Question 1

₹8,000 is lent at 5% per annum compound interest. The difference between CI and SI for 3 years is ₹61. What is the compound interest for 3 years?

Accepted Answer

Step 1: Use the formula for difference: CI - SI = P × R² × (R + 300) / (100)³ for 3 years, or calculate directly. Step 2: SI = (8000 × 5 × 3) / 100 = ₹1,200. Step 3: A = 8000(1.05)³ = 8000 × 1.157625 = ₹9,261. Step 4: CI = 9261 - 8000 = ₹1,261. Step 5: Verify difference: 1261 - 1200 = ₹61 ✓

Question 2

A principal amount earns ₹400 as simple interest in 2 years at 8% per annum. If the same principal is invested at 8% compound interest for 2 years, how much more interest will be earned?

Accepted Answer

Step 1: Find principal from SI formula: SI = (P × R × T) / 100, so 400 = (P × 8 × 2) / 100, thus P = 400 × 100 / 16 = ₹2,500. Step 2: Calculate CI: A = 2500(1.08)² = 2500 × 1.1664 = ₹2,916. Step 3: CI = 2916 - 2500 = ₹416. Step 4: Additional interest = CI - SI = 416 - 400 = ₹16.

Question 3

Arun invested ₹20,000 at 6% simple interest per annum. What will be the total amount after 4 years?

Accepted Answer

Step 1: Calculate Simple Interest: SI = (P × R × T) / 100 = (20000 × 6 × 4) / 100 = 480000 / 100 = ₹4,800. Step 2: Total Amount = Principal + SI = 20000 + 4800 = ₹24,800. Therefore, the total amount is ₹24,800.

Question 4

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 5

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, the difference formula is: CI - SI = P × R² / (100)². Step 2: Substitute: 144 = P × (12)² / (100)² = P × 144 / 10000. Step 3: Solve for P: P = 144 × 10000 / 144 = ₹10,000.

Question 6

If ₹15,000 amounts to ₹18,600 at simple interest in 2 years, what is the rate of interest per annum?

Accepted Answer

Step 1: Calculate Simple Interest: SI = 18600 - 15000 = ₹3,600. Step 2: Use the formula R = (SI × 100) / (P × T). Step 3: R = (3600 × 100) / (15000 × 2) = 360000 / 30000 = 12% per annum. Therefore, the rate of interest is 12% p.a.

Question 7

A sum of ₹6,000 is invested at 15% per annum. The simple interest for 1 year is ₹900. If the same sum is invested at compound interest for 1 year at the same rate, what is the difference between CI and SI?

Accepted Answer

Step 1: For 1 year, compound interest and simple interest are always equal because there is no compounding effect in the first year. Step 2: CI for 1 year = A - P = 6000(1.15) - 6000 = 6900 - 6000 = ₹900. Step 3: SI for 1 year = ₹900 (given). Step 4: Difference = 900 - 900 = ₹0.

Question 8

A sum of ₹12,000 becomes ₹15,600 in 3 years at simple interest. What is the rate of interest per annum?

Accepted Answer

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

Question 9

Priya lent ₹8,000 to her friend at 5% simple interest per annum. After how many years will the interest amount to ₹2,000?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged as T = (SI × 100) / (P × R). Step 2: Substitute: T = (2000 × 100) / (8000 × 5) = 200000 / 40000 = 5 years. Therefore, the time period is 5 years.

Question 10

The difference between compound interest and simple interest on ₹4,000 for 2 years is ₹40. What is the rate of interest per annum?

Accepted Answer

Step 1: Use the formula for 2 years: CI - SI = P × R² / (100)². Step 2: Substitute: 40 = 4000 × R² / 10000. Step 3: Simplify: 40 = 4R² / 10 = 0.4R². Step 4: Solve: R² = 40 / 0.4 = 100, so R = 10% per annum.

Question 11

Rajesh 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 12

Two sums of money are in the ratio 3:4. If both are invested at 10% simple interest per annum, after 5 years the difference in their interests will be ₹500. What is the larger sum?

Accepted Answer

Step 1: Let the two sums be 3x and 4x. Step 2: Calculate SI for first sum: SI₁ = (3x × 10 × 5) / 100 = 1.5x. Step 3: Calculate SI for second sum: SI₂ = (4x × 10 × 5) / 100 = 2x. Step 4: Find the difference: SI₂ - SI₁ = 2x - 1.5x = 0.5x. Step 5: Given that this difference equals ₹500: 0.5x = 500, so x = 1,000. Step 6: The larger sum = 4x = 4 × 1,000 = ₹4,000. Therefore, the answer is ₹4,000.

Question 13

The difference between compound interest and simple interest on ₹10,000 for 2 years at 5% per annum is:

Accepted Answer

Step 1: Calculate simple interest: SI = (P × R × T)/100 = (10000 × 5 × 2)/100 = ₹1,000. Step 2: Calculate compound interest: A = P(1 + r/100)^n = 10000(1.05)^2 = 10000 × 1.1025 = ₹11,025. CI = 11025 - 10000 = ₹1,025. Step 3: Difference = CI - SI = 1025 - 1000 = ₹25.

Question 14

A sum of ₹8,000 is invested at a simple interest rate of 12% per annum. How much interest will be earned in 3 years and 6 months?

Accepted Answer

Step 1: Identify the formula for Simple Interest: SI = (P × R × T) / 100. Step 2: Convert time to years: 3 years 6 months = 3.5 years. Step 3: Substitute values: SI = (8000 × 12 × 3.5) / 100 = (336,000) / 100 = ₹3,360. Therefore, the interest earned is ₹3,360.

Question 15

A person invests ₹6,400 at 12.5% per annum compound interest. After how many years will the amount become ₹10,240?

Accepted Answer

Step 1: Use A = P(1 + R/100)^T. Here, 10,240 = 6,400(1 + 12.5/100)^T ⟹ 10,240 = 6,400(1.125)^T. Step 2: Simplify: 10,240 / 6,400 = (1.125)^T ⟹ 1.6 = (1.125)^T. Step 3: Note that 1.125 = 9/8. So (9/8)^T = 1.6 = 8/5. Step 4: (9/8)^T = 8/5. Testing T = 2: (9/8)² = 81/64 ≈ 1.266 (too small). Testing T = 3: (9/8)³ = 729/512 ≈ 1.424 (close). Testing T = 4: (9/8)⁴ = 6561/4096 ≈ 1.601 ≈ 1.6 ✓. Therefore T = 4 years.

Question 16

A principal amount becomes ₹1,44,000 after 2 years at 20% per annum compound interest. What was the original principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: Substitute A = 144000, r = 20, n = 2. Step 3: 144000 = P(1 + 20/100)^2 = P(1.2)^2 = P × 1.44. Step 4: P = 144000/1.44 = ₹1,00,000. Therefore, the original principal was ₹1,00,000.

Question 17

The simple interest on a sum for 2 years at 6% per annum is ₹480. If the same sum is invested at 6% compound interest for 2 years, how much more interest will be earned compared to simple interest?

Accepted Answer

Step 1: Find principal from SI: SI = (P × R × T) / 100 ⟹ 480 = (P × 6 × 2) / 100 ⟹ P = ₹4,000. Step 2: Calculate CI: A = P(1 + R/100)^T = 4,000(1.06)² = 4,000 × 1.1236 = ₹4,494.40. CI = 4,494.40 − 4,000 = ₹494.40. Step 3: Difference = CI − SI = 494.40 − 480 = ₹14.40.

Question 18

At what rate per annum will ₹5,000 become ₹6,050 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: Substitute A = 6050, P = 5000, n = 2. Step 3: 6050 = 5000(1 + r/100)^2. Step 4: (1 + r/100)^2 = 6050/5000 = 1.21. Step 5: 1 + r/100 = √1.21 = 1.1. Step 6: r/100 = 0.1, so r = 10% per annum.

Question 19

A sum becomes ₹1,210 in 2 years and ₹1,331 in 3 years under compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Let principal = P and rate = R% p.a. From the given data: P(1 + R/100)² = 1,210 and P(1 + R/100)³ = 1,331. Step 2: Divide the second equation by the first: [P(1 + R/100)³] / [P(1 + R/100)²] = 1,331 / 1,210 ⟹ (1 + R/100) = 1.1 ⟹ R/100 = 0.1 ⟹ R = 10%. Step 3: Verify: P(1.1)² = 1,210 ⟹ P = 1,000. Check: 1,000(1.1)³ = 1,331 ✓

Question 20

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: Substitute P = 8000, r = 10, n = 2. Step 3: A = 8000(1 + 10/100)^2 = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680. Therefore, the amount after 2 years is ₹9,680.

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