Question 1

If the simple interest on a sum for 3 years at 8% per annum is ₹2,400, what will be the compound interest on the same sum at the same rate for 2 years?

Accepted Answer

Step 1: Find principal using SI formula: SI = P×R×T/100, so 2400 = P×8×3/100 = 0.24P. Step 2: P = 2400/0.24 = ₹10,000. Step 3: Calculate CI for 2 years: A = P(1 + R/100)^T = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. Step 4: CI = 11664 - 10000 = ₹1,664.

Question 2

A sum of money doubles itself in 5 years at simple interest. In how many years will it triple itself at the same rate?

Accepted Answer

Step 1: If principal is P and it doubles in 5 years, then SI = P. Using SI = P×R×T/100: P = P×R×5/100, so R = 20% per annum. Step 2: For the sum to triple, total amount = 3P, so SI needed = 3P - P = 2P. Step 3: Using SI = P×R×T/100: 2P = P×20×T/100. Step 4: 2 = 0.2T, so T = 10 years.

Question 3

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

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 4

The difference between compound interest and simple interest on a sum of money for 2 years at 10% per annum is ₹40. Find the principal amount.

Accepted Answer

Step 1: Let principal = P. For 2 years at 10% p.a., SI = (P × 10 × 2)/100 = 0.2P. Step 2: For CI, Amount = P(1 + 10/100)² = P(1.1)² = 1.21P, so CI = 1.21P − P = 0.21P. Step 3: Difference = CI − SI = 0.21P − 0.2P = 0.01P. Step 4: Given difference = ₹40, so 0.01P = 40, therefore P = ₹4000.

Question 5

The difference between compound interest and simple interest on ₹6,000 for 2 years is ₹60. Find the rate of interest per annum.

Accepted Answer

Step 1: Use the 2-year difference formula: Difference = P × R² / 10000. Step 2: Substitute values: 60 = 6000 × R² / 10000. Step 3: 60 = 0.6 × R². Step 4: R² = 100, so R = 10% per annum.

Question 6

The difference between Compound Interest and Simple Interest on a sum of ₹1,000 at 10% per annum for 2 years is:

Accepted Answer

Step 1: For 2 years, the difference between CI and SI is given by the formula: Difference = P × (R/100)². Step 2: Difference = 1000 × (10/100)² = 1000 × (0.1)² = 1000 × 0.01 = ₹10. Therefore, the answer is ₹10.

Question 7

The difference between compound interest and simple interest on a sum of ₹8,000 at 10% per annum for 2 years is:

Accepted Answer

Step 1: Calculate Simple Interest using SI = (P × R × T) / 100 = (8000 × 10 × 2) / 100 = ₹1,600. Step 2: Calculate Compound Interest using A = P(1 + R/100)^T = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680, so CI = 9680 - 8000 = ₹1,680. Step 3: Difference = CI - SI = 1680 - 1600 = ₹80.

Question 8

At what rate per annum will the difference between compound interest and simple interest on ₹8,000 for 2 years be ₹80?

Accepted Answer

Step 1: For 2 years, the difference formula is: Difference = P × R² / (100)². Step 2: Substitute: 80 = 8000 × R² / 10000. Step 3: 80 = 0.8 × R². Step 4: R² = 100, so R = 10% per annum.

Question 9

At what rate per annum will the difference between compound interest and simple interest on ₹5,000 for 2 years be ₹200?

Accepted Answer

Step 1: For 2 years, the difference formula is: Difference = P × R² / (100)² = 5000 × R² / 10000 = R²/2. Step 2: Given difference = ₹200, so R²/2 = 200 → R² = 400 → R = 20. Step 3: Therefore, rate = 20% per annum.

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:

Accepted Answer

Step 1: Calculate Simple Interest: SI = (10000 × 8 × 2) / 100 = ₹1,600. Step 2: Calculate Compound Interest: A = 10000(1 + 8/100)² = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. CI = 11664 - 10000 = ₹1,664. Step 3: Difference = CI - SI = 1664 - 1600 = ₹64.

Question 11

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 12

The simple interest on a sum for 2 years at 8% per annum is ₹1,280. If the same sum is invested at the same rate for the same period at compound interest, what is the difference between CI and SI?

Accepted Answer

Step 1: Find principal from SI formula: 1,280 = (P × 8 × 2) / 100. So P = (1,280 × 100) / 16 = ₹8,000. Step 2: Calculate CI: A = 8,000(1.08)² = 8,000 × 1.1664 = ₹9,331.20. CI = 9,331.20 - 8,000 = ₹1,331.20. Step 3: Difference = 1,331.20 - 1,280 = ₹51.20.

Question 13

A principal becomes ₹13,310 after 3 years at 10% per annum 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 13,310 = P(1.10)³ = P × 1.331. Thus P = 13,310 / 1.331 = ₹10,000. Step 2: Calculate SI = (P × R × T) / 100 = (10,000 × 10 × 3) / 100 = ₹3,000.

Question 14

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

Accepted Answer

Step 1: Use the formula for difference between CI and SI for 3 years: Difference = P × r² × (300 + r)/(100)³. Step 2: Substitute values: 61.25 = P × 25 × 305/(1000000). Step 3: 61.25 = P × 7625/1000000. Step 4: P = (61.25 × 1000000)/7625 = 61250000/7625 = 8000.

Question 15

A sum of money amounts to ₹9,680 in 2 years at 10% per annum under simple interest. What will be the difference between compound interest and simple interest on the same sum for the same period and rate?

Accepted Answer

Step 1: Find Principal using SI formula. Amount = P + SI, where SI = (P × R × T)/100. So 9680 = P + (P × 10 × 2)/100 = P + 0.2P = 1.2P. Therefore P = 8066.67. Step 2: Calculate SI for 2 years = (8066.67 × 10 × 2)/100 = 1613.33. Step 3: Calculate CI using A = P(1 + r/100)^t = 8066.67 × (1.1)^2 = 8066.67 × 1.21 = 9760.67. CI = 9760.67 - 8066.67 = 1694. Step 4: Difference = CI - SI = 1694 - 1613.33 ≈ 80.67. Recalculating with exact P = 8066⅔: SI = 1613⅓, CI = 1693⅓, Difference = 80.

Question 16

A principal of ₹10,000 is invested at 5% per annum for 2 years. By what percentage is the compound interest more than the simple interest?

Accepted Answer

Step 1: Calculate SI: SI = (10,000 × 5 × 2) / 100 = ₹1,000. Step 2: Calculate CI: A = 10,000(1.05)² = 10,000 × 1.1025 = ₹11,025. CI = 11,025 - 10,000 = ₹1,025. Step 3: Difference = 1,025 - 1,000 = ₹25. Step 4: Percentage = (25 / 1,000) × 100 = 2.5%.

Question 17

The difference between compound interest and simple interest on a principal for 3 years at 10% per annum is ₹93. Find the principal.

Accepted Answer

Step 1: Use the formula for difference over 3 years: Difference = P × R² × (300 + R) / (100)³. Step 2: Substitute values: 93 = P × 100 × 310 / 1,000,000. Step 3: 93 = P × 31,000 / 1,000,000 = P × 0.031. Step 4: P = 93 / 0.031 = 3,000.

Question 18

The simple interest on a sum for 2 years at 12% per annum is ₹2,880. What will be the compound interest on the same sum for the same period and rate?

Accepted Answer

Step 1: Find Principal from SI formula. SI = (P × R × T)/100, so 2880 = (P × 12 × 2)/100 = 0.24P. Therefore P = 12000. Step 2: Calculate Amount under CI: A = P(1 + r/100)^t = 12000(1.12)² = 12000 × 1.2544 = 15052.8. Step 3: CI = A - P = 15052.8 - 12000 = 3052.8. Rounding to nearest rupee: ₹3,053 or exactly ₹3052.80. For clean answer, verify: 12000 × (1.12)² = 12000 × 1.2544 = 15052.8, so CI = 3052.8 ≈ ₹3,053.

Question 19

The difference between compound interest and simple interest on a certain sum for 2 years at 10% per annum is ₹80. 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 at rate r, CI - SI = P × r² / 10000. Step 2: At 10%, 80 = P × 100 / 10000, so P × 0.01 = 80, thus P = 8,000. Step 3: At 15% for 2 years, CI - SI = 8,000 × 225 / 10000 = 1,800,000 / 10000 = 180.

Question 20

A principal amount becomes ₹14,641 after 3 years at 10% per annum compound interest. If the same principal is invested at 10% per annum simple interest for 3 years, what is the difference between the compound interest earned and simple interest earned?

Accepted Answer

Step 1: Amount with CI = P(1.10)³ = 14,641. So P × 1.331 = 14,641, thus P = 11,000. Step 2: SI for 3 years = (11,000 × 10 × 3)/100 = 3,300. Step 3: CI for 3 years = 14,641 - 11,000 = 3,641. Step 4: Difference = 3,641 - 3,300 = 341.

Question 21

The difference between compound interest and simple interest on a certain principal for 2 years at 8% per annum is ₹128. If the same principal is invested for 3 years at the same rate under compound interest, what will be the compound interest earned?

Accepted Answer

Step 1: Use the formula for CI-SI difference for 2 years: CI - SI = P × r² / 100². So 128 = P × 64 / 10000. Therefore P = 128 × 10000 / 64 = 20,000. Step 2: Calculate CI for 3 years: A = P(1 + r/100)³ = 20000 × (1.08)³ = 20000 × 1.259712 = 25,194.24. Step 3: CI = 25,194.24 - 20,000 = 5,194.24 ≈ 5,194.

Question 22

If the difference between compound interest and simple interest on a principal for 2 years at 5% per annum is ₹25, what is the principal amount?

Accepted Answer

Step 1: Use the formula for 2 years: Difference = P × R² / (100)². Step 2: 25 = P × 25 / 10000, so P = 25 × 10000 / 25 = ₹10,000. Step 3: Verify: SI = (10000 × 5 × 2)/100 = 1000; CI = 10000(1.05)² - 10000 = 10000(1.1025 - 1) = 1025; Difference = 1025 - 1000 = 25 ✓

Question 23

On a principal of ₹8,000 at 5% per annum for 3 years, the compound interest exceeds simple interest by ₹61. Verify this and find the compound interest.

Accepted Answer

Step 1: Calculate SI = (8000 × 5 × 3) / 100 = ₹1,200. Step 2: Calculate CI using A = 8000(1.05)³ = 8000 × 1.157625 = ₹9,261, so CI = 9261 - 8000 = ₹1,261. Step 3: Difference = 1261 - 1200 = ₹61 (verified). Step 4: Compound Interest = ₹1,261.

Question 24

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

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 25

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 26

The difference between compound interest and simple interest on a sum of money at 10% per annum for 2 years is ₹40. What is the principal amount?

Accepted Answer

Step 1: Let principal = P. For SI: SI = (P × 10 × 2) / 100 = 0.2P. Step 2: For CI: Amount = P(1 + 10/100)² = P(1.1)² = 1.21P, so CI = 1.21P − P = 0.21P. Step 3: Difference = CI − SI = 0.21P − 0.2P = 0.01P. Step 4: Given difference = ₹40, so 0.01P = 40, therefore P = ₹4000.

Question 27

A principal amount earns ₹400 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 formula: 400 = (P × 8 × 2) / 100, so P = 400 × 100 / 16 = ₹2,500. Step 2: Calculate CI using A = 2500(1.08)² = 2500 × 1.1664 = ₹2,916. Step 3: CI = 2916 - 2500 = ₹416.

Question 28

A principal of ₹10,000 is invested at 8% per annum. The simple interest for 3 years is ₹2,400. If the same principal and rate are used for compound interest over 3 years, how much more interest is earned?

Accepted Answer

Step 1: Verify SI = (10000 × 8 × 3) / 100 = 2400 ✓. Step 2: Calculate CI using A = P(1 + R/100)^T = 10000(1.08)³. Step 3: (1.08)³ = 1.08 × 1.08 × 1.08 = 1.259712, so A = 10000 × 1.259712 = 12,597.12. Step 4: CI = 12597.12 - 10000 = 2597.12. Step 5: Additional interest = CI - SI = 2597.12 - 2400 = ₹197.12 ≈ ₹197.

Question 29

A sum of ₹6,000 is invested at 10% per annum. What is the additional amount earned due to compounding over simple interest for 2 years?

Accepted Answer

Step 1: Calculate SI = (6000 × 10 × 2) / 100 = ₹1,200. Step 2: Calculate CI using A = 6000(1.10)² = 6000 × 1.21 = ₹7,260, so CI = 7260 - 6000 = ₹1,260. Step 3: Additional amount = CI - SI = 1260 - 1200 = ₹60.

Question 30

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

Accepted Answer

Step 1: Use the formula for difference: Difference = P × R² / (100)² for 2 years. Step 2: 144 = P × 144 / 10000, so P = 144 × 10000 / 144 = ₹10,000. Step 3: Verify: SI = (10000 × 12 × 2)/100 = 2400; CI = 10000(1.12)² - 10000 = 10000(1.2544 - 1) = 2544; Difference = 2544 - 2400 = 144 ✓

Question 31

The simple interest on a sum for 2 years at 12% per annum is ₹2,400. If the same sum is invested at the same rate for the same period at compound interest, what is the difference between CI and SI?

Accepted Answer

Step 1: Find the principal from SI formula: SI = (P × R × T) / 100. Therefore, 2400 = (P × 12 × 2) / 100. Solve: P = (2400 × 100) / 24 = 10,000. Step 2: Calculate CI: A = P(1 + R/100)^T = 10,000(1.12)² = 10,000 × 1.2544 = 12,544. CI = 12,544 - 10,000 = 2,544. Step 3: Difference = CI - SI = 2,544 - 2,400 = ₹144.

Question 32

A sum of ₹4,000 is invested at a certain rate per annum for 2 years. The compound interest exceeds the simple interest by ₹40. At what rate per annum is the sum invested?

Accepted Answer

Step 1: Use the 2-year difference formula: Difference = P × R² / 10,000. Step 2: Substitute: 40 = 4000 × R² / 10,000. Step 3: Simplify: 40 = 4R² / 10 = 0.4R². Step 4: Solve: R² = 100. Therefore, R = 10% per annum.

Question 33

A principal of ₹6,000 is invested at 10% per annum. If the difference between compound interest and simple interest for 3 years is ₹183, what is the rate of interest? (Assume the given difference is approximate.)

Accepted Answer

Step 1: Calculate SI for 3 years: SI = (6000 × R × 3) / 100 = 180R. Step 2: For 3 years, use approximation: Difference ≈ P × R² × (300 + R) / 1,000,000. Step 3: Test R = 10: Difference = 6000 × 100 × 310 / 1,000,000 = 186,000,000 / 1,000,000 = 186 ≈ 183. Step 4: Verify with exact calculation: CI = 6000(1.1)³ - 6000 = 7986 - 6000 = 1986. SI = 1800. Difference = 186. This matches approximately.

Question 34

The difference between compound interest and simple interest on a principal for 3 years at 10% per annum is ₹93. Find the principal.

Accepted Answer

Step 1: For 3 years, use the formula: Difference = P × R² × (300 + R) / (100)³. Step 2: Substitute: 93 = P × 100 × 310 / 1,000,000. Step 3: 93 = P × 31,000 / 1,000,000 = P × 0.031. Step 4: P = 93 / 0.031 = ₹3,000.

Question 35

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 36

The difference between compound interest and simple interest on a sum of money for 2 years at 10% per annum is ₹40. What is the principal amount?

Accepted Answer

Step 1: Let principal = P. For 2 years at 10% p.a., SI = (P × 10 × 2)/100 = 0.2P. Step 2: For CI, Amount = P(1.1)² = 1.21P, so CI = 0.21P. Step 3: Difference = CI − SI = 0.21P − 0.2P = 0.01P. Step 4: Given difference = ₹40, so 0.01P = 40, therefore P = ₹4000.

Question 37

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: For 2 years, Difference = P × R² / (100)². Step 2: Substitute: 50 = 5,000 × R² / 10,000. Step 3: 50 = R² / 2. Step 4: R² = 100. Step 5: R = 10% per annum.

Question 38

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, the difference formula is: Difference = P × R² / 10,000. Step 2: Substitute: 64 = P × 64 / 10,000. Step 3: Solve for P: P = (64 × 10,000) / 64 = 10,000.

Question 39

A principal becomes ₹1,331 after 3 years at 10% per annum compound interest. What is the difference between the compound interest and simple interest earned?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T: 1,331 = P(1.1)³ = P × 1.331, so P = ₹1,000. Step 2: Calculate CI = A - P = 1,331 - 1,000 = ₹331. Step 3: Calculate SI = (1,000 × 10 × 3) / 100 = ₹300. Step 4: Difference = 331 - 300 = ₹31.

Question 40

A certain sum becomes ₹1,728 in 3 years and ₹2,592 in 4 years under compound interest. What is the rate of interest per annum, and what will be the simple interest on the original principal for 2 years at the same rate?

Accepted Answer

Step 1: Find the rate from the ratio of amounts. A₄/A₃ = 2592/1728 = 1.5 = (1 + r/100). So r/100 = 0.5, thus r = 50% p.a. Step 2: Find the principal. A₃ = P(1.5)³ = 1,728, so P × 3.375 = 1,728, thus P = ₹512. Step 3: Calculate SI for 2 years at 50%. SI = (512 × 50 × 2)/100 = ₹512.

Question 41

A sum of ₹10,000 is invested for 3 years. Under simple interest at rate R% p.a., the amount becomes ₹13,000. Under compound interest at the same rate, what is the difference between the compound interest and simple interest?

Accepted Answer

Step 1: Find the rate from SI. SI = 13,000 - 10,000 = 3,000. Using SI = (P × R × T)/100: 3,000 = (10,000 × R × 3)/100, so R = 10% p.a. Step 2: Calculate CI for 3 years at 10%. A = 10,000 × (1.10)³ = 10,000 × 1.331 = 13,310. Step 3: CI = 13,310 - 10,000 = 3,310. Step 4: Difference = CI - SI = 3,310 - 3,000 = ₹310.

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