On your child's $1$ st birthday, you open an account to fund his college education. You deposit $$3,600$ to open the account. Each year, on his birthday, you make another deposit. Each subsequent deposit is $8\mathrm{.}5\%$ larger than the previous. The account pays interest at $5\frac{\%}{?}$ year compounded annually. How much money is in the account immediately after the deposit on his $18$ th birthday? $

Carry all interim calculations to $5$ decimal places and then round your final answer to the nearest dollar. The tolerance is $+-50.$