Question 1

₹6,400 is invested at 12.5% per annum compound interest, compounded quarterly. What is the compound interest earned after 6 months?

Accepted Answer

For quarterly CI over 6 months (2 quarters): A = 6400(1 + 12.5/400)^2 = 6400(1.03125)^2 = 6406.25; CI = 6406.25 − 6400 = ₹406.25.

Question 2

A principal amount becomes ₹9,261 in 1.5 years at 20% per annum compound interest, compounded half-yearly. What was the principal?

Accepted Answer

For half-yearly CI: A = P(1 + r/200)^(2n); 9261 = P(1.10)^3 = P × 1.331; P = 9261 ÷ 1.331 = ₹7,500.

Question 3

A principal amounts to ₹9,261 in 3 years at 10% per annum compound interest. Find the principal.

Accepted Answer

Using A = P(1 + r/100)^n, we have 9261 = P(1.10)³ = P × 1.331, so P = 9261 ÷ 1.331 = ₹7,000.

Question 4

A sum of ₹1000 is invested for 2 years at 10% per annum. What is the difference between the compound interest and simple interest earned?

Accepted Answer

SI = (1000 × 10 × 2)/100 = ₹200; CI = 1000(1.1)² − 1000 = ₹210; Difference = 210 − 200 = ₹10.

Question 5

Rajesh borrowed ₹5,000 at a simple interest rate of 8% per annum. How much interest will he pay after 3 years?

Accepted Answer

Using SI = (P × R × T) / 100 = (5000 × 8 × 3) / 100 = ₹1,200.

Question 6

A sum of ₹8,000 is invested at 5% simple interest per annum. What will be the total amount after 2 years?

Accepted Answer

SI = (8000 × 5 × 2) / 100 = ₹800; Total Amount = Principal + SI = 8000 + 800 = ₹8,800.

Question 7

Priya borrowed some money at 10% simple interest per annum. If she paid ₹600 as interest after 4 years, what was the principal amount?

Accepted Answer

Using SI = (P × R × T) / 100, we get 600 = (P × 10 × 4) / 100; solving gives P = ₹1,500.

Question 8

If ₹5000 is borrowed for 3 years at 5% per annum, by how much does compound interest exceed simple interest?

Accepted Answer

SI = (5000 × 5 × 3)/100 = ₹750; CI = 5000(1.05)³ − 5000 = ₹788.125 − 5000 = ₹788.13 − 5000 ≈ ₹788.13; Difference ≈ ₹38.13 rounds to ₹37.50 (using exact calculation: 788.125 − 750 = 38.125).

Question 9

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

Accepted Answer

For 2 years, difference = P × r² / 10000; so 64 = P × 64 / 10000, giving P = ₹10000.

Question 10

At what rate of compound interest per annum will ₹2,000 become ₹2,420 in 2 years?

Accepted Answer

Using A = P(1 + r/100)^n, we have 2420 = 2000(1 + r/100)², so (1 + r/100)² = 1.21, giving r = 10%.

Question 11

A sum of ₹8,000 is invested at 10% per annum compound interest, compounded half-yearly. What will be the amount after 1 year?

Accepted Answer

For half-yearly CI: A = P(1 + r/200)^(2n) = 8000(1 + 10/200)^2 = 8000(1.05)^2 = 8000 × 1.1025 = ₹8,820.

Question 12

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

Accepted Answer

Using A = P(1 + r/100)^n, we get A = 5000(1.10)² = 5000 × 1.21 = ₹6,050.

Question 13

At what time will ₹2,400 amount to ₹3,000 at a simple interest rate of 12.5% per annum?

Accepted Answer

Interest earned = ₹3,000 − ₹2,400 = ₹600; using T = (SI × 100) / (P × R) = (600 × 100) / (2400 × 12.5) = 2 years.

Question 14

A principal amount becomes ₹4,950 in 3 years at a simple interest rate of 10% per annum. What was the principal amount?

Accepted Answer

Using A = P + SI and SI = (P × R × T) / 100, we get 4950 = P + (P × 10 × 3) / 100, solving gives P = ₹3,750.

Question 15

A principal of ₹5,000 is invested at 10% per annum compound interest for 2 years. What is the total amount after 2 years?

Accepted Answer

Using A = P(1 + r/100)^n, we get A = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050.

Question 16

If ₹2,000 amounts to ₹2,662 in 2 years at compound interest, what is the rate of interest per annum?

Accepted Answer

Using A = P(1 + r/100)^n, we get 2662 = 2000(1 + r/100)^2; solving gives r = 15% per annum.

Question 17

A sum of money doubles itself in 3 years at compound interest. In how many years will it become 8 times itself at the same rate?

Accepted Answer

If amount doubles in 3 years, it becomes 2^3 = 8 times in 3 × 3 = 9 years (since 8 = 2^3).

Question 18

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

Accepted Answer

CI on ₹4,000 = 4000(1.05)^2 - 4000 = 410; CI on ₹5,000 = 5000(1.05)^2 - 5000 = 512.50; difference = ₹102.50.

Question 19

A sum of ₹5,000 is invested at 10% per annum for 2 years. What is the difference between the compound interest and simple interest?

Accepted Answer

SI = (5000 × 10 × 2)/100 = ₹1,000; CI = 5000(1.1)² - 5000 = ₹1,050; Difference = ₹1,050 - ₹1,000 = ₹50.

Question 20

Principal ₹8,000 is lent at 5% per annum for 3 years. How much more interest is earned under compound interest compared to simple interest?

Accepted Answer

SI = (8000 × 5 × 3)/100 = ₹1,200; CI = 8000(1.05)³ - 8000 = ₹1,261.25; Difference = ₹1,261.25 - ₹1,200 = ₹61.25.

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