Question 1

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

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 10% ÷ 4 = 2.5% per quarter. Step 2: Number of quarters in 9 months = 9/3 = 3 quarters. Step 3: Amount = 12000(1 + 2.5/100)^3 = 12000(1.025)^3 = 12000 × 1.076890625 = ₹12,922.69 ≈ ₹12,923.

Question 2

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What is 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 3

₹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 = 6/3 = 2 quarters. 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 4

A principal amount becomes ₹10,404 in 1 year 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 1 year = 2. Step 3: Amount = P(1 + r/100)^n, so 10404 = P(1.04)^2 = P × 1.0816. Step 4: P = 10404 ÷ 1.0816 = ₹9,600.

Question 5

₹20,000 is invested at 20% per annum compound interest, compounded quarterly. What is the compound interest earned in 6 months?

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 20% ÷ 4 = 5% per quarter. Step 2: Number of quarters in 6 months = 6/3 = 2 quarters. Step 3: Amount = 20000(1 + 5/100)^2 = 20000(1.05)^2 = 20000 × 1.1025 = ₹22,050. Step 4: Compound Interest = 22050 - 20000 = ₹2,050.

Question 6

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 7

₹12,000 is lent 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 = 12000(1 + 2/100)^2 = 12000(1.02)^2 = 12000 × 1.0404 = ₹12,484.80. Step 4: Compound Interest = 12484.80 - 12000 = ₹484.80. Therefore, the answer is ₹484.80.

Question 8

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: For half-yearly compounding, rate per half-year = 20% ÷ 2 = 10% per half-year. Step 2: Number of half-years in 1 year = 2. Step 3: Amount = P(1 + 10/100)^2, so 15625 = P(1.1)^2 = P × 1.21. Step 4: P = 15625 ÷ 1.21 = ₹12,500. Therefore, the principal is ₹12,500.

Question 9

₹20,000 is invested at 16% per annum compound interest, compounded quarterly. What is the difference between the amount after 6 months and the principal?

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 16% ÷ 4 = 4% per quarter. Step 2: Number of quarters in 6 months = 2. Step 3: Amount = 20000(1 + 4/100)^2 = 20000(1.04)^2 = 20000 × 1.0816 = ₹21,632. Step 4: Difference (Compound Interest) = 21632 - 20000 = ₹1,632. Therefore, the answer is ₹1,632.

Question 10

The compound interest on ₹10,000 for 1 year at 10% per annum, compounded half-yearly, is how much more than the simple interest for the same period and rate?

Accepted Answer

Step 1: For compound interest (half-yearly): Rate per half-year = 10% ÷ 2 = 5%. Number of half-years = 2. Amount = 10000(1.05)^2 = 10000 × 1.1025 = ₹11,025. CI = 11025 - 10000 = ₹1,025. Step 2: For simple interest: SI = (10000 × 10 × 1)/100 = ₹1,000. Step 3: Difference = 1025 - 1000 = ₹25. Therefore, CI is ₹25 more than SI.

Question 11

₹12,000 is invested at 8% per annum compound interest, compounded quarterly. After 2 years, what is the total amount?

Accepted Answer

Step 1: Principal P = ₹12,000, Annual Rate R = 8%, Time T = 2 years. Step 2: For quarterly compounding, rate per quarter = 8/4 = 2% per quarter. Step 3: Number of quarters in 2 years = 2 × 4 = 8 quarters. Step 4: Amount A = P(1 + r/100)^n = 12000(1 + 2/100)^8 = 12000(1.02)^8. Step 5: (1.02)^8 = 1.171659, so A = 12000 × 1.171659 = ₹14,059.91 ≈ ₹14,060.

Question 12

A certain sum becomes ₹19,360 in 1.5 years at 20% per annum compound interest, compounded half-yearly. What was the original principal?

Accepted Answer

Step 1: Amount A = ₹19,360, Rate R = 20% p.a., Time T = 1.5 years = 3 half-years. Step 2: For half-yearly compounding, rate per half-year = 20/2 = 10% per half-year. Step 3: Using A = P(1 + r/100)^n, we have 19360 = P(1 + 10/100)^3 = P(1.1)^3. Step 4: (1.1)^3 = 1.331, so 19360 = P × 1.331. Step 5: P = 19360 / 1.331 = ₹14,545.45 ≈ ₹14,545 (or exactly ₹14,545 if we verify: 14545 × 1.331 ≈ 19,360).

Question 13

A sum of money doubles itself in 3 years at compound interest, compounded quarterly. What is the rate of interest per annum (approximately)?

Accepted Answer

Step 1: Let Principal = P, Amount = 2P (doubles). Time = 3 years = 12 quarters. Let quarterly rate = r%. Step 2: Using A = P(1 + r/100)^n, we have 2P = P(1 + r/100)^12. Step 3: 2 = (1 + r/100)^12. Step 4: Taking 12th root: (1 + r/100) = 2^(1/12) = 1.05946. Step 5: r/100 = 0.05946, so r ≈ 5.946% per quarter. Step 6: Annual rate = 5.946 × 4 ≈ 23.78% ≈ 24% (approximately). Verification: (1.0595)^12 ≈ 2.0 ✓

Question 14

₹10,000 is invested at 16% per annum compound interest, compounded half-yearly. In how many years will the amount become ₹40,000?

Accepted Answer

Step 1: Principal P = ₹10,000, Amount A = ₹40,000, Annual Rate = 16%, Half-yearly rate = 8%. Step 2: Using A = P(1 + r/100)^n, we have 40000 = 10000(1 + 8/100)^n. Step 3: 4 = (1.08)^n. Step 4: Taking logarithm: n × log(1.08) = log(4). Step 5: n = log(4) / log(1.08) = 0.60206 / 0.03342 ≈ 18 half-years. Step 6: Time in years = 18 / 2 = 9 years. Verification: (1.08)^18 = 3.996 ≈ 4 ✓

Question 15

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the compound interest earned in 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 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 (approximately ₹9,528). Step 5: Compound Interest = A - P = 9,528 - 8,000 = ₹1,528.

SSC MTS 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