Question 1

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. Therefore, the answer is ₹8,988.80.

Question 2

₹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. Therefore, the answer is ₹202.

Question 3

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 (approximately). Therefore, the answer is ₹9,100.

Question 4

₹12,000 is invested at 10% per annum compound interest, compounded half-yearly. What is the compound interest earned in 1.5 years?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 10% ÷ 2 = 5% per half-year. Step 2: Number of half-years in 1.5 years = 3. Step 3: Amount = 12000(1 + 5/100)^3 = 12000(1.05)^3. Step 4: (1.05)^3 = 1.157625. Step 5: Amount = 12000 × 1.157625 = ₹13,891.50. Step 6: Compound Interest = 13891.50 - 12000 = ₹1,891.50. Therefore, the answer is ₹1,891.50.

Question 5

A sum of ₹6,400 becomes ₹7,056 in 2 years at a certain rate of compound interest, compounded half-yearly. What is the rate of interest per annum?

Accepted Answer

Step 1: For half-yearly compounding, let the half-yearly rate be r%. Step 2: Number of half-years in 2 years = 4. Step 3: Amount = P(1 + r/100)^n, so 7056 = 6400(1 + r/100)^4. Step 4: (1 + r/100)^4 = 7056/6400 = 1.1025. Step 5: Taking the fourth root: 1 + r/100 = (1.1025)^(1/4) = 1.05. Step 6: r/100 = 0.05, so r = 5% per half-year. Step 7: Annual rate = 5 × 2 = 10% per annum. Therefore, the answer is 10% per annum.

Question 6

₹20,000 is invested at 6% per annum compound interest, compounded quarterly. What will be the amount after 9 months?

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 6% ÷ 4 = 1.5% per quarter. Step 2: Number of quarters in 9 months = 3. Step 3: Amount = 20000(1 + 1.5/100)^3 = 20000(1.015)^3. Step 4: (1.015)^3 = 1.045678375 ≈ 1.04568. Step 5: Amount = 20000 × 1.04568 = ₹20,913.60. Therefore, the answer is ₹20,913.60.

Question 7

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

Accepted Answer

Step 1: Principal P = ₹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 = 12000(1 + 2/100)^2 = 12000(1.02)^2 = 12000 × 1.0404 = ₹12,484.80. Step 4: CI = 12,484.80 - 12,000 = ₹484.80.

Question 8

A principal amount becomes ₹15,625 after 2 years 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 = 2 years, compounded half-yearly. Step 2: For half-yearly compounding, rate per half-year = 20/2 = 10%, and number of periods = 2 × 2 = 4. Step 3: A = P(1 + r/100)^n → 15625 = P(1.10)^4 = P × 1.4641. Step 4: P = 15625 / 1.4641 = ₹10,000.

Question 9

The difference between compound interest and simple interest on a sum for 1 year at 16% per annum, compounded half-yearly, is ₹40. What is the principal?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 16/2 = 8%, number of periods = 2. Step 2: Amount with CI = P(1.08)^2 = P × 1.1664. Step 3: CI = P(1.1664 - 1) = 0.1664P. Step 4: SI = (P × 16 × 1)/100 = 0.16P. Step 5: Difference = CI - SI = 0.1664P - 0.16P = 0.0064P = 40. Step 6: P = 40 / 0.0064 = ₹6,250.

Question 10

A sum of ₹20,000 is invested at a certain rate per annum compound interest, compounded quarterly. If the amount becomes ₹21,550.625 after 1 year, what is the rate of interest per annum?

Accepted Answer

Step 1: Principal P = ₹20,000, Amount A = ₹21,550.625, Time T = 1 year, compounded quarterly. Step 2: For quarterly compounding, number of periods = 4. Step 3: A = P(1 + r/100)^n → 21550.625 = 20000(1 + r/400)^4. Step 4: (1 + r/400)^4 = 21550.625 / 20000 = 1.07753125. Step 5: 1 + r/400 = (1.07753125)^(1/4) = 1.01875. Step 6: r/400 = 0.01875 → r = 7.5% per annum.

Question 11

₹5,000 is invested at 10% per annum compound interest, compounded half-yearly. After how many years will the amount become ₹6,050.625?

Accepted Answer

Step 1: Principal P = ₹5,000, Amount A = ₹6,050.625, Rate R = 10% p.a., compounded half-yearly. Step 2: For half-yearly compounding, rate per half-year = 10/2 = 5%, and A = P(1 + r/100)^n. Step 3: 6050.625 = 5000(1.05)^n → (1.05)^n = 6050.625 / 5000 = 1.2101250. Step 4: Testing values: (1.05)^4 = 1.2155... ≈ 1.2101. Step 5: n = 4 half-years = 2 years.

Question 12

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded quarterly. 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 quarterly means n = 4. Step 2: Use formula A = P(1 + R/(100×4))^(4×T) = 8000(1 + 12/400)^4 = 8000(1 + 0.03)^4 = 8000(1.03)^4. Step 3: Calculate (1.03)^4 = 1.12550881. Step 4: A = 8000 × 1.12550881 = ₹9,004.07 ≈ ₹9,004.

Question 13

₹12,000 is invested at 8% per annum compound interest, compounded half-yearly. After how many years will the amount become ₹15,972?

Accepted Answer

Step 1: P = ₹12,000, A = ₹15,972, R = 8% p.a., compounded half-yearly means rate per half-year = 4%. Step 2: Use A = P(1 + r/100)^n where n is number of half-years. Step 3: 15,972 = 12,000(1.04)^n. Step 4: (1.04)^n = 15,972/12,000 = 1.331. Step 5: (1.04)^8 = 1.36857... (too high), (1.04)^7 = 1.31593... ≈ 1.331. Step 6: n = 7 half-years = 3.5 years.

Question 14

A principal amount doubles in 5 years at a certain rate of compound interest, compounded quarterly. What is the rate of interest per annum (approximately)?

Accepted Answer

Step 1: Let P = principal, A = 2P (doubles), T = 5 years, compounded quarterly means n = 20 quarters. Step 2: Use 2P = P(1 + r/400)^20, so (1 + r/400)^20 = 2. Step 3: Take 20th root: 1 + r/400 = 2^(1/20) = 1.03526. Step 4: r/400 = 0.03526, so r = 14.104% ≈ 14.1% p.a.

Question 15

The difference between compound interest and simple interest on a sum for 1 year at 16% per annum, compounded half-yearly, is ₹160. What is the principal?

Accepted Answer

Step 1: For 1 year with half-yearly compounding, there are 2 periods at 8% each. Step 2: Amount under CI = P(1.08)^2 = P × 1.1664. CI = 0.1664P. Step 3: SI for 1 year = (P × 16 × 1)/100 = 0.16P. Step 4: Difference = CI - SI = 0.1664P - 0.16P = 0.0064P. Step 5: 0.0064P = 160, so P = 160/0.0064 = ₹25,000.

Question 16

₹10,000 is invested at 20% per annum compound interest, compounded quarterly. What is the amount after 9 months?

Accepted Answer

Step 1: P = ₹10,000, R = 20% p.a., T = 9 months = 3 quarters, compounded quarterly. Step 2: Quarterly rate = 20/4 = 5%. Step 3: A = P(1 + 5/100)^3 = 10,000(1.05)^3. Step 4: (1.05)^3 = 1.157625. Step 5: A = 10,000 × 1.157625 = ₹11,576.25 ≈ ₹11,576.

Question 17

A sum becomes ₹6,655 after 2 years at 10% per annum compound interest, compounded half-yearly. What was the original principal?

Accepted Answer

Step 1: A = ₹6,655, R = 10% p.a., T = 2 years, compounded half-yearly means n = 4 half-years, rate per half-year = 5%. Step 2: Use A = P(1 + r/100)^n, so 6,655 = P(1.05)^4. Step 3: Calculate (1.05)^4 = 1.21550625. Step 4: P = 6,655 / 1.21550625 = ₹5,475.60 ≈ ₹5,476.

SSC CPO Half-Yearly / Quarterly CI

Half-Yearly / Quarterly CI— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Half-Yearly / Quarterly CI — Practice Questions

60-Second Revision — Half-Yearly / Quarterly CI