The effective rate of interest corresponding to a nominal rate 3% p.a. payable half yearly is:

To calculate the effective rate of interest corresponding to a nominal rate of 3% per annum payable half yearly, we need to take into consideration the compounding frequency.

Since the interest is payable half yearly, it means that the interest is compounded twice a year. We can use the formula for calculating the effective annual interest rate with compounding:

Effective Interest Rate = (1 + (Nominal Interest Rate / Number of Compounding Periods)) ^ Number of Compounding Periods - 1

In this case:
Nominal Interest Rate = 3% (or 0.03)
Number of Compounding Periods = 2 (since the interest is compounded twice a year)

Plugging in these values, we can calculate the effective interest rate:

Effective Interest Rate = (1 + (0.03 / 2)) ^ 2 - 1

Simplifying the equation:

Effective Interest Rate = (1 + 0.015) ^ 2 - 1

Effective Interest Rate = (1.015) ^ 2 - 1

Calculating (1.015) ^ 2, we get:

Effective Interest Rate = 1.030225 - 1

Effective Interest Rate = 0.030225 or 3.0225%

Therefore, the effective rate of interest corresponding to a nominal rate of 3% p.a. payable half yearly is 3.0225%.