Nathan and Gabrielle are saving for their daughter Tanisha's college

education. Tanisha just turned $10($at t $=$ o$),$ and she will be entering

college $8$ years from now $($at t $=8.$ College tuition and expenses at

State U$.$ are currently $$14,000$ a year, but they are expected to increase at a rate of $4\mathrm{.}0\%$ a year. Tanisha 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, Nathan and Gabrielle have accumulated $$12,000$ in their

college savings account $($at t $=$ o$).$ Their long$-$run financial plan is to

add an additional $$6,000$ 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 $10\%.$ How large must the annual

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

costs?