You are planning to retire in $30$ years. You want to be able to spend $$40,000$ per year in retirement, adjusted for inflation $($so you will spend the equivalent in each year of $$40,000$ in today$$s dollars$).$ You will withdraw your retirement spending at the end of each year. So your first retirement withdrawal will be at the end of year $31.$ Assume you will live for $25$ years after retirement and the effective annual interest rate $($EAR$)$ is $8\%$ throughout.

A$.$ How much is the first retirement withdrawal at the end of year $31$ if the annual inflation rate is $2\%$ per year?