What is the compound interest (approximately) on Rs. 10,000 at 12% per annum for 2 years, compounded half-yearly?

To calculate compound interest compounded half-yearly, we use the formula:

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 = 12% or 0.12 (in decimal), n = 2 (since it's compounded half-yearly), and t = 2 years.

So, the formula becomes:

A = 10000 (1 + 0.12/2)^(2*2)

Let's calculate it step by step:

1. Calculate r/n: 0.12/2 = 0.06
2. Add 1 to the above result: 1 + 0.06 = 1.06
3. Raise the result to the power nt: 1.06^(2*2) = 1.06^4 = 1.262476
4. Multiply the above result with the principal amount: 10000 * 1.262476 = Rs. 12624.76

So, the total amount after 2 years would be approximately Rs. 12624.76

To find the compound interest, we subtract the principal from the total amount:

Compound Interest = Total Amount - Principal = Rs. 12624.76 - Rs. 10000 = Rs. 2624.76

So, the compound interest on Rs. 10,000 at 12% per annum for 2 years, compounded half-yearly, is approximately Rs. 2624.76.