Effective Annual Rate of Interest (EAR) is the actual rate of interest earned or paid on an investment or loan after considering the effect of compounding.

To calculate the effective annual rate of interest corresponding to the nominal rate of 4% per annum payable half yearly, we need to consider the compounding frequency and adjust the nominal rate accordingly.

Given:
Nominal rate = 4% per annum payable half yearly

Step 1: Determine the compounding frequency
The nominal rate is payable half yearly, which means interest is compounded twice a year.

Step 2: Convert the nominal rate to the periodic interest rate
Since the nominal rate is payable half yearly, we need to divide it by the number of compounding periods in a year. In this case, the number of compounding periods is 2.

Periodic interest rate = Nominal rate / Number of compounding periods
= 4% / 2
= 2% per half year

Step 3: Calculate the effective annual rate of interest
To calculate the effective annual rate of interest, we use the formula:

EAR = (1 + Periodic interest rate)^Number of compounding periods - 1

Substituting the values:
EAR = (1 + 2%)^2 - 1
= (1 + 0.02)^2 - 1
= (1.02)^2 - 1
= 1.0404 - 1
= 0.0404

Step 4: Convert the effective annual rate to a percentage
To express the EAR as a percentage, we multiply it by 100.

EAR = 0.0404 * 100
= 4.04%

Therefore, the effective annual rate of interest corresponding to the nominal rate of 4% per annum payable half yearly is 4.04% (option C).