Question 1

The difference between compound interest and simple interest on a certain principal at 6% per annum for 2 years is ₹36. What is the principal?

Accepted Answer

Step 1: Use the formula for 2 years: CI - SI = (P × R²) / 10000. Step 2: Substitute: 36 = (P × 36) / 10000. Step 3: 36 × 10000 = P × 36. Step 4: P = 360000 / 36 = ₹10,000.

Question 2

A sum of ₹8,000 earns ₹960 as simple interest in 2 years. What is the rate of interest per annum?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to find R: R = (SI × 100) / (P × T). Step 2: Substitute values: R = (960 × 100) / (8000 × 2) = 96000 / 16000 = 6% per annum. Therefore, the rate is 6% p.a.

Question 3

If ₹6,000 becomes ₹7,200 in 2 years under simple interest, what is the rate of interest per annum?

Accepted Answer

Step 1: Calculate Simple Interest: SI = Amount - Principal = 7200 - 6000 = ₹1,200. Step 2: Use R = (SI × 100) / (P × T) = (1200 × 100) / (6000 × 2) = 120000 / 12000 = 10% per annum. Therefore, the rate is 10% p.a.

Question 4

A sum of ₹4,000 is invested at 12% per annum for 2 years. How much more interest is earned under compound interest compared to simple interest?

Accepted Answer

Step 1: SI = (4000 × 12 × 2) / 100 = ₹960. Step 2: Amount under CI = 4000(1.12)^2 = 4000 × 1.2544 = ₹5,017.60, so CI = 5017.60 - 4000 = ₹1,017.60. Step 3: Additional interest = 1017.60 - 960 = ₹57.60.

Question 5

Priya borrowed ₹20,000 at 5% per annum simple interest. How long will it take for the interest to become ₹5,000?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to find T: T = (SI × 100) / (P × R). Step 2: Substitute values: T = (5000 × 100) / (20000 × 5) = 500000 / 100000 = 5 years. Therefore, it will take 5 years.

Question 6

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 7

Rajesh deposits ₹5,000 in a bank at a simple interest rate of 8% per annum. How much interest will he earn in 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 earned is ₹1,200.

Question 8

A principal of ₹10,000 is invested at 7% per annum simple interest. What will be the total amount after 4 years?

Accepted Answer

Step 1: Calculate Simple Interest: SI = (P × R × T) / 100 = (10000 × 7 × 4) / 100 = 280000 / 100 = ₹2,800. Step 2: Calculate Amount: A = P + SI = 10000 + 2800 = ₹12,800. Therefore, the total amount is ₹12,800.

Question 9

At what rate per annum will ₹8,000 amount to ₹9,680 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 9680 = 8000(1 + r/100)^2. Step 2: (1 + r/100)^2 = 9680/8000 = 1.21. Step 3: 1 + r/100 = √1.21 = 1.1. Step 4: r/100 = 0.1, so r = 10% per annum.

Question 10

A principal amount becomes ₹12,100 in 2 years at 10% per annum compound interest. What is the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 12100 = P(1 + 10/100)^2. Step 2: 12100 = P(1.1)^2 = P × 1.21. Step 3: P = 12100/1.21 = ₹10,000.

Question 11

What is the compound interest on ₹6,000 at 5% per annum for 2 years?

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 6000(1 + 5/100)^2 = 6000(1.05)^2 = 6000 × 1.1025 = ₹6,615. Step 2: Compound Interest = A - P = 6615 - 6000 = ₹615.

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 (1 + r/100)^5 = 2. Step 2: We need to find n such that (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 13

The difference between compound interest and simple interest on ₹4,000 for 2 years at 5% per annum is:

Accepted Answer

Step 1: Simple Interest = (4000 × 5 × 2)/100 = ₹400. Step 2: Amount at CI = 4000(1 + 5/100)^2 = 4000(1.05)^2 = 4000 × 1.1025 = ₹4,410. Step 3: Compound Interest = 4410 - 4000 = ₹410. Step 4: Difference = CI - SI = 410 - 400 = ₹10.

Question 14

At what rate per annum will ₹12,000 amount to ₹15,600 in 3 years under simple interest?

Accepted Answer

Step 1: Calculate Simple Interest: SI = Amount - Principal = 15600 - 12000 = ₹3,600. Step 2: Use R = (SI × 100) / (P × T) = (3600 × 100) / (12000 × 3) = 360000 / 36000 = 10% per annum. Therefore, the rate is 10% p.a.

Question 15

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 correct?

Accepted Answer

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

Question 16

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

Question 17

A sum of ₹5,000 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 = 5000(1 + 10/100)^2 = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050. Therefore, the amount after 2 years is ₹6,050.

Question 18

The difference between compound interest and simple interest on ₹8,000 for 2 years at 10% per annum is ₹___.

Accepted Answer

Step 1: Simple Interest = (P × R × T) / 100 = (8000 × 10 × 2) / 100 = ₹1,600. Step 2: Compound Interest = P[(1 + r/100)^n - 1] = 8000[(1.1)^2 - 1] = 8000[1.21 - 1] = 8000 × 0.21 = ₹1,680. Step 3: Difference = CI - SI = 1680 - 1600 = ₹80. Therefore, the difference is ₹80.

Question 19

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

Accepted Answer

Step 1: Use the 2-year difference formula: Difference = P × R² / 10,000. Step 2: Substitute: 100 = P × 100 / 10,000 = P / 100. Step 3: P = 100 × 100 = ₹10,000.

Question 20

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, so CI = ₹2,035.20. Step 3: Difference = CI - SI = 2,035.20 - 1,920 = ₹115.20.

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