What is the difference between the compound interests on a sum Rs. 10,000 for 1 year at 10%per annum, when compounded yearly and half-yearly

To find the difference between the compound interests when compounded yearly and half-yearly, we first need to calculate the compound interest in both cases.

1. When compounded yearly: The formula for compound interest is A = P(1 + r/n)^(nt), where: A = the amount of money accumulated after n years, including interest. P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

In this case, P = Rs. 10,000, r = 10% or 0.10, n = 1 (since it's compounded yearly), and t = 1 year.

So, A = 10000(1 + 0.10/1)^(1*1) = Rs. 11,000

The compound interest is A - P = Rs. 11,000 - Rs. 10,000 = Rs. 1,000

2. When compounded half-yearly: In this case, n = 2 (since it's compounded half-yearly).

So, A = 10000(1 + 0.10/2)^(2*1) = Rs. 11,025

The compound interest is A - P = Rs. 11,025 - Rs. 10,000 = Rs. 1,025

3. The difference between the compound interests when compounded yearly and half-yearly is Rs. 1,025 - Rs. 1,000 = Rs. 25.