Question 1

₹20,000 is invested at 16% per annum compound interest, compounded quarterly. What is the difference between the compound interest for the 1st quarter and the 2nd quarter?

Accepted Answer

Step 1: Principal P = ₹20,000, Rate R = 16% p.a., Compounded quarterly. Step 2: Quarterly rate = 16/4 = 4%. Step 3: Interest for 1st quarter = (20,000 × 4)/100 = ₹800. Step 4: Amount after 1st quarter = 20,000 + 800 = ₹20,800. Step 5: Interest for 2nd quarter = (20,800 × 4)/100 = ₹832. Step 6: Difference = 832 - 800 = ₹32.

Question 2

₹12,000 is invested at 8% per annum compound interest, compounded quarterly. Find the compound interest earned in 6 months.

Accepted Answer

Step 1: Principal P = ₹12,000, Rate R = 8% p.a., Time T = 6 months = 0.5 years, Compounded quarterly. Step 2: For quarterly compounding, rate per quarter = 8/4 = 2%, and number of quarters in 6 months = 2. Step 3: Amount = P(1 + r/100)^n = 12000(1 + 2/100)^2 = 12000(1.02)^2 = 12000 × 1.0404 = ₹12,484.80. Step 4: Compound Interest = Amount - Principal = 12,484.80 - 12,000 = ₹484.80.

Question 3

A sum of money becomes ₹9,331 in 18 months at 20% per annum compound interest, compounded half-yearly. Find the principal.

Accepted Answer

Step 1: Amount A = ₹9,331, Rate R = 20% p.a., Time T = 18 months = 1.5 years, Compounded half-yearly. Step 2: For half-yearly compounding, rate per half-year = 20/2 = 10%, and number of periods = 1.5 × 2 = 3. Step 3: A = P(1 + r/100)^n, so 9,331 = P(1.1)^3 = P × 1.331. Step 4: P = 9,331 / 1.331 = ₹7,000.

Question 4

A principal amount becomes ₹15,625 in 1 year at 20% per annum compound interest, compounded half-yearly. What is the principal?

Accepted Answer

Step 1: Amount A = ₹15,625, Rate R = 20% p.a., Time T = 1 year, Compounded half-yearly. Step 2: For half-yearly compounding, rate per half-year = 20/2 = 10%, and number of periods = 1 × 2 = 2. Step 3: A = P(1 + r/100)^n, so 15,625 = P(1 + 10/100)^2 = P(1.1)^2 = P × 1.21. Step 4: P = 15,625 / 1.21 = ₹12,500.

Question 5

A bank offers two schemes: Scheme A gives 12% per annum simple interest, and Scheme B gives 10% per annum compound interest, compounded half-yearly. A person invests ₹10,000 in each scheme for 2 years. What is the difference in the final amounts?

Accepted Answer

Step 1: Scheme A (Simple Interest): SI = (P × R × T) / 100 = (10,000 × 12 × 2) / 100 = ₹2,400. Amount = 10,000 + 2,400 = ₹12,400. Step 2: Scheme B (Compound Interest, half-yearly): R = 10% p.a. = 5% per half-year, T = 2 years = 4 half-years. Step 3: A = P(1 + r/100)^n = 10,000(1.05)^4. Step 4: (1.05)^4 = 1.21550625. Step 5: A = 10,000 × 1.21550625 = ₹12,155.06. Step 6: Difference = 12,400 - 12,155.06 = ₹244.94 ≈ ₹245. (Scheme A gives more.)

Question 6

A sum of money doubles itself in 3 years at a certain rate of compound interest, compounded half-yearly. At the same rate, in how many years will it become 8 times?

Accepted Answer

Step 1: Let principal = P. After 3 years (6 half-years), amount = 2P. Step 2: 2P = P(1 + r/100)^6, so (1 + r/100)^6 = 2. Step 3: Let (1 + r/100) = x. Then x^6 = 2, so x = 2^(1/6). Step 4: For amount to become 8P: 8P = P × x^n, so x^n = 8 = 2^3. Step 5: (2^(1/6))^n = 2^3, so 2^(n/6) = 2^3, thus n/6 = 3, so n = 18 half-years. Step 6: n = 18 half-years = 9 years.

Question 7

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What is the compound interest earned in 18 months?

Accepted Answer

Step 1: Principal P = ₹8,000, Rate R = 12% p.a., Time = 18 months = 3 half-years. Step 2: For half-yearly compounding, effective rate per half-year = 12/2 = 6%. Step 3: Amount A = P(1 + r/100)^n = 8000(1 + 6/100)^3 = 8000(1.06)^3. Step 4: (1.06)^3 = 1.191016, so A = 8000 × 1.191016 = ₹9,528.13. Step 5: CI = A - P = 9,528.13 - 8,000 = ₹1,528.13 ≈ ₹1,528.

Question 8

A principal amount becomes ₹9,261 in 1.5 years at 20% per annum compound interest, compounded half-yearly. What is the principal?

Accepted Answer

Step 1: Amount (A) = ₹9,261, Rate (R) = 20% p.a., Time (T) = 1.5 years. Step 2: For half-yearly compounding, rate per half-year = 20/2 = 10%, and number of half-years in 1.5 years = 3. Step 3: A = P(1 + r/100)^n, so 9261 = P(1.10)^3. Step 4: (1.10)^3 = 1.331, therefore P = 9261/1.331 = ₹6,950.

Question 9

₹12,000 is invested at 10% per annum compound interest, compounded quarterly. What is the compound interest earned after 9 months?

Accepted Answer

Step 1: Principal (P) = ₹12,000, Rate (R) = 10% p.a., Time = 9 months. Step 2: For quarterly compounding, rate per quarter = 10/4 = 2.5%, and number of quarters in 9 months = 3. Step 3: Amount = 12000(1.025)^3 = 12000 × 1.0769 = ₹12,922.80. Step 4: Compound Interest = 12,922.80 - 12,000 = ₹922.80.

Question 10

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: Principal (P) = ₹8,000, Rate (R) = 12% p.a., Time (T) = 1 year, Compounded half-yearly. Step 2: For half-yearly compounding, rate per half-year = 12/2 = 6%, and 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 11

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

Accepted Answer

Step 1: Principal (P) = ₹5,000, Rate (R) = 8% p.a., Time = 6 months = 0.5 years. Step 2: For quarterly compounding, rate per quarter = 8/4 = 2%, and number of quarters in 6 months = 2. Step 3: Amount = P(1 + r/100)^n = 5000(1 + 2/100)^2 = 5000(1.02)^2 = 5000 × 1.0404 = ₹5,202. Step 4: Compound Interest = Amount - Principal = 5202 - 5000 = ₹202.

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