Question 1

Rajesh invests ₹8,000 at 10% per annum for 2 years. What is the difference between the compound interest and simple interest earned on this amount?

Accepted Answer

Step 1: Calculate Simple Interest (SI) using SI = (P × R × T) / 100
SI = (8,000 × 10 × 2) / 100 = 160,000 / 100 = ₹1,600

Step 2: Calculate Compound Interest (CI) using CI = P(1 + R/100)^T - P
Amount = 8,000(1 + 10/100)^2 = 8,000(1.1)^2 = 8,000 × 1.21 = ₹9,680
CI = 9,680 - 8,000 = ₹1,680

Step 3: Find the difference
Difference = CI - SI = 1,680 - 1,600 = ₹80

Alternatively, for 2 years: Difference = (P × R^2) / (100)^2 = (8,000 × 10 × 10) / 10,000 = ₹80

Therefore, the answer is ₹80.

Question 2

A principal of ₹10,000 is invested at 5% per annum. What is the difference between compound interest and simple interest after 3 years?

Accepted Answer

Step 1: Calculate Simple Interest: SI = (10000 × 5 × 3) / 100 = ₹1,500. Step 2: Calculate Amount under Compound Interest: A = 10000(1.05)³ = 10000 × 1.157625 = ₹11,576.25. CI = 11576.25 - 10000 = ₹1,576.25. Step 3: Difference = CI - SI = 1576.25 - 1500 = ₹76.25.

Question 3

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

Accepted Answer

Step 1: For 2 years, the difference between CI and SI is given by: Difference = P × R² / 10000. Step 2: Substitute the given values: 64 = P × 8² / 10000 = P × 64 / 10000. Step 3: Solve for P: P = (64 × 10000) / 64 = ₹10,000.

Question 4

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 SI for 2 years: SI = (P × R × T) / 100 = (8000 × 10 × 2) / 100 = ₹1,600. Step 2: Calculate CI for 2 years: Amount = P(1 + R/100)^T = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680. CI = 9680 - 8000 = ₹1,680. Step 3: Difference = CI - SI = 1680 - 1600 = ₹80.

Question 5

A principal of ₹10,000 is invested at 5% per annum. The difference between CI and SI after 3 years is:

Accepted Answer

Step 1: Calculate SI for 3 years: SI = (10000 × 5 × 3) / 100 = ₹1,500. Step 2: Calculate CI for 3 years: Amount = 10000(1.05)³ = 10000 × 1.157625 = ₹11,576.25. CI = 11576.25 - 10000 = ₹1,576.25. Step 3: Difference = 1576.25 - 1500 = ₹76.25.

Question 6

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

Accepted Answer

Step 1: For 2 years, the difference formula is: Difference = P × R² / 10000, where R is the rate. Step 2: Substitute: 50 = 5000 × R² / 10000. Step 3: 50 = R² / 2. Step 4: R² = 100. Step 5: R = 10% per annum.

Question 7

If the difference between CI and SI on a sum for 2 years at 12% per annum is ₹144, what is the principal?

Accepted Answer

Step 1: Use the 2-year difference formula: Difference = P × R² / 10000. Step 2: Substitute: 144 = P × 12² / 10000. Step 3: 144 = P × 144 / 10000. Step 4: P = (144 × 10000) / 144 = ₹10,000.

Question 8

The simple interest on ₹4,000 for 2 years is ₹800. What will be the compound interest on the same sum at the same rate for the same period?

Accepted Answer

Step 1: Find the rate from SI: SI = (P × R × T) / 100 → 800 = (4000 × R × 2) / 100 → 800 = 80R → R = 10% per annum. Step 2: Calculate CI: Amount = 4000(1.1)² = 4000 × 1.21 = ₹4,840. Step 3: CI = 4840 - 4000 = ₹840.

Question 9

The difference between CI and SI on ₹6,000 at 8% per annum for 2 years is ₹x. Find the value of x.

Accepted Answer

Step 1: For 2 years, use the formula: Difference = P × R² / 10000. Step 2: Difference = (6000 × 8²) / 10000 = (6000 × 64) / 10000 = 384000 / 10000 = ₹38.40.

Question 10

A sum of money becomes ₹6050 in 2 years and ₹6655 in 3 years under compound interest. Find 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 = 6050. Step 3: After 3 years: P(1 + R/100)³ = 6655. Step 4: Divide equation 3 by equation 2: [P(1 + R/100)³]/[P(1 + R/100)²] = 6655/6050. Step 5: (1 + R/100) = 6655/6050 = 1.1. Step 6: R/100 = 0.1, so R = 10% p.a.

Question 11

A principal amount is invested at 20% per annum. The difference between compound interest for 2 years and simple interest for 2 years is ₹800. What is the principal?

Accepted Answer

Step 1: For 2 years, Difference = P × (R/100)². Step 2: Substitute R = 20: Difference = P × (20/100)² = P × 0.04. Step 3: Given Difference = ₹800, so P × 0.04 = 800. Step 4: P = 800 ÷ 0.04 = ₹20000.

Question 12

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

Accepted Answer

Step 1: Use the difference formula. For 3 years, CI - SI = P × R² × (300 + R) / (100)³. Step 2: Substitute: 61.25 = P × 25 × 305 / 1000000. Step 3: 61.25 = P × 7625 / 1000000. Step 4: P = 61.25 × 1000000 / 7625 = 8000.

Question 13

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.

Accepted Answer

Step 1: For 2 years, the difference between CI and SI is given by the formula: Difference = P × (R/100)² = P × (10/100)² = P × 0.01. Step 2: We are told this difference equals ₹40, so P × 0.01 = 40. Step 3: Therefore, P = 40 ÷ 0.01 = ₹4000.

Question 14

The difference between CI and SI on a certain sum for 2 years at 5% per annum is ₹12.50. What is the principal?

Accepted Answer

Step 1: For 2 years, Difference = P × (R/100)². Step 2: Substitute R = 5: Difference = P × (5/100)² = P × 0.0025. Step 3: Given Difference = ₹12.50, so P × 0.0025 = 12.50. Step 4: P = 12.50 ÷ 0.0025 = ₹5000.

Question 15

A sum of money amounts to ₹2,640 in 2 years at 10% per annum under simple interest. What will be the difference between simple interest and compound interest on the same sum for the same period and rate?

Accepted Answer

Step 1: Find Principal using SI formula. SI = (P × R × T) / 100, so 2640 = P + (P × 10 × 2)/100 = P + 0.2P = 1.2P. Therefore P = 2200. Step 2: Calculate SI for 2 years: SI = (2200 × 10 × 2)/100 = ₹440. Step 3: Calculate CI: A = P(1 + R/100)^T = 2200(1.1)^2 = 2200 × 1.21 = ₹2,662. CI = 2662 - 2200 = ₹462. Step 4: Difference = CI - SI = 462 - 440 = ₹22.

Question 16

A principal becomes ₹5,500 in 2 years and ₹6,050 in 3 years under compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Let P be principal and r be rate. After 2 years: P(1 + r/100)² = 5500. After 3 years: P(1 + r/100)³ = 6050. Step 2: Divide the second by the first: [P(1 + r/100)³] / [P(1 + r/100)²] = 6050/5500. Step 3: (1 + r/100) = 6050/5500 = 1.1. Step 4: r/100 = 0.1, so r = 10% per annum.

Question 17

The simple interest on a sum for 2 years at 12% per annum is ₹2,880. If the same sum is invested at the same rate for the same period under compound interest, how much more interest will be earned?

Accepted Answer

Step 1: Find Principal from SI formula. SI = (P × R × T)/100, so 2880 = (P × 12 × 2)/100 = 0.24P. Therefore P = 12,000. Step 2: Calculate CI: A = P(1 + R/100)^T = 12000(1.12)² = 12000 × 1.2544 = 15,052.80. CI = 15,052.80 - 12,000 = 3,052.80. Step 3: Additional interest = CI - SI = 3,052.80 - 2,880 = ₹172.80.

Question 18

A sum of ₹5,000 is invested at 12% per annum. The difference between compound interest for 2 years and simple interest for 2 years is ₹X. If the same sum is invested at 12% per annum for 3 years, the difference between CI and SI becomes ₹Y. What is the value of (Y - X)?

Accepted Answer

Step 1: For 2 years at 12%, Difference X = P × r² / 10000 = 5000 × 144 / 10000 = ₹72. Step 2: For 3 years, SI = (5000 × 12 × 3) / 100 = ₹1,800. A = 5000 × (1.12)³ = 5000 × 1.404928 = ₹7,024.64. CI = ₹2,024.64. Difference Y = 2024.64 - 1800 = ₹224.64 ≈ ₹225 (or ₹224 for clean calculation). Step 3: Y - X = 225 - 72 = ₹153 (or 224 - 72 = ₹152).

Question 19

The difference between compound interest and simple interest on a sum for 2 years at a certain rate per annum is ₹400. If the rate of interest is 20% per annum, what is the principal?

Accepted Answer

Step 1: Use the formula for 2-year difference: CI - SI = P × r² / 10000. Step 2: Substitute: 400 = P × 400 / 10000. Step 3: P = 400 × 10000 / 400 = ₹10,000.

Question 20

A person invests ₹8,000 at 15% per annum for 2 years under compound interest. Another person invests the same amount at 15% per annum for 2 years under simple interest. What is the difference between the amounts they receive?

Accepted Answer

Step 1: Compound Interest: A = P(1 + r/100)^t = 8000 × (1.15)² = 8000 × 1.3225 = ₹10,580. Step 2: Simple Interest: A = P + (P × r × t) / 100 = 8000 + (8000 × 15 × 2) / 100 = 8000 + 2400 = ₹10,400. Step 3: Difference = 10580 - 10400 = ₹180.

Question 21

The difference between compound interest and simple interest on a certain principal for 2 years at 12% per annum is ₹144. If the same principal is invested at 10% per annum for 3 years under compound interest, what will be the compound interest earned?

Accepted Answer

Step 1: Find principal using the difference formula. For 2 years, CI - SI = P × r²/100². So 144 = P × (12)²/10000 = P × 144/10000. Therefore P = 10000. Step 2: Calculate CI for 3 years at 10%: A = 10000 × (1.1)³ = 10000 × 1.331 = 13310. Step 3: CI = 13310 - 10000 = 3310.

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