You are looking to save for retirement. You just turned $25$ years old and have $$10,000$ to deposit

today. Starting next month, you will make deposits of $$500$ per month for the next $30$ years $($a total of $360$ monthly

deposits with your last deposit being on your $55$th birthday$).$ You will then leave your money invested for $5$ more years

until your $60$th birthday. On your $60$th birthday you want to buy an annuity that will provide you monthly payments

$($starting in one month$)$ for the next $20$ years $(240$ payments$).$ At the end of these payments, you want to have $$400,000$

in your account at age $80.$ How much can you withdraw each month in retirement if your interest rate is $7\mathrm{.}2\%$ APR

compounded monthly $(0\mathrm{.}6\%$ per month$)?$