Joseph and Dalia are saving for their daughter Nylah's college education. Nylah just turned $10($at t $=0),$ and she will be entering college $8$ years from now $($at t $=8).$ College tuition and expenses at State U$.$ are currently $$12,500$ a year, but they are expected to increase at a rate of $4\mathrm{.}0\%$ a year. Nylah 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, Joseph and Dalia have accumulated $$8,000$ in their college savings account $($at t $=0).$ Their long$-$run financial plan is to add an additional $$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 Nylah's anticipated college costs?

a$.$ $$4,988\mathrm{.}48$

b$.$ $$4,618\mathrm{.}96$

c$.$ $$5,644\mathrm{.}16$

d$.$ $$6,095\mathrm{.}69$

e$.$ $$3,908\mathrm{.}99$