For 2 years, Difference = P × (R/100)². Step 2: 64 = 6,400 × (R/100)². Step 3: (R/100)² = 64/6,400 = 0.01. Step 4: R/100 = 0.1. Step 5: R = 10% per annum.

Question 25

A sum of ₹8,000 is invested at 12% per annum. What is the difference between the compound interest and simple interest earned over 2 years?

Accepted Answer

Step 1: Calculate SI for 2 years: SI = (P × R × T) / 100 = (8000 × 12 × 2) / 100 = ₹1,920. Step 2: Calculate CI for 2 years: A = P(1 + R/100)^T = 8000(1.12)^2 = 8000 × 1.2544 = ₹10,035.20. CI = 10,035.20 - 8,000 = ₹2,035.20. Step 3: Difference = CI - SI = 2,035.20 - 1,920 = ₹115.20.

Question 26

A sum of ₹20,000 is invested at 5% per annum. If the difference between compound interest for 3 years and simple interest for 3 years is ₹x, find x.

Accepted Answer

Step 1: SI for 3 years = (20,000 × 5 × 3) / 100 = ₹3,000. Step 2: Amount at CI = 20,000 × (1.05)³ = 20,000 × 1.157625 = ₹23,152.50. Step 3: CI = 23,152.50 - 20,000 = ₹3,152.50. Step 4: Difference = 3,152.50 - 3,000 = ₹152.50.

Question 27

The difference between compound interest and simple interest on a sum for 3 years at 10% per annum is ₹310. What is the principal amount?

Accepted Answer

Step 1: For 3 years, the difference between CI and SI is given by: Difference = P × R/100 × [(R/100)² + 2 × R/100] = P × (R/100) × [R²/10000 + 2R/100]. Alternatively, use: Difference = P[(1 + R/100)³ - 1 - 3R/100]. Step 2: Expanding (1.10)³ = 1.331, so CI = P(1.331 - 1) = 0.331P. SI = P × 3 × 0.10 = 0.30P. Difference = 0.331P - 0.30P = 0.031P. Step 3: 310 = 0.031P. P = 310 / 0.031 = ₹10,000.

Question 28

A principal amount becomes ₹11,664 in 2 years at 8% per annum compound interest. What would be the simple interest earned on the same principal at the same rate for the same period?

Accepted Answer

Step 1: Find the principal using A = P(1 + R/100)^T. 11,664 = P(1.08)². 11,664 = P × 1.1664. P = 11,664 / 1.1664 = ₹10,000. Step 2: Calculate Simple Interest using SI = (P × R × T) / 100 = (10,000 × 8 × 2) / 100 = ₹1,600.

Question 29

The difference between compound interest and simple interest on a sum for 3 years at 10% per annum is ₹310. What is the principal?

Accepted Answer

Step 1: For 3 years at 10%, the difference formula is: CI - SI = P × r²(300 + r)/1,000,000 = P × 100 × 310/1,000,000 = P × 31,000/1,000,000 = P × 0.031. Step 2: Given CI - SI = 310, so 310 = P × 0.031, thus P = 10,000. Verification: SI₃ = (10,000 × 10 × 3)/100 = 3,000. CI₃ = 10,000 × [(1.1)³ - 1] = 10,000 × 0.331 = 3,310. Difference = 310. ✓

Question 30

The difference between compound interest and simple interest on a sum for 2 years at rate r% per annum is ₹100. If the rate is increased by 2%, the difference for the same period becomes ₹144. Find the principal.

Accepted Answer

Step 1: For 2 years, CI - SI = P × r² / 10,000. So, 100 = P × r² / 10,000 → P × r² = 1,000,000. Step 2: At (r+2)%, difference = P × (r+2)² / 10,000 = 144 → P × (r+2)² = 1,440,000. Step 3: Divide: (r+2)² / r² = 1.44 → (r+2)/r = 1.2 → r + 2 = 1.2r → r = 20. Step 4: P × 400 = 1,000,000 → P = 2,500. Therefore, the principal is ₹2,500.

Question 31

A sum of ₹5,000 is invested at a certain rate per annum. The compound interest for 2 years exceeds the simple interest for 2 years by ₹50. What is the rate of interest per annum?

Accepted Answer

Step 1: For 2 years, CI - SI = P × r² / 10,000. Step 2: 50 = 5,000 × r² / 10,000 → 50 = r² / 2 → r² = 100 → r = 10. Therefore, the rate is 10% per annum.

Question 32

A principal amount is invested at 12% per annum. The difference between compound interest for 2 years and simple interest for 2 years is ₹144. If the same principal is now invested at 12% per annum for 4 years, what is the difference between CI and SI?

Accepted Answer

Step 1: For 2 years at 12%, CI - SI = P × r²/10,000 = P × 144/10,000. Given this equals 144, so P = 10,000. Step 2: For 4 years, SI = (10,000 × 12 × 4)/100 = 4,800. Step 3: CI = 10,000 × [(1.12)⁴ - 1] = 10,000 × [1.5735 - 1] = 5,735.10. Step 4: Difference = 5,735.10 - 4,800 = 935.10 ≈ ₹935. Using exact: (1.12)⁴ = 1.57351936, so CI = 5,735.19, Difference ≈ ₹935.

Question 33

The difference between CI and SI on a certain sum for 2 years at 10% per annum is ₹40. If the same sum is invested at 15% per annum for 2 years, what will be the difference between CI and SI?

Accepted Answer

Step 1: For 2 years, difference = P × r² / 10,000. At 10%: 40 = P × 100 / 10,000 → P = 4,000. Step 2: At 15% for 2 years, difference = 4,000 × 225 / 10,000 = 90. Therefore, the difference is ₹90.

Question 34

The difference between CI and SI on a principal for 3 years at 5% per annum is ₹61.25. If the same principal is invested at 5% per annum for 4 years under compound interest, what will be the compound interest earned?

Accepted Answer

Step 1: For 3 years at 5%, CI - SI = P × r²(300 + r) / (100)³ = P × 25 × 305 / 1,000,000 = 7,625P / 1,000,000. Step 2: 61.25 = 7,625P / 1,000,000 → P = 61.25 × 1,000,000 / 7,625 = 8,000. Step 3: For 4 years at 5%, A = 8,000 × (1.05)⁴ = 8,000 × 1.21550625 = 9,724.05. Step 4: CI = 9,724.05 - 8,000 = 1,724.05 ≈ ₹1,724. Therefore, the compound interest is ₹1,724.

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