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

For yearly compounding, n = 1. So, the formula becomes A = P(1 + r)^(t).

Substituting the given values, we get A = 10000(1 + 0.10)^(1) = Rs. 11000.

So, the compound interest when compounded yearly is Rs. 11000 - Rs. 10000 = Rs. 1000.

2. When compounded half-yearly: For half-yearly compounding, n = 2. So, the formula becomes A = P(1 + r/2)^(2t).

Substituting the given values, we get A = 10000(1 + 0.10/2)^(2*1) = Rs. 11025.

So, the compound interest when compounded half-yearly is Rs. 11025 - Rs. 10000 = Rs. 1025.

Therefore, the difference between the compound interests when compounded yearly and half-yearly is Rs. 1025 - Rs. 1000 = Rs. 25.