Question 1

At what rate per annum will ₹8,000 amount to ₹9,680 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 9680 = 8000(1 + r/100)^2. Step 2: (1 + r/100)^2 = 9680/8000 = 1.21. Step 3: 1 + r/100 = √1.21 = 1.1. Step 4: r/100 = 0.1, so r = 10% per annum.

Question 2

A sum of ₹5,000 is invested at 10% per annum compound interest. What will be the amount after 2 years?

Accepted Answer

Step 1: Use the compound interest formula A = P(1 + r/100)^n. Step 2: A = 5000(1 + 10/100)^2 = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050. Therefore, the amount after 2 years is ₹6,050.

Question 3

A principal amount becomes ₹12,100 in 2 years at 10% per annum compound interest. What is the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 12100 = P(1 + 10/100)^2. Step 2: 12100 = P(1.1)^2 = P × 1.21. Step 3: P = 12100/1.21 = ₹10,000.

Question 4

What is the compound interest on ₹6,000 at 5% per annum for 2 years?

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 6000(1 + 5/100)^2 = 6000(1.05)^2 = 6000 × 1.1025 = ₹6,615. Step 2: Compound Interest = A - P = 6615 - 6000 = ₹615.

Question 5

A sum of money doubles itself in 5 years at compound interest. In how many years will it become 8 times at the same rate?

Accepted Answer

Step 1: If principal P becomes 2P in 5 years, then (1 + r/100)^5 = 2. Step 2: We need to find n such that (1 + r/100)^n = 8. Step 3: Note that 8 = 2^3, so (1 + r/100)^n = [(1 + r/100)^5]^3 = (1 + r/100)^15. Step 4: Therefore, n = 15 years.

Question 6

The difference between compound interest and simple interest on ₹4,000 for 2 years at 5% per annum is:

Accepted Answer

Step 1: Simple Interest = (4000 × 5 × 2)/100 = ₹400. Step 2: Amount at CI = 4000(1 + 5/100)^2 = 4000(1.05)^2 = 4000 × 1.1025 = ₹4,410. Step 3: Compound Interest = 4410 - 4000 = ₹410. Step 4: Difference = CI - SI = 410 - 400 = ₹10.

Question 7

A sum of ₹8,000 is invested at 10% per annum compound interest. What will be the amount after 2 years?

Accepted Answer

Step 1: Use the compound interest formula A = P(1 + r/100)^n. Step 2: A = 8000(1 + 10/100)^2 = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680. Therefore, the amount after 2 years is ₹9,680.

Question 8

The difference between compound interest and simple interest on ₹8,000 for 2 years at 10% per annum is ₹___.

Accepted Answer

Step 1: Simple Interest = (P × R × T) / 100 = (8000 × 10 × 2) / 100 = ₹1,600. Step 2: Compound Interest = P[(1 + r/100)^n - 1] = 8000[(1.1)^2 - 1] = 8000[1.21 - 1] = 8000 × 0.21 = ₹1,680. Step 3: Difference = CI - SI = 1680 - 1600 = ₹80. Therefore, the difference is ₹80.

Question 9

Rajesh invests ₹5,000 at 12% per annum compound interest compounded half-yearly. What is the amount after 1 year?

Accepted Answer

Step 1: When compounded half-yearly, the rate per half-year = 12/2 = 6% and number of periods n = 2. Step 2: A = P(1 + r/100)^n = 5000(1 + 6/100)^2 = 5000(1.06)^2 = 5000 × 1.1236 = ₹5,618. Therefore, the amount is ₹5,618.

Question 10

The compound interest on ₹10,000 at 5% per annum for 2 years is how much less than the compound interest on ₹12,000 at 5% per annum for 2 years?

Accepted Answer

Step 1: CI on ₹10,000 = 10000[(1.05)^2 - 1] = 10000[1.1025 - 1] = 10000 × 0.1025 = ₹1,025. Step 2: CI on ₹12,000 = 12000[(1.05)^2 - 1] = 12000 × 0.1025 = ₹1,230. Step 3: Difference = 1230 - 1025 = ₹205. Therefore, the first CI is ₹205 less.

Question 11

A principal becomes ₹14,400 in 2 years at 20% per annum compound interest. What is the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 14400 = P(1 + 20/100)^2 = P(1.2)^2 = P × 1.44. Step 3: P = 14400 / 1.44 = ₹10,000. Therefore, the principal is ₹10,000.

Question 12

A sum of money becomes ₹9,680 after 2 years at 10% per annum compound interest. What was the principal amount?

Accepted Answer

Step 1: Use the compound interest formula A = P(1 + r/100)^n. Step 2: Substitute values: 9680 = P(1 + 10/100)^2 = P(1.1)^2 = P(1.21). Step 3: Solve for P: P = 9680 ÷ 1.21 = 8000. Therefore, the principal is ₹8,000.

Question 13

A principal amount doubles itself in 5 years at compound interest. In how many years will it become 8 times itself at the same rate?

Accepted Answer

Step 1: If P doubles in 5 years, then 2P = P(1 + r/100)^5, so (1 + r/100)^5 = 2. Step 2: For amount to become 8P: 8P = P(1 + r/100)^n, so (1 + r/100)^n = 8. Step 3: Since 8 = 2³, we have [(1 + r/100)^5]^3 = (1 + r/100)^15 = 8. Step 4: Therefore n = 15 years.

Question 14

The difference between compound interest and simple interest on a sum for 2 years at 8% per annum is ₹64. What is the principal?

Accepted Answer

Step 1: For 2 years, CI - SI = P × r² / 100². Step 2: Substitute: 64 = P × 8² / 100² = P × 64 / 10000. Step 3: Solve for P: P = 64 × 10000 / 64 = 10,000. Therefore, the principal is ₹10,000.

Question 15

A sum becomes ₹2,420 in 2 years and ₹2,662 in 3 years at compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Amount after 2 years: A₂ = 2,420. Amount after 3 years: A₃ = 2,662. Step 2: The interest earned in the 3rd year = 2,662 - 2,420 = 242. Step 3: This interest is earned on the principal of 2,420 (the amount at end of year 2). Step 4: Rate = (242 / 2,420) × 100 = 10% per annum.

IBPS Clerk Compound Interest

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