Question 1

A sum of ₹8,000 is invested at 10% per annum compounded half-yearly for 1 year. What is the compound interest earned?

Accepted Answer

Step 1: For half-yearly compounding, Rate per half-year = 10/2 = 5%, Number of periods = 1 × 2 = 2. Step 2: Amount = 8000 × (1 + 5/100)² = 8000 × (1.05)² = 8000 × 1.1025 = ₹8,820. Step 3: CI = 8820 − 8000 = ₹820. Common mistake: Using annual rate directly gives CI = 8000 × 10/100 = ₹800 (option a). Therefore, answer is ₹820.

Question 2

A sum of ₹16,000 is invested at 10% per annum compounded half-yearly. What is the compound interest accrued after 1.5 years?

Accepted Answer

Step 1: When compounded half-yearly, rate per period = 10/2 = 5%, and number of periods for 1.5 years = 1.5 × 2 = 3. Step 2: Amount = P × (1 + r/100)^n = 16000 × (1.05)^3. Step 3: (1.05)^3 = 1.157625. Step 4: Amount = 16000 × 1.157625 = ₹18,522. Step 5: CI = 18522 − 16000 = ₹2,522. Therefore, the answer is ₹2,522.

Question 3

What is the compound interest on ₹5,000 at 8% per annum for 1 year, compounded quarterly?

Accepted Answer

Step 1: Principal (P) = ₹5,000, Rate (R) = 8% p.a., Time (T) = 1 year, Compounded quarterly. Step 2: For quarterly compounding, use A = P(1 + R/400)^(4T). Step 3: A = 5000(1 + 8/400)^(4×1) = 5000(1 + 0.02)^4 = 5000(1.02)^4. Step 4: (1.02)^4 = 1.08243216. Step 5: A = 5000 × 1.08243216 = ₹5,412.16. Step 6: Compound Interest = A - P = 5412.16 - 5000 = ₹412.16.

Question 4

A principal amount becomes ₹6,760 after 2 years at 10% per annum compound interest, compounded half-yearly. What was the principal?

Accepted Answer

Step 1: Amount (A) = ₹6,760, Rate (R) = 10% p.a., Time (T) = 2 years, Compounded half-yearly. Step 2: For half-yearly compounding, A = P(1 + R/200)^(2T). Step 3: 6760 = P(1 + 10/200)^(2×2) = P(1 + 0.05)^4 = P(1.05)^4. Step 4: (1.05)^4 = 1.21550625. Step 5: P = 6760 / 1.21550625 = ₹5,560.36 ≈ ₹5,560.

Question 5

At what rate per annum will ₹4,000 amount to ₹4,410 in 1 year, if the interest is compounded half-yearly?

Accepted Answer

Step 1: Principal (P) = ₹4,000, Amount (A) = ₹4,410, Time (T) = 1 year, Compounded half-yearly. Step 2: For half-yearly compounding, A = P(1 + R/200)^(2T). Step 3: 4410 = 4000(1 + R/200)^2. Step 4: 4410/4000 = (1 + R/200)^2. Step 5: 1.1025 = (1 + R/200)^2. Step 6: Taking square root: 1.05 = 1 + R/200. Step 7: R/200 = 0.05, so R = 10% per annum.

Question 6

₹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 = 5,202 - 5,000 = ₹202.

Question 7

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 + 4/100)^4, so 10,648 = P(1.04)^4. Step 4: (1.04)^4 = 1.16985856 ≈ 1.1699. Step 5: P = 10,648 ÷ 1.1699 ≈ ₹9,100 (approximately). Let me verify: 9,100 × (1.04)^4 = 9,100 × 1.16985856 ≈ 10,645.91 ≈ ₹10,646. Closest answer is ₹9,100.

Question 8

₹12,000 is invested at 10% per annum compound interest, compounded half-yearly. What is the compound interest earned in the first 6 months?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 10% ÷ 2 = 5% per half-year. Step 2: For the first 6 months (1 half-year), Amount = 12,000(1 + 5/100)^1 = 12,000 × 1.05 = ₹12,600. Step 3: Compound Interest = 12,600 - 12,000 = ₹600.

Question 9

A sum becomes ₹6,655 after 1 year at 10% per annum compound interest, compounded quarterly. What is the original principal?

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 10% ÷ 4 = 2.5% per quarter. Step 2: Number of quarters in 1 year = 4. Step 3: Amount = P(1 + 2.5/100)^4, so 6,655 = P(1.025)^4. Step 4: (1.025)^4 = 1.10381289... ≈ 1.1038. Step 5: P = 6,655 ÷ 1.1038 ≈ ₹6,025. Verify: 6,025 × (1.025)^4 ≈ 6,655.

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: 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 11

₹20,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the amount after 1.5 years?

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 1.5 years = 3. Step 3: Amount = P(1 + r/100)^n = 20,000(1.06)^3. Step 4: (1.06)^3 = 1.191016. Step 5: Amount = 20,000 × 1.191016 = ₹23,820.32 ≈ ₹23,820.

Question 12

₹5,000 is invested at 16% per annum compound interest, compounded quarterly. What is the difference between the compound interest for the first quarter and the second quarter?

Accepted Answer

Step 1: Quarterly rate = 16% ÷ 4 = 4% per quarter. Step 2: Interest for first quarter = 5000 × 4/100 = ₹200. Step 3: Amount after first quarter = 5000 + 200 = ₹5,200. Step 4: Interest for second quarter = 5200 × 4/100 = ₹208. Step 5: Difference = 208 - 200 = ₹8.

Question 13

The difference between compound interest (compounded quarterly) and simple interest on ₹10,000 at 16% per annum for 1 year is:

Accepted Answer

Step 1: Principal (P) = ₹10,000, Rate (R) = 16% p.a., Time (T) = 1 year. Step 2: For Simple Interest: SI = (P × R × T)/100 = (10000 × 16 × 1)/100 = ₹1,600. Step 3: For Compound Interest (quarterly): Effective rate per quarter = 16/4 = 4%, number of periods = 4. Amount = 10000(1.04)^4 = 10000 × 1.16985856 = ₹11,698.59 (approx). CI = 11698.59 − 10000 = ₹1,698.59. Step 4: Difference = CI − SI = 1698.59 − 1600 = ₹98.59 ≈ ₹98.60.

Question 14

A principal amount becomes ₹15,625 after 2 years at 20% per annum compound interest, compounded half-yearly. What is the principal?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 20% ÷ 2 = 10% per half-year. Step 2: Number of half-years in 2 years = 4. Step 3: Amount = P(1 + 10/100)^4 = P(1.1)^4 = 15625. Step 4: P(1.4641) = 15625. Step 5: P = 15625 ÷ 1.4641 = ₹10,000.

Question 15

₹12,000 is invested at 8% per annum compound interest, compounded quarterly. Find the compound interest earned after 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 = 12000(1 + 2/100)^2 = 12000(1.02)^2 = 12000 × 1.0404 = ₹12,484.80. Step 4: Compound Interest = 12484.80 - 12000 = ₹484.80.

Question 16

₹6,400 is invested at a certain rate per annum compound interest, compounded quarterly. If the amount becomes ₹8,100 after 1 year, what is the rate of interest per annum?

Accepted Answer

Step 1: For quarterly compounding, let rate per quarter = r%. Step 2: Number of quarters in 1 year = 4. Step 3: Amount = P(1 + r/100)^4 = 8100. Step 4: 6400(1 + r/100)^4 = 8100. Step 5: (1 + r/100)^4 = 8100/6400 = 1.265625. Step 6: (1 + r/100) = (1.265625)^(1/4) = 1.06. Step 7: r/100 = 0.06, so r = 6% per quarter. Step 8: Annual rate = 6 × 4 = 24% per annum.

Question 17

A principal amount becomes ₹15,625 in 1 year when invested at 20% per annum compound interest, compounded half-yearly. What was the original 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, effective rate per half-year = 20/2 = 10%, and number of periods = 1 × 2 = 2. Step 3: A = P(1 + r/100)^n, so 15625 = P(1 + 10/100)^2 = P(1.1)^2 = P × 1.21. Step 4: P = 15625/1.21 = ₹12,500.

Question 18

A principal amount doubles in 5 years at a certain rate of compound interest, compounded half-yearly. What will be the amount after 10 years at the same rate?

Accepted Answer

Step 1: Let Principal = P. After 5 years (10 half-years), Amount = 2P. Step 2: 2P = P(1 + r/100)^10, so (1 + r/100)^10 = 2. Step 3: After 10 years (20 half-years), Amount = P(1 + r/100)^20 = P[(1 + r/100)^10]^2 = P × 2^2 = 4P. Step 4: Therefore, the amount after 10 years is 4 times the principal.

Question 19

The difference between compound interest and simple interest on a sum for 2 years at 8% per annum, compounded half-yearly, is ₹61.44. What is the principal?

Accepted Answer

Step 1: Let Principal = P. For half-yearly compounding over 2 years (4 half-years) at 8% p.a. (4% per half-year): Amount = P(1.04)^4. Step 2: (1.04)^4 = 1.16985856 ≈ 1.16986. Step 3: CI = P(1.16986 - 1) = 0.16986P. Step 4: SI = (P × 8 × 2) / 100 = 0.16P. Step 5: Difference = CI - SI = 0.16986P - 0.16P = 0.00986P. Step 6: Given difference = ₹61.44, so 0.00986P = 61.44. Step 7: P = 61.44 / 0.00986 ≈ 6,230.02 ≈ ₹6,230. (Recalculating more precisely: (1.04)^4 = 1.16985856, CI = 0.16985856P, SI = 0.16P, Difference = 0.00985856P = 61.44, P = 61.44/0.00985856 ≈ 6,230.)

Question 20

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the amount after 1.5 years?

Accepted Answer

Step 1: Principal P = ₹8,000, Rate R = 12% p.a., Time T = 1.5 years = 3 half-years. Step 2: For half-yearly compounding, rate per half-year = 12/2 = 6% per half-year. Step 3: Amount = P(1 + r/100)^n = 8000(1 + 6/100)^3 = 8000(1.06)^3. Step 4: (1.06)^3 = 1.191016. Step 5: Amount = 8000 × 1.191016 = ₹9,528.13 ≈ ₹9,528.

Question 21

₹12,000 is lent at 8% per annum compound interest, compounded quarterly. Find the compound interest earned in 2 years.

Accepted Answer

Step 1: Principal P = ₹12,000, Rate R = 8% p.a., Time T = 2 years = 8 quarters. Step 2: For quarterly compounding, rate per quarter = 8/4 = 2% per quarter. Step 3: Amount = P(1 + r/100)^n = 12000(1 + 2/100)^8 = 12000(1.02)^8. Step 4: (1.02)^8 = 1.171659. Step 5: Amount = 12000 × 1.171659 = ₹14,059.91 ≈ ₹14,060. Step 6: CI = Amount - Principal = 14060 - 12000 = ₹2,060.

Question 22

A certain sum becomes ₹18,522 in 2 years at 10% per annum compound interest, compounded half-yearly. What is the principal?

Accepted Answer

Step 1: Amount A = ₹18,522, Rate R = 10% p.a., Time T = 2 years = 4 half-years. Step 2: For half-yearly compounding, rate per half-year = 10/2 = 5% per half-year. Step 3: A = P(1 + r/100)^n → 18522 = P(1.05)^4. Step 4: (1.05)^4 = 1.21550625. Step 5: P = 18522 / 1.21550625 = ₹15,240.

SSC CHSL Half-Yearly / Quarterly CI

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Half-Yearly / Quarterly CI — Practice Questions

60-Second Revision — Half-Yearly / Quarterly CI