Question 1

If 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: For 2 years, CI - SI = (P × R²) / (100)². Step 2: 144 = (P × 144) / 10000. Step 3: 144 × 10000 = P × 144. Step 4: P = 10000.

Question 2

A principal of ₹10,000 is invested at 5% per annum. The difference between compound interest and simple interest for 3 years is ₹76.25. Which of the following is closest to this difference?

Accepted Answer

Step 1: Calculate SI = (10000 × 5 × 3) / 100 = ₹1,500. Step 2: Calculate Amount for CI: A = 10000(1.05)³ = 10000 × 1.157625 = ₹11,576.25. Step 3: CI = 11576.25 - 10000 = ₹1,576.25. Step 4: Difference = 1576.25 - 1500 = ₹76.25.

Question 3

In how many years will ₹4,500 amount to ₹5,400 at 5% per annum simple interest?

Accepted Answer

Step 1: Calculate SI = Amount - Principal = 5400 - 4500 = ₹900. Step 2: Use T = (SI × 100) / (P × R). Step 3: T = (900 × 100) / (4500 × 5) = 90000 / 22500 = 4 years. Therefore, the time period is 4 years.

Question 4

Raj borrowed ₹5,000 at a simple interest rate of 8% per annum. How much interest will he pay after 3 years?

Accepted Answer

Step 1: Use the Simple Interest formula: SI = (P × R × T) / 100. Step 2: Substitute values: SI = (5000 × 8 × 3) / 100 = 120000 / 100 = ₹1,200. Therefore, the interest is ₹1,200.

Question 5

A sum becomes ₹12,100 in 2 years at 10% per annum under compound interest. What would be the simple interest on the same sum for the same period at the same rate?

Accepted Answer

Step 1: Find Principal using A = P(1 + R/100)^T: 12100 = P(1.1)². Step 2: 12100 = P × 1.21, so P = ₹10,000. Step 3: Calculate SI = (10000 × 10 × 2) / 100 = ₹2,000.

Question 6

The simple interest on a sum for 2 years at 8% per annum is ₹1,600. What will be the compound interest on the same sum at the same rate for the same period?

Accepted Answer

Step 1: From SI formula, find Principal: SI = (P × R × T) / 100, so 1600 = (P × 8 × 2) / 100. Step 2: 1600 = 16P/100, so P = ₹10,000. Step 3: Calculate CI: A = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. Step 4: CI = 11664 - 10000 = ₹1,664.

Question 7

The difference between compound interest and simple interest on ₹8,000 at 12.5% per annum for 2 years is:

Accepted Answer

Step 1: Calculate Simple Interest: SI = (8000 × 12.5 × 2)/100 = ₹2,000. Step 2: Calculate Compound Interest: A = 8000(1 + 12.5/100)^2 = 8000(1.125)^2 = 8000 × 1.265625 = ₹10,125. CI = 10125 - 8000 = ₹2,125. Step 3: Difference = CI - SI = 2125 - 2000 = ₹125. Therefore, the difference is ₹125.

Question 8

At what rate per annum will ₹6,000 yield a simple interest of ₹1,200 in 4 years?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to R = (SI × 100) / (P × T). Step 2: Substitute: R = (1200 × 100) / (6000 × 4) = 120000 / 24000 = 5% per annum. Therefore, the rate is 5% per annum.

Question 9

A principal of ₹12,000 earns ₹2,880 as simple interest over a certain period at 8% per annum. What is the time period?

Accepted Answer

Step 1: Use the formula T = (SI × 100) / (P × R). Step 2: Substitute values: T = (2880 × 100) / (12000 × 8) = 288000 / 96000 = 3 years. Therefore, the time period is 3 years.

Question 10

Priya lent ₹10,000 to her friend at 6% per annum simple interest. After how many months will the interest amount to ₹600?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to T = (SI × 100) / (P × R). Step 2: T = (600 × 100) / (10000 × 6) = 60000 / 60000 = 1 year. Step 3: Convert to months: 1 year = 12 months. Therefore, the answer is 12 months.

Question 11

A sum of ₹8,000 is lent at 5% per annum simple interest. What will be the total amount (Principal + Interest) after 4 years?

Accepted Answer

Step 1: Calculate SI using SI = (P × R × T) / 100 = (8000 × 5 × 4) / 100 = 1600. Step 2: Total Amount = Principal + SI = 8000 + 1600 = ₹9,600. Therefore, the answer is ₹9,600.

Question 12

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 13

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 = (P × R²) / 10000. Step 2: Substitute values: 80 = (8000 × R²) / 10000. Step 3: 80 = 0.8 × R². Step 4: R² = 100, so R = 10% per annum.

Question 14

₹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 15

A sum of money becomes ₹2,420 in 2 years and ₹2,662 in 3 years at compound interest. What is the principal amount?

Accepted Answer

Step 1: Let principal = P and rate = r% per annum. Step 2: After 2 years: P(1 + r/100)^2 = 2420. Step 3: After 3 years: P(1 + r/100)^3 = 2662. Step 4: Divide equation 3 by equation 2: [P(1 + r/100)^3] / [P(1 + r/100)^2] = 2662/2420. Step 5: (1 + r/100) = 2662/2420 = 1.1, so r = 10%. Step 6: Substitute back: P(1.1)^2 = 2420, so P × 1.21 = 2420, thus P = 2420/1.21 = ₹2,000.

Question 16

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 17

A sum of money doubles itself in 5 years under 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% p.a. Step 2: For the sum to triple, SI = 2P. Using 2P = (P × 20 × T) / 100: 2P = 0.2PT, so T = 10 years.

Question 18

A principal amount becomes ₹12,100 in 2 years at 10% per annum under compound interest. What would be the simple interest earned on the same principal for the same period and rate?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T: 12,100 = P(1.10)^2 = P × 1.21, so P = 10,000. Step 2: Calculate SI: SI = (10,000 × 10 × 2) / 100 = ₹2,000.

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

Question 20

The compound interest on ₹6,000 at 5% per annum for 2 years is how much more than the simple interest on the same principal at the same rate and time?

Accepted Answer

Step 1: Calculate SI: SI = (6,000 × 5 × 2) / 100 = ₹600. Step 2: Calculate CI: A = 6,000(1.05)^2 = 6,000 × 1.1025 = ₹6,615. CI = 6,615 - 6,000 = ₹615. Step 3: Difference = CI - SI = 615 - 600 = ₹15.

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