You want to have $$400,000$ in savings when you retire in $20$ years. Your monthly salary is expected to grow by $0\mathrm{.}6\%$ every month between now and your retirement date and you always save a constant fraction of your salary. The interest rate is $7\%($EAR$).$How much do you have to save in the first month, i$.$e$.,$ one month from now?