A child was born today. The parents immediately established a college account for $18$ years from now. Starting one month from today, the parents will be depositing monthly payments into a relatively risky account expected to generate APR of $9\mathrm{.}6\%.$ The first monthly payment will be $$500,$ and all subsequent payments will grow by $0\mathrm{.}3\%$ every subsequent month. The last deposit will be made exactly on the child$$s $18$th birthday. How much money do you expect to be in the college account by the child$$s $18$th birthday?