Jaylen and Diamond are saving for their daughter Cadence's college education. Cadence just turned $10(at=0),$ and she

will be entering college $8$ years from now $(at=8).$ College tuition and expenses at State $U.$ are currently $$13,000$ a year,

but they are expected to increase at a rate of $3\mathrm{.}0\%$ a year. Cadence 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, Jaylen and Diamond have accumulated $$12,000$ in their college savings account $(att=0).$ Their long$-$run financial

plan is to add an additional $$4,000$ 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 $9\%.$ How large

must the annual payments at $t=5,6,$ and $7$ be to cover Cadence's anticipated college costs?

a$.$ $$3,324\mathrm{.}42$

b$.$ $$4,199\mathrm{.}15$

c$.$ $$3,049\mathrm{.}93$

d$.$ $$4,577\mathrm{.}07$

e$.$ $$2,555\mathrm{.}71$