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: Principal (P) = ₹8,000, Rate (R) = 12% p.a., Time (T) = 1 year, Compounded half-yearly. Step 2: For half-yearly compounding, we use the formula A = P(1 + R/200)^(2T). Step 3: A = 8000(1 + 12/200)^(2×1) = 8000(1 + 0.06)^2 = 8000(1.06)^2 = 8000 × 1.1236 = ₹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: Principal (P) = ₹5,000, Rate (R) = 8% p.a., Time (T) = 6 months = 0.5 years, Compounded quarterly. Step 2: For quarterly compounding, A = P(1 + R/400)^(4T). Step 3: A = 5000(1 + 8/400)^(4×0.5) = 5000(1 + 0.02)^2 = 5000(1.02)^2 = 5000 × 1.0404 = ₹5,202. Step 4: Compound Interest = A - P = 5202 - 5000 = ₹202.

Question 3

₹10,000 is invested at 10% per annum compound interest, compounded quarterly. What is the compound interest earned in 6 months?

Accepted Answer

Step 1: Principal (P) = ₹10,000, Rate (R) = 10% p.a., Time (T) = 6 months = 0.5 years, Compounded quarterly. Step 2: For quarterly compounding, A = P(1 + R/400)^(4T). Step 3: A = 10000(1 + 10/400)^(4×0.5) = 10000(1 + 0.025)^2 = 10000(1.025)^2 = 10000 × 1.050625 = ₹10,506.25. Step 4: Compound Interest = A - P = 10506.25 - 10000 = ₹506.25.

Question 4

A sum of ₹4,000 becomes ₹4,410 in 1 year at a certain rate of compound interest, compounded half-yearly. What is the rate of interest per annum?

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)^(2×1) = 4000(1 + R/200)^2. Step 4: (1 + R/200)^2 = 4410/4000 = 1.1025. Step 5: 1 + R/200 = √1.1025 = 1.05. Step 6: R/200 = 0.05, so R = 10% per annum.

Question 5

₹2,000 is invested at 20% per annum compound interest, compounded half-yearly. In how many years will it become ₹2,662?

Accepted Answer

Step 1: Principal (P) = ₹2,000, Amount (A) = ₹2,662, Rate (R) = 20% p.a., Compounded half-yearly. Step 2: For half-yearly compounding, A = P(1 + R/200)^(2T). Step 3: 2662 = 2000(1 + 20/200)^(2T) = 2000(1.1)^(2T). Step 4: (1.1)^(2T) = 2662/2000 = 1.331. Step 5: Recognize that (1.1)^3 = 1.331. Step 6: 2T = 3, so T = 1.5 years.

Question 6

A principal amount becomes ₹14,641 in 2 years at 20% per annum compound interest, compounded half-yearly. What is the principal?

Accepted Answer

Step 1: Amount A = ₹14,641, 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, so 14641 = P(1.10)^4. Step 4: (1.10)^4 = 1.4641. Step 5: P = 14641 / 1.4641 = ₹10,000.

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: 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 8

₹5,000 is invested at 20% per annum compound interest, compounded half-yearly. What is the difference between the amount after 1 year and the simple interest for the same period?

Accepted Answer

Step 1: Principal P = ₹5,000, Rate R = 20% p.a., Time T = 1 year. Step 2: For half-yearly CI, rate per half-year = 20/2 = 10%, and number of half-years = 2. Step 3: Amount (CI) = 5000(1.10)^2 = 5000 × 1.21 = ₹6,050. Step 4: Simple Interest = (5000 × 20 × 1)/100 = ₹1,000. Step 5: Amount after 1 year with SI = 5000 + 1000 = ₹6,000. Step 6: Difference = 6,050 - 6,000 = ₹50.

Question 9

At what rate per annum will ₹6,400 amount to ₹7,056 in 1 year, if the interest is compounded half-yearly?

Accepted Answer

Step 1: Principal P = ₹6,400, Amount A = ₹7,056, Time T = 1 year, Compounded half-yearly. Step 2: For half-yearly compounding, number of periods = 2. Let rate per half-year = r%. Step 3: A = P(1 + r/100)^n, so 7056 = 6400(1 + r/100)^2. Step 4: (1 + r/100)^2 = 7056/6400 = 1.1025. Step 5: 1 + r/100 = √1.1025 = 1.05. Step 6: r/100 = 0.05, so r = 5% (per half-year). Step 7: Annual rate = 5 × 2 = 10% p.a.

Question 10

₹80,000 is invested at 12% per annum compound interest, compounded quarterly. After how many complete quarters will the amount exceed ₹1,00,000 for the first time?

Accepted Answer

Step 1: P = ₹80,000, R = 12% p.a. = 3% per quarter. We need A > 1,00,000. Step 2: A = 80,000(1.03)^n, where n is the number of quarters. Step 3: 80,000(1.03)^n > 1,00,000. (1.03)^n > 1.25. Step 4: Test values: (1.03)^8 = 1.2668, (1.03)^7 = 1.2299. Step 5: (1.03)^7 = 1.2299 < 1.25, so A₇ = 80,000 × 1.2299 = ₹98,392 < ₹1,00,000. Step 6: (1.03)^8 = 1.2668 > 1.25, so A₈ = 80,000 × 1.2668 = ₹1,01,344 > ₹1,00,000. Step 7: The amount exceeds ₹1,00,000 after 8 quarters.

Question 11

₹50,000 becomes ₹72,900 in 2 years when invested at a certain rate of compound interest, compounded half-yearly. What is the rate of interest per annum?

Accepted Answer

Step 1: P = ₹50,000, A = ₹72,900, T = 2 years. For half-yearly compounding, n = 4 half-years. Step 2: A = P(1 + r/100)^n, where r is the half-yearly rate. Step 3: 72,900 = 50,000(1 + r/100)^4. Step 4: (1 + r/100)^4 = 72,900/50,000 = 1.458. Step 5: (1 + r/100)^2 = √1.458 = 1.2075. Step 6: 1 + r/100 = √1.2075 = 1.099 ≈ 1.10. Step 7: r/100 = 0.10, so r = 10% per half-year. Step 8: Annual rate = 10 × 2 = 20% p.a.

Question 12

A principal amount doubles in 3 years at a certain rate of compound interest, compounded quarterly. In how many years will it become 8 times the original amount at the same rate?

Accepted Answer

Step 1: Let P be the principal. After 3 years (12 quarters), A = 2P. Step 2: 2P = P(1 + r/100)^12, so (1 + r/100)^12 = 2. Step 3: We need to find T such that 8P = P(1 + r/100)^(4T), i.e., (1 + r/100)^(4T) = 8. Step 4: Since (1 + r/100)^12 = 2, we have [(1 + r/100)^12]^3 = 2^3 = 8. Step 5: (1 + r/100)^36 = 8. Step 6: 4T = 36, so T = 9 years.

Question 13

A sum of ₹1,00,000 is invested at 16% per annum compound interest, compounded half-yearly. What is the difference between the compound interest for the 2nd and 3rd half-years?

Accepted Answer

Step 1: P = ₹1,00,000, R = 16% p.a. = 8% per half-year. Step 2: After 1st half-year: A₁ = 1,00,000(1.08) = ₹1,08,000. Step 3: After 2nd half-year: A₂ = 1,08,000(1.08) = ₹1,16,640. CI for 2nd half-year = 1,16,640 - 1,08,000 = ₹8,640. Step 4: After 3rd half-year: A₃ = 1,16,640(1.08) = ₹1,25,971.20. CI for 3rd half-year = 1,25,971.20 - 1,16,640 = ₹9,331.20. Step 5: Difference = 9,331.20 - 8,640 = ₹691.20.

Question 14

A sum of ₹40,000 is invested at 20% per annum compound interest, compounded quarterly. What is the compound interest earned in 1.5 years?

Accepted Answer

Step 1: Principal P = ₹40,000, Rate R = 20% p.a., Time T = 1.5 years = 6 quarters. Step 2: For quarterly CI, effective rate per quarter = 20/4 = 5% per quarter. Step 3: Amount A = P(1 + r/100)^n = 40,000(1 + 5/100)^6 = 40,000(1.05)^6. Step 4: (1.05)^6 = 1.3401. Step 5: A = 40,000 × 1.3401 = ₹53,604. Step 6: CI = A - P = 53,604 - 40,000 = ₹13,604.

Question 15

A certain sum becomes ₹1,21,000 in 2 years and ₹1,33,100 in 3 years at compound interest, compounded annually. What is the principal?

Accepted Answer

Step 1: Let P be the principal and r be the rate. After 2 years: A₂ = P(1 + r/100)^2 = 1,21,000. After 3 years: A₃ = P(1 + r/100)^3 = 1,33,100. Step 2: Divide A₃ by A₂: [P(1 + r/100)^3] / [P(1 + r/100)^2] = 1,33,100 / 1,21,000. Step 3: (1 + r/100) = 1,33,100 / 1,21,000 = 1.10. Step 4: r = 10% p.a. Step 5: P(1.10)^2 = 1,21,000. P × 1.21 = 1,21,000. P = ₹1,00,000.

SBI PO 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