Question 1

Rajesh borrowed ₹12,000 at 5% simple interest per annum. How much total amount will he repay after 4 years?

Accepted Answer

Step 1: Calculate Simple Interest using SI = (P × R × T) / 100 = (12000 × 5 × 4) / 100 = 2400. Step 2: Total Amount = Principal + SI = 12000 + 2400 = ₹14,400. Therefore, Rajesh will repay ₹14,400.

Question 2

At what rate of simple interest per annum will ₹8,000 become ₹9,600 in 2 years?

Accepted Answer

Step 1: Calculate SI = Amount - Principal = 9600 - 8000 = ₹1,600. Step 2: Use SI = (P × R × T) / 100, so 1600 = (8000 × R × 2) / 100. Step 3: 1600 = 160R, therefore R = 10% per annum.

Question 3

A sum becomes ₹4,410 in 2 years at 5% per annum under compound interest. What would be the difference between CI and SI on this principal for 2 years?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T. 4410 = P(1.05)^2 = P × 1.1025. P = 4410 / 1.1025 = ₹4,000. Step 2: Calculate SI = (4000 × 5 × 2) / 100 = ₹400. Step 3: Calculate CI = 4410 - 4000 = ₹410. Step 4: Difference = 410 - 400 = ₹10.

Question 4

A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the interest earned 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 earned is ₹1,200.

Question 5

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 = (P × R × T)/100 = (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 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: SI = (P × R × T) / 100 = (5000 × 10 × 2) / 100 = ₹1,000. Step 2: Calculate Compound Interest: A = P(1 + R/100)^T = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050. CI = 6050 - 5000 = ₹1,050. Step 3: Difference = CI - SI = 1050 - 1000 = ₹50.

Question 7

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 doubles in 5 years, then 2P = P(1 + r/100)^5, so (1 + r/100)^5 = 2. Step 2: For amount to be 8 times: 8P = P(1 + r/100)^n, so (1 + r/100)^n = 8. Step 3: Since 8 = 2^3, we have [(1 + r/100)^5]^3 = (1 + r/100)^15 = 8. Step 4: Therefore, n = 15 years.

Question 8

On a sum of ₹6,000 at 12% per annum, the difference between CI and SI for 2 years is:

Accepted Answer

Step 1: Calculate SI = (6000 × 12 × 2) / 100 = ₹1,440. Step 2: Calculate CI: A = 6000(1.12)^2 = 6000 × 1.2544 = ₹7,526.40. CI = 7526.40 - 6000 = ₹1,526.40. Step 3: Difference = 1526.40 - 1440 = ₹86.40.

Question 9

The difference between CI and SI on ₹9,000 at 20% per annum for 2 years is:

Accepted Answer

Step 1: Calculate SI = (9000 × 20 × 2) / 100 = ₹3,600. Step 2: Calculate CI: A = 9000(1.20)^2 = 9000 × 1.44 = ₹12,960. CI = 12960 - 9000 = ₹3,960. Step 3: Difference = 3960 - 3600 = ₹360.

Question 10

At what rate per annum will ₹8,000 amount to ₹9,261 in 3 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 9261 = 8000(1 + r/100)^3. Step 3: (1 + r/100)^3 = 9261/8000 = 1.157625. Step 4: Taking cube root: 1 + r/100 = 1.05. Step 5: r/100 = 0.05, so r = 5% per annum.

Question 11

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the amount after 1 year?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 12% ÷ 2 = 6% per half-year. Step 2: Number of half-years in 1 year = 2. Step 3: Amount = P(1 + r/100)^n = 8000(1 + 6/100)^2 = 8000(1.06)^2 = 8000 × 1.1236 = ₹8,988.80.

Question 12

₹5,000 is invested at 8% per annum compound interest, compounded quarterly. Find the compound interest earned in 6 months.

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 8% ÷ 4 = 2% per quarter. Step 2: Number of quarters in 6 months = 2. Step 3: Amount = 5000(1 + 2/100)^2 = 5000(1.02)^2 = 5000 × 1.0404 = ₹5,202. Step 4: Compound Interest = 5202 - 5000 = ₹202.

Question 13

A principal amount becomes ₹10,648 in 2 years at 8% per annum compound interest, compounded half-yearly. What is the principal?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 8% ÷ 2 = 4% per half-year. Step 2: Number of half-years in 2 years = 4. Step 3: Amount = P(1 + r/100)^n, so 10648 = P(1.04)^4. Step 4: (1.04)^4 = 1.16985856 ≈ 1.1699. Step 5: P = 10648 ÷ 1.1699 ≈ ₹9,100 (exact: 10648 ÷ 1.16985856 = 9100).

Question 14

₹12,000 is invested at 10% per annum compound interest, compounded half-yearly. After how many half-years will the amount become ₹13,230?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 10% ÷ 2 = 5% per half-year. Step 2: Amount = P(1 + r/100)^n, so 13230 = 12000(1.05)^n. Step 3: (1.05)^n = 13230 ÷ 12000 = 1.1025. Step 4: (1.05)^2 = 1.1025. Step 5: n = 2 half-years.

Question 15

The compound interest on ₹6,400 at 12.5% per annum for 1 year, compounded quarterly, is:

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 12.5% ÷ 4 = 3.125% per quarter. Step 2: Number of quarters in 1 year = 4. Step 3: Amount = 6400(1 + 3.125/100)^4 = 6400(1.03125)^4. Step 4: (1.03125)^4 = 1.13141... ≈ 1.1314. Step 5: Amount = 6400 × 1.1314 = 7,241 (exact: 7240.96). Step 6: CI = 7241 - 6400 = ₹841.

Question 16

What is the compound interest on ₹6,400 for 2 years at 12.5% per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: A = 6400(1 + 12.5/100)^2 = 6400(1.125)^2 = 6400 × 1.265625 = ₹8,100. Step 3: Compound Interest = A - P = 8100 - 6400 = ₹1,700.

Question 17

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

Question 18

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 true or false?

Accepted Answer

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

Question 19

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 20

A principal amount becomes ₹6,500 in 5 years at 6% simple interest per annum. What was the original principal?

Accepted Answer

Step 1: Let Principal = P. Amount = P + SI, where SI = (P × 6 × 5) / 100 = 30P / 100 = 0.3P. Step 2: 6500 = P + 0.3P = 1.3P. Step 3: P = 6500 / 1.3 = ₹5,000. Therefore, the original principal was ₹5,000.

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