Question 1

What is the compound interest on ₹8,000 at 10% per annum for 2 years, compounded annually?

Accepted Answer

Step 1: Use formula CI = P[(1 + r/100)^n - 1]. Step 2: CI = 8000[(1 + 10/100)^2 - 1] = 8000[(1.1)^2 - 1] = 8000[1.21 - 1] = 8000 × 0.21 = ₹1,680. Therefore, answer is ₹1,680.

Question 2

Rajesh invested ₹8,000 in a bank at 10% per annum compound interest, compounded annually. After 2 years, he withdrew half of the amount. The remaining amount was kept for another 1 year at the same rate. What is the final amount with Rajesh?

Accepted Answer

Step 1: Calculate amount after 2 years using CI formula A = P(1 + r/100)^n
A = 8,000 × (1 + 10/100)²
A = 8,000 × (1.1)²
A = 8,000 × 1.21
A = ₹9,680

Step 2: After 2 years, Rajesh withdraws half
Amount remaining = 9,680 ÷ 2 = ₹4,840

Step 3: This ₹4,840 is invested for 1 more year at 10% p.a.
A = 4,840 × (1 + 10/100)¹
A = 4,840 × 1.1
A = ₹5,324

Therefore, the final amount is ₹5,324

Question 3

A sum of money becomes ₹9,680 after 2 years at 10% per annum compound interest. If the same sum is invested at 12% per annum simple interest for 3 years, what will be the total interest earned?

Accepted Answer

Step 1: Find the Principal using the compound interest formula.
Using A = P(1 + r/100)^n
9,680 = P(1 + 10/100)²
9,680 = P(1.1)²
9,680 = P × 1.21
P = 9,680 ÷ 1.21 = ₹8,000

Step 2: Calculate simple interest on ₹8,000 at 12% p.a. for 3 years.
Simple Interest = (P × R × T) / 100
SI = (8,000 × 12 × 3) / 100
SI = 288,000 / 100
SI = ₹2,880

Step 3: Therefore, the total interest earned under simple interest is ₹2,880.

Question 4

₹5,000 becomes ₹6,050 in 2 years at compound interest compounded annually. What is the rate of interest per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 6050 = 5000(1 + r/100)^2. Step 2: Divide both sides by 5000: 1.21 = (1 + r/100)^2. Step 3: Take square root: 1.1 = 1 + r/100. Step 4: r/100 = 0.1, so r = 10% per annum.

Question 5

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 6

₹6,400 becomes ₹7,776 in 2 years at compound interest. What is the rate per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 7776 = 6400(1 + r/100)^2. Step 3: (1 + r/100)^2 = 7776/6400 = 1.215. Step 4: Taking square root: 1 + r/100 = 1.1. Step 5: r = 10% per annum.

Question 7

A principal amount becomes ₹10,800 after 2 years at 20% per annum compound interest. What was the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n, so 10800 = P(1 + 20/100)^2. Step 2: 10800 = P(1.2)^2 = P × 1.44. Step 3: P = 10800 ÷ 1.44 = ₹7,500. Therefore, the principal was ₹7,500.

Question 8

What is the compound interest on ₹4,000 at 5% per annum for 2 years, compounded annually?

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 4000(1 + 5/100)^2 = 4000(1.05)^2 = 4000 × 1.1025 = ₹4,410. Step 2: Compound Interest = A - P = 4410 - 4000 = ₹410.

Question 9

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 10

A principal of ₹10,000 is invested at 8% 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 = 10000(1 + 8/100)^2 = 10000(1.08)^2 = 10000 × 1.1664 = ₹11,664. Step 2: Compound Interest = A - P = 11664 - 10000 = ₹1,664.

Question 11

A sum of ₹12,000 is invested at 5% per annum compound interest compounded annually. What will be the amount after 3 years?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: A = 12000(1 + 5/100)^3 = 12000(1.05)^3. Step 3: (1.05)^3 = 1.157625. Step 4: A = 12000 × 1.157625 = ₹13,891.50.

Question 12

What is the compound interest on ₹20,000 at 10% per annum for 2 years, compounded annually?

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 20000(1 + 10/100)^2 = 20000(1.1)^2 = 20000 × 1.21 = ₹24,200. Step 2: Compound Interest = A - P = 24200 - 20000 = ₹4,200.

Question 13

At what rate per annum will ₹8,000 amount to ₹9,261 in 3 years at compound interest?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 9261 = 8000(1 + r/100)^3. Step 3: (1 + r/100)^3 = 9261/8000 = 1.157625. Step 4: Taking cube root: 1 + r/100 = 1.05. Step 5: r/100 = 0.05, so r = 5% per annum.

Question 14

₹5,000 becomes ₹6,050 in 2 years at compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. 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 15

The difference between compound interest and simple interest on ₹10,000 for 2 years at 5% per annum is ₹X. Find X.

Accepted Answer

Step 1: Simple Interest = (P × R × T)/100 = (10000 × 5 × 2)/100 = ₹1,000. Step 2: Compound Interest: A = 10000(1 + 5/100)^2 = 10000(1.05)^2 = 10000 × 1.1025 = ₹11,025. CI = 11025 - 10000 = ₹1,025. Step 3: Difference = CI - SI = 1025 - 1000 = ₹25.

Question 16

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

Question 17

A sum of money becomes ₹13,310 after 3 years at 10% per annum compound interest. What was the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 13310 = P(1 + 10/100)^3 = P(1.1)^3. Step 3: (1.1)^3 = 1.1 × 1.1 × 1.1 = 1.331. Step 4: 13310 = P × 1.331. Step 5: P = 13310/1.331 = ₹10,000.

Question 18

A bank offers 8% compound interest per annum. If ₹6,250 is deposited, what will be the total amount after 2 years? (Assume interest is compounded annually)

Accepted Answer

Step 1: Use A = P(1 + r/100)^n where P = 6250, r = 8, n = 2. Step 2: A = 6250(1 + 8/100)^2 = 6250(1.08)^2. Step 3: (1.08)^2 = 1.1664. Step 4: A = 6250 × 1.1664 = ₹7,290.

Question 19

The compound interest on ₹5,000 for 3 years at 8% per annum is how much more than the simple interest for the same period?

Accepted Answer

Step 1: Calculate CI using A = P(1 + r/100)^n = 5000(1.08)^3 = 5000 × 1.259712 = 6298.56. CI = 6298.56 − 5000 = 1298.56. Step 2: Calculate SI = (P × R × T)/100 = (5000 × 8 × 3)/100 = 1200. Step 3: Difference = 1298.56 − 1200 = 98.56 ≈ ₹99 (rounded to nearest rupee). Therefore, CI exceeds SI by approximately ₹99.

Question 20

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

Accepted Answer

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

Question 21

₹12,000 is invested at 5% per annum compound interest. After 2 years, ₹5,000 is withdrawn. The remaining amount continues to earn interest at the same rate. What is the total amount after 4 years from the initial investment?

Accepted Answer

Step 1: Amount after 2 years = 12000(1.05)^2 = 12000 × 1.1025 = 13230. Step 2: After withdrawal: 13230 − 5000 = 8230. Step 3: This amount earns interest for 2 more years (from year 2 to year 4). Amount after 4 years = 8230(1.05)^2 = 8230 × 1.1025 = 9074.775 ≈ ₹9,075. Therefore, the total amount is ₹9,075.

Question 22

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 23

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

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 the amount to become 8 times: 8P = P(1 + r/100)^n, so (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.

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60-Second Revision — Compound Interest