The parents of Mr$.$ and Mrs$.$ Smith have decided to give their newborn grandchild $$392$ at the end of each month for the next $18$ years to help pay for college. If the rate of return on their college investment is $9\mathrm{.}25\%,$ how much money will their grandchild have for college?

How much money will they have saved if the $$392$ contributions start a the start of the month?