Telani and Angel are saving for their daughter Candice's college education. Candice just turned $),$ and she will be entering college $8$ years from now $($at $t=8).$ College tuition and

expenses at State U$.$ are currently $$14,500$ a year, but they are expected to increase at a rate of $4\mathrm{.}0\%$ a year. Candice should graduate in $4$ years$--$if she takes longer or wants to go to graduate

ichool, 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, Jelani and Angel have accumulated $$8,000$ in their college savings account $($ att$=0).$ Their long$-$run financial plan is to add an additional $$4,500$ 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 $10\%.$ How large must the annual

payments at $t=5,6,$ and $7$ be to cover Candice's anticipated college costs?

a$.$ $$6,973\mathrm{.}29$

b$.$ $$6,200\mathrm{.}94$

c$.$ $$7,670\mathrm{.}62$

d$.$ $$8,164\mathrm{.}92$

e$.$ $$8,981\mathrm{.}41$