Assume next month you begin saving $$500$ per month for retirement in an account that earns a return of $6\%$ compounded monthly. You plan to retire in $30$ years and expect to live for $20$ years after retirement. Upon retirement, you will shift your savings into an account that earns a rate of $3\%$ compounded monthly. Calculate how much you can withdraw each year during retirement, assuming you withdraw the same amount annually. Please show all work.