You want to have $$500,000$ in savings when you retire in $45$ years. Your monthly $.$ salary is expected to grow by $0\mathrm{.}5\%$ every month between now and your retirement date and you always save a constant fraction of your salary. The interest rate is$9\%($EAR$).$

$1.$ How much do you have to save in the first month, i$.$e$.,$ one month from now?