Question 1

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 2

The difference between compound interest and simple interest on a certain principal 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 values: 144 = P × (12)² / (100)² = P × 144 / 10000. Step 3: Solve for P: P = (144 × 10000) / 144 = ₹10,000.

Question 3

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 payable is ₹1,200.

Question 4

A sum of ₹8,000 earns ₹1,600 as simple interest in 4 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: R = (1600 × 100) / (8000 × 4) = 160000 / 32000 = 5% per annum. Therefore, the rate is 5% p.a.

Question 5

A sum of ₹10,000 is invested at 8% per annum for 3 years. By how much does the compound interest exceed the simple interest?

Accepted Answer

Step 1: SI = (10000 × 8 × 3) / 100 = ₹2,400. Step 2: A = 10000(1.08)^3 = 10000 × 1.259712 ≈ ₹12,597.12, so CI ≈ ₹2,597.12. Step 3: Difference ≈ ₹197.12 ≈ ₹197 (rounding to nearest rupee).

Question 6

Arun lent ₹15,000 to his friend at 4% per annum simple interest. After how many months will the interest be ₹600?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to find T: T = (SI × 100) / (P × R) = (600 × 100) / (15000 × 4) = 60000 / 60000 = 1 year. Step 2: Convert to months: 1 year = 12 months. Therefore, the interest will be ₹600 after 12 months.

Question 7

A person borrowed ₹10,000 at 5% per annum simple interest. What will be the total amount to be repaid after 2.5 years?

Accepted Answer

Step 1: Calculate Simple Interest: SI = (P × R × T) / 100 = (10000 × 5 × 2.5) / 100 = 125000 / 100 = ₹1,250. Step 2: Calculate Amount: A = P + SI = 10000 + 1250 = ₹11,250. Therefore, the total amount to be repaid is ₹11,250.

Question 8

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

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 9

Priya invested ₹20,000 at 6% simple interest per annum. In how many years will the interest earned be ₹7,200?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to find T: T = (SI × 100) / (P × R). Step 2: Substitute: T = (7200 × 100) / (20000 × 6) = 720000 / 120000 = 6 years. Therefore, the time period is 6 years.

Question 10

The difference between compound interest and simple interest on a principal of ₹8,000 at 5% per annum for 2 years is ₹X. Find X.

Accepted Answer

Step 1: SI = (8000 × 5 × 2) / 100 = ₹800. Step 2: A = 8000(1.05)^2 = 8000 × 1.1025 = ₹8,820, so CI = 8820 - 8000 = ₹820. Step 3: Difference = 820 - 800 = ₹20.

Question 11

A principal amount earns ₹500 as simple interest in 2 years at 10% per annum. If the same principal is invested at the same rate for the same period under compound interest, what will be the difference between CI and SI?

Accepted Answer

Step 1: From SI formula, P = (SI × 100) / (R × T) = (500 × 100) / (10 × 2) = ₹2,500. Step 2: SI = ₹500 (given). Step 3: A = 2500(1.10)^2 = 2500 × 1.21 = ₹3,025, so CI = 3025 - 2500 = ₹525. Step 4: Difference = 525 - 500 = ₹25.

Question 12

At what rate of interest per annum will the difference between CI and SI on ₹4,000 for 2 years be ₹40?

Accepted Answer

Step 1: Use the formula for difference: CI - SI = P × R² / (100)² for 2 years (approximately). More precisely: SI = (4000 × R × 2)/100 = 80R. Step 2: A = 4000(1 + R/100)^2, so CI = 4000[(1 + R/100)^2 - 1] = 4000[2R/100 + R²/10000] = 80R + 4R²/100. Step 3: Difference = 4R²/100 = 40, so R² = 1000, but let's verify: 4R²/100 = 40 means R² = 1000... Let me recalculate: For 2 years, CI - SI = PR²/10000 = 4000 × R²/10000 = 2R²/5. Setting this equal to 40: 2R²/5 = 40, so R² = 100, thus R = 10% per annum.

Question 13

Two sums are invested at 10% per annum. Sum A earns simple interest and Sum B earns compound interest, both for 2 years. If the difference in their final amounts is ₹100, what is Sum A (assuming both principals are equal)?

Accepted Answer

Step 1: Let principal = P. After 2 years with SI: Amount_A = P + (P × 10 × 2)/100 = P + 0.2P = 1.2P. Step 2: After 2 years with CI: Amount_B = P(1.10)² = 1.21P. Step 3: Difference = Amount_B - Amount_A = 1.21P - 1.2P = 0.01P = 100. Step 4: P = 10,000. Therefore, Sum A (principal) = ₹10,000.

Question 14

Priya deposits ₹5,000 in a bank offering 8% per annum compound interest, compounded half-yearly. What will be the amount after 1 year?

Accepted Answer

Step 1: When compounded half-yearly, the rate becomes 8/2 = 4% per half-year and time becomes 1 × 2 = 2 half-years. Step 2: A = P(1 + r/100)^n = 5000(1.04)^2. Step 3: (1.04)^2 = 1.0816, so A = 5000 × 1.0816 = ₹5,408. Therefore, the amount after 1 year is ₹5,408.

Question 15

Priya lent ₹15,000 to her friend at 8% per annum simple interest. After 2.5 years, how much total interest will she receive?

Accepted Answer

Step 1: Use SI formula: SI = (P × R × T) / 100. Step 2: P = 15,000, R = 8%, T = 2.5 years. Step 3: SI = (15,000 × 8 × 2.5) / 100. Step 4: SI = (15,000 × 20) / 100. Step 5: SI = 300,000 / 100 = 3,000.

Question 16

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 2 = (1 + r/100)^5. Step 2: For the amount to become 8P, we need 8 = (1 + r/100)^n. Step 3: Since 8 = 2^3, we have (1 + r/100)^n = [(1 + r/100)^5]^3. Step 4: Therefore, n = 5 × 3 = 15 years. The sum will become 8 times in 15 years.

Question 17

At what rate per annum will ₹10,000 become ₹12,100 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, where A = 12,100, P = 10,000, n = 2. Step 2: 12,100 = 10,000(1 + r/100)^2. Step 3: (1 + r/100)^2 = 12,100 ÷ 10,000 = 1.21. Step 4: 1 + r/100 = √1.21 = 1.1. Step 5: r/100 = 0.1, so r = 10%. Therefore, the rate is 10% per annum.

Question 18

The simple interest on a sum for 2 years at 9% per annum is ₹900. If the same sum is invested at the same rate for the same period at compound interest, what will be the difference between the compound interest and simple interest?

Accepted Answer

Step 1: From SI formula, find principal: SI = (P × R × T) / 100 → 900 = (P × 9 × 2) / 100 → 900 = 18P → P = 50. Step 2: Calculate CI: A = P(1 + R/100)^T = 50(1.09)² = 50 × 1.1881 = 59.405. CI = 59.405 - 50 = 9.405. Step 3: Difference = CI - SI = 9.405 - 9 = 0.405. Wait, recalculate: P = 900 × 100 / (9 × 2) = 90000 / 18 = 5000. Step 2 (revised): A = 5000(1.09)² = 5000 × 1.1881 = 5940.5. CI = 5940.5 - 5000 = 940.5. Step 3: Difference = 940.5 - 900 = 40.5.

Question 19

A sum of ₹6,000 is invested at a certain rate per annum. The compound interest for 2 years is ₹1,260 and the simple interest for the same period is ₹1,200. What is the rate of interest?

Accepted Answer

Step 1: From SI formula: SI = (P × R × T) / 100 → 1200 = (6000 × R × 2) / 100 → 1200 = 120R → R = 10% per annum. Step 2: Verify with CI: A = P(1 + R/100)^T = 6000(1.10)² = 6000 × 1.21 = 7260. CI = 7260 - 6000 = 1260. ✓ Confirmed.

Question 20

A certain sum of money is lent at 10% per annum simple interest. If the interest earned in 4 years is ₹2,400, what is the principal?

Accepted Answer

Step 1: Use SI formula: SI = (P × R × T) / 100. Step 2: Given SI = 2,400, R = 10%, T = 4 years. Step 3: Rearrange for P: P = (SI × 100) / (R × T). Step 4: P = (2,400 × 100) / (10 × 4). Step 5: P = 240,000 / 40 = 6,000.

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