Question 1

At what rate per annum will ₹6,000 become ₹7,260 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 7,260 = 6,000(1 + r/100)^2. Step 2: 7,260 ÷ 6,000 = (1 + r/100)^2, which gives 1.21 = (1 + r/100)^2. Step 3: Taking square root: 1.1 = 1 + r/100, so r/100 = 0.1, thus r = 10%. Therefore, the rate is 10% per annum.

Question 2

The compound interest on ₹4,000 at 5% per annum for 2 years is how much more than the simple interest for the same period?

Accepted Answer

Step 1: Calculate compound interest. A = 4000(1 + 5/100)^2 = 4000(1.05)^2 = 4000 × 1.1025 = ₹4,410. CI = 4410 - 4000 = ₹410. Step 2: Calculate simple interest. SI = (4000 × 5 × 2)/100 = ₹400. Step 3: Difference = CI - SI = 410 - 400 = ₹10. Therefore, CI is ₹10 more than SI.

Question 3

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

Accepted Answer

Step 1: Principal (P) = ₹6,400, Amount (A) = ₹7,056, Time (T) = 2 years, compounded half-yearly. Step 2: For half-yearly compounding, number of periods = 2 × 2 = 4. Step 3: A = 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 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% p.a.

Question 4

₹5,000 is invested at 20% per annum compound interest. What is the compound interest earned in 2 years?

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 5000(1 + 20/100)^2 = 5000(1.2)^2 = 5000 × 1.44 = ₹7,200. Step 2: Compound Interest = A − P = 7,200 − 5,000 = ₹2,200. Therefore, the compound interest is ₹2,200.

Question 5

The compound interest on ₹4,000 at 50% per annum for 2 years is:

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 4,000(1 + 50/100)^2 = 4,000(1.5)^2 = 4,000 × 2.25 = ₹9,000. Step 2: Compound Interest = A − P = 9,000 − 4,000 = ₹5,000. Therefore, the compound interest is ₹5,000.

Question 6

At what rate per annum will ₹5,000 amount to ₹6,050 in 2 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, where A = 6050, P = 5000, n = 2. Step 2: 6050 = 5000(1 + r/100)^2. Step 3: (1 + r/100)^2 = 6050/5000 = 1.21. Step 4: 1 + r/100 = √1.21 = 1.1. Step 5: r/100 = 0.1, so r = 10% per annum.

Question 7

A sum of ₹8,000 is invested at 12% per annum compound interest, compounded half-yearly. What is the compound interest earned 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, rate per half-year = 12/2 = 6%, and number of periods = 1 × 2 = 2. Step 3: Amount = P(1 + r/100)^n = 8000(1 + 6/100)^2 = 8000(1.06)^2 = 8000 × 1.1236 = ₹8,988.80. Step 4: Compound Interest = Amount − Principal = 8988.80 − 8000 = ₹988.80.

Question 8

The difference between compound interest and simple interest on a sum of ₹8,000 at 10% per annum for 2 years is:

Accepted Answer

Step 1: Calculate Simple Interest using SI = (P × R × T) / 100 = (8000 × 10 × 2) / 100 = ₹1,600. Step 2: Calculate Compound Interest using A = P(1 + R/100)^T = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680, so CI = 9680 - 8000 = ₹1,680. Step 3: Difference = CI - SI = 1680 - 1600 = ₹80.

Question 9

₹4,000 is invested at 16% per annum compound interest, compounded quarterly. What will be the amount after 9 months?

Accepted Answer

Step 1: Principal (P) = ₹4,000, Rate (R) = 16% p.a., Time (T) = 9 months = 9/12 = 0.75 years, compounded quarterly. Step 2: For quarterly compounding, rate per quarter = 16/4 = 4%, and number of periods = 0.75 × 4 = 3 quarters. Step 3: Amount = P(1 + r/100)^n = 4000(1 + 4/100)^3 = 4000(1.04)^3. Step 4: (1.04)^3 = 1.124864. Step 5: Amount = 4000 × 1.124864 = ₹4,499.46.

Question 10

₹12,000 is invested at 10% per annum compound interest, compounded quarterly. What is the difference between the amount after 6 months and after 3 months?

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 10% ÷ 4 = 2.5% per quarter. Step 2: After 3 months (1 quarter): A₁ = 12,000(1.025)^1 = 12,000 × 1.025 = ₹12,300. Step 3: After 6 months (2 quarters): A₂ = 12,000(1.025)^2 = 12,000 × 1.050625 = ₹12,607.50. Step 4: Difference = 12,607.50 − 12,300 = ₹307.50. Therefore, the answer is ₹307.50.

Question 11

At what rate per annum will ₹2,400 amount to ₹3,120 in 3 years under simple interest?

Accepted Answer

Step 1: Calculate Simple Interest: SI = Amount - Principal = 3120 - 2400 = ₹720. Step 2: Use SI = (P × R × T) / 100 to find R. Step 3: 720 = (2400 × R × 3) / 100. Step 4: 720 = 72R, so R = 10% per annum.

Question 12

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 10,404 = P(1.04)^2 = P × 1.0816. Step 4: P = 10,404 ÷ 1.0816 = ₹9,600. Therefore, the principal is ₹9,600.

Question 13

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 14

₹12,000 is invested at 10% per annum compound interest, compounded quarterly. What is the compound interest earned after 1 year?

Accepted Answer

Step 1: Principal (P) = ₹12,000, Rate (R) = 10% p.a., Time (T) = 1 year, compounded quarterly. Step 2: For quarterly compounding, rate per quarter = 10/4 = 2.5%, and number of periods = 1 × 4 = 4. Step 3: Amount = P(1 + r/100)^n = 12000(1 + 2.5/100)^4 = 12000(1.025)^4. Step 4: (1.025)^4 = 1.10381289... ≈ 1.10381. Step 5: Amount = 12000 × 1.10381 = ₹13,245.72. Step 6: Compound Interest = 13245.72 − 12000 = ₹1,245.72.

Question 15

If the simple interest on a sum for 3 years at 8% per annum is ₹2,400, what will be the compound interest on the same sum at the same rate for 2 years?

Accepted Answer

Step 1: Find principal using SI formula: SI = P×R×T/100, so 2400 = P×8×3/100 = 0.24P. Step 2: P = 2400/0.24 = ₹10,000. Step 3: Calculate CI for 2 years: A = P(1 + R/100)^T = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. Step 4: CI = 11664 - 10000 = ₹1,664.

Question 16

A sum of ₹10,000 is invested at 8% per annum. The difference between compound interest for 2 years and simple interest for 2 years is:

Accepted Answer

Step 1: Calculate Simple Interest: SI = (10000 × 8 × 2) / 100 = ₹1,600. Step 2: Calculate Compound Interest: A = 10000(1 + 8/100)² = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. CI = 11664 - 10000 = ₹1,664. Step 3: Difference = CI - SI = 1664 - 1600 = ₹64.

Question 17

₹5,000 is invested at 8% per annum compound interest, compounded quarterly. What will be the amount after 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, rate per quarter = 8/4 = 2%, and number of periods = 0.5 × 4 = 2 quarters. Step 3: Amount = P(1 + r/100)^n = 5000(1 + 2/100)^2 = 5000(1.02)^2 = 5000 × 1.0404 = ₹5,202.

Question 18

A sum of money doubles itself in 5 years at simple interest. In how many years will it triple itself at the same rate?

Accepted Answer

Step 1: If principal is P and it doubles in 5 years, then SI = P. Using SI = P×R×T/100: P = P×R×5/100, so R = 20% per annum. Step 2: For the sum to triple, total amount = 3P, so SI needed = 3P - P = 2P. Step 3: Using SI = P×R×T/100: 2P = P×20×T/100. Step 4: 2 = 0.2T, so T = 10 years.

Question 19

₹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 = 5,202 − 5,000 = ₹202. Therefore, the answer is ₹202.

Question 20

The difference between Compound Interest and Simple Interest on a sum of ₹1,000 at 10% per annum for 2 years is:

Accepted Answer

Step 1: For 2 years, the difference between CI and SI is given by the formula: Difference = P × (R/100)². Step 2: Difference = 1000 × (10/100)² = 1000 × (0.1)² = 1000 × 0.01 = ₹10. Therefore, the answer is ₹10.

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