Question 1

A sum of money doubles itself in 5 years at a certain rate of compound interest, compounded half-yearly. In how many years will it become 8 times itself at the same rate?

Accepted Answer

Step 1: Let Principal = P, and it doubles in 5 years at half-yearly compounding. So 2P = P(1 + r/100)^10 (since 5 years = 10 half-years). Step 2: (1 + r/100)^10 = 2. Step 3: Let (1 + r/100) = x. Then x^10 = 2. Step 4: We need to find time T such that 8P = P × x^(2T), where 2T is the number of half-years. So x^(2T) = 8. Step 5: Since x^10 = 2, we have (x^10)^3 = 2^3 = 8, which means x^30 = 8. Step 6: Therefore, 2T = 30, so T = 15 years.

Question 2

A sum of ₹12,800 is invested at 15% per annum compound interest, compounded half-yearly. What will be the amount after 1.5 years?

Accepted Answer

Step 1: Principal P = ₹12,800, Rate R = 15% p.a., Time T = 1.5 years = 3 half-years. Step 2: For half-yearly compounding, rate per half-year = 15/2 = 7.5% per half-year. Step 3: Amount = P(1 + r/100)^n = 12,800 × (1 + 7.5/100)^3 = 12,800 × (1.075)^3. Step 4: (1.075)^3 = 1.242297... ≈ 1.242297. Step 5: Amount = 12,800 × 1.242297 = ₹15,901.40. Rounding to nearest rupee: ₹15,901.

Question 3

₹8,000 is invested at 20% per annum compound interest, compounded quarterly. Find the compound interest earned in 9 months.

Accepted Answer

Step 1: Principal P = ₹8,000, Rate R = 20% p.a., Time T = 9 months = 3 quarters. Step 2: For quarterly compounding, rate per quarter = 20/4 = 5% per quarter. Step 3: Amount = P(1 + r/100)^n = 8,000 × (1 + 5/100)^3 = 8,000 × (1.05)^3. Step 4: (1.05)^3 = 1.157625. Step 5: Amount = 8,000 × 1.157625 = ₹9,261. Step 6: Compound Interest = Amount - Principal = 9,261 - 8,000 = ₹1,261.

Question 4

A principal becomes ₹18,522 in 2 years when invested 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, so 18,522 = P(1.05)^4. Step 4: (1.05)^4 = 1.21550625. Step 5: P = 18,522 / 1.21550625 = ₹15,240.

Question 5

₹10,000 is invested at a certain rate of compound interest, compounded quarterly. If the amount becomes ₹11,038.13 in 1 year, what is the rate of interest per annum?

Accepted Answer

Step 1: Principal P = ₹10,000, Amount A = ₹11,038.13, Time T = 1 year = 4 quarters. Step 2: For quarterly compounding, A = P(1 + r/100)^4, where r is the quarterly rate. Step 3: 11,038.13 = 10,000(1 + r/100)^4. Step 4: (1 + r/100)^4 = 1.103813. Step 5: Taking the fourth root: 1 + r/100 = (1.103813)^(1/4) = 1.025. Step 6: r/100 = 0.025, so r = 2.5% per quarter. Step 7: Annual rate = 2.5 × 4 = 10% per annum.

Question 6

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: 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. Therefore, the amount is ₹8,988.80.

Question 7

What is the compound interest on ₹5,000 at 8% per annum for 6 months, compounded half-yearly?

Accepted Answer

Step 1: Principal (P) = ₹5,000, Rate (R) = 8% p.a., Time (T) = 6 months = 0.5 years, compounded half-yearly. Step 2: For half-yearly compounding, the rate per half-year = 8/2 = 4%. Step 3: Amount after 6 months = 5000(1 + 4/100)^1 = 5000 × 1.04 = ₹5,200. Step 4: Compound Interest = 5200 - 5000 = ₹200. Therefore, the CI is ₹200.

Question 8

The difference between compound interest and simple interest on ₹6,400 for 1 year at 12.5% per annum, compounded half-yearly, is:

Accepted Answer

Step 1: Principal (P) = ₹6,400, Rate (R) = 12.5% p.a., Time (T) = 1 year, compounded half-yearly. Step 2: For CI with half-yearly compounding, half-yearly rate = 12.5/2 = 6.25%. Step 3: Amount (CI) = 6400(1 + 6.25/100)^2 = 6400(1.0625)^2 = 6400 × 1.12890625 = ₹7,225. Step 4: CI = 7225 - 6400 = ₹825. Step 5: For SI, SI = (P × R × T)/100 = (6400 × 12.5 × 1)/100 = ₹800. Step 6: Difference = CI - SI = 825 - 800 = ₹25. Therefore, the difference is ₹25.

Question 9

At what rate per annum will ₹4,000 become ₹4,410 in 1 year, 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: (1 + R/200)^2 = 4410/4000 = 1.1025. Step 5: Taking square root: 1 + R/200 = √1.1025 = 1.05. Step 6: R/200 = 0.05, so R = 10. Therefore, the rate is 10% per annum.

Question 10

A sum of ₹2,000 is invested at 20% per annum compound interest, compounded quarterly. What is the amount after 6 months?

Accepted Answer

Step 1: Principal (P) = ₹2,000, Rate (R) = 20% p.a., Time (T) = 6 months = 0.5 years, compounded quarterly. Step 2: For quarterly compounding, quarterly rate = 20/4 = 5%. Step 3: Number of quarters in 6 months = 2. Step 4: Amount = 2000(1 + 5/100)^2 = 2000(1.05)^2 = 2000 × 1.1025 = ₹2,205. Therefore, the amount after 6 months is ₹2,205.

Question 11

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, effective 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 12

₹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, effective 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 = 12484.80 - 12000 = ₹484.80.

Question 13

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, effective rate per half-year = 20/2 = 10%, and number of half-years = 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 14

₹20,000 is invested at 16% per annum compound interest, compounded quarterly. What is the difference between the amount after 6 months and 9 months?

Accepted Answer

Step 1: Principal (P) = ₹20,000, Rate (R) = 16% p.a., Compounded quarterly. Step 2: Quarterly rate = 16/4 = 4%. Step 3: Amount after 6 months (2 quarters) = 20000(1.04)^2 = 20000 × 1.0816 = ₹21,632. Step 4: Amount after 9 months (3 quarters) = 20000(1.04)^3 = 20000 × 1.124864 = ₹22,497.28. Step 5: Difference = 22497.28 - 21632 = ₹865.28.

Question 15

A sum becomes ₹2,916 in 1 year at 20% per annum compound interest, compounded half-yearly. What will be the compound interest if the same sum is invested for 2 years at the same rate and compounding frequency?

Accepted Answer

Step 1: First, find the principal. Amount after 1 year = ₹2,916, Rate = 20% p.a., half-yearly rate = 10%, periods = 2. Step 2: 2916 = P(1.1)^2 = P × 1.21, so P = 2916 / 1.21 = ₹2,400. Step 3: For 2 years with half-yearly compounding, number of periods = 4. Step 4: Amount after 2 years = 2400(1.1)^4 = 2400 × 1.4641 = ₹3,513.84. Step 5: Compound Interest = 3513.84 - 2400 = ₹1,113.84.

Question 16

₹10,000 is invested at a certain rate per annum compound interest, compounded quarterly. If the amount becomes ₹11,038.13 in 1 year, what is the rate of interest per annum?

Accepted Answer

Step 1: Principal (P) = ₹10,000, Amount (A) = ₹11,038.13, Time (T) = 1 year, Compounded quarterly. Step 2: Number of quarters = 4. Step 3: A = P(1 + r/400)^4, so 11038.13 = 10000(1 + r/400)^4. Step 4: (1 + r/400)^4 = 1.103813. Step 5: Taking fourth root: 1 + r/400 = 1.025, so r/400 = 0.025, thus r = 10% per annum.

IBPS Clerk Half-Yearly / Quarterly CI

IBPS Clerk Half-Yearly / Quarterly CI — Past Exam Questions

Half-Yearly / Quarterly CI— Rules & Concept

Key Points to Remember

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Half-Yearly / Quarterly CI — Practice Questions

60-Second Revision — Half-Yearly / Quarterly CI