At the end of two years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.2000?

Sure, here's how you can calculate the compound interest:

Step 1: Identify the principal amount, the interest rate, and the time period. In this case, the principal (P) is Rs. 2000, the interest rate (r) is 10% per annum, and the time (t) is 2 years.

Step 2: Convert the interest rate from a percentage to a decimal by dividing it by 100. So, r = 10/100 = 0.1.

Step 3: Use the formula for compound interest, which is A = P (1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest. n is the number of times that interest is compounded per unit t, for example if interest is compounded yearly then n = 1, if semi-annually then n = 2, quarterly then n = 4, etc. In this case, as it is not mentioned, we assume that interest is compounded yearly, so n = 1.

Step 4: Substitute the values into the formula: A = 2000 (1 + 0.1/1)^(1*2) = 2000 (1.1)^2.

Step 5: Calculate the amount: A = 2000 * 1.21 = Rs. 2420.

Step 6: Subtract the initial principal from the calculated amount to get the compound interest. So, the compound interest is Rs. 2420 - Rs. 2000 = Rs. 420.

So, the compound interest on an amount of Rs. 2000 at the rate of 10% per annum for 2 years is Rs. 420.