Gabriel and Jordan are saving for their daughter Zahra's college education. Zahra just turned $)=(0,$ and she will be entering college $8$ years from now $($ att$=8).$ College tuition and expenses at State U$.$ are currently $$16,000$ a year, but they are expected to increase at a rate of $4\mathrm{.}5\%$ a year. Zahra should graduate in $4$ years$--$if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year $($at $t=8,9,10,$ and $11).$

So far, Gabriel and Jordan have accumulated $$12,000$ in their college savings account $($at $t=0).$ Their long$-$run financial plan is to add an additional $$5,500$ in each of the next $4$ years $($at $t=1,2,3,$ and $4).$ Then they plan to make $3$ equal annual contributions in each of the following years, $t=5,6,$ and $7.$ They expect their investment account to earn $8\%.$ How large must the annual payments at $t=5,6,$ and $7$ be to cover Zahra's anticipated college costs?