Jamir and alyssa are saving for their daughter taylors college education. Taylor just turned $10($at t$=0),$ and ahe will be entering college $8$ years from now at $($t$=8).$ College tuition and expenses at State U are currently $16000$ a year, but they are expected to increase at a rate of $2\mathrm{.}5\%$ a year. Taylor 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 jamir and alyssa have accumulated $17000$ in college savings account $($at t$=0).$ Their long$-$run financial plan is to add an additional $5000$ in each of the mext $4$ years. Then they plan to make $3$ equal annual contributions in each of the following years t$=5,6,7.$ They expect their investment account to earn $9\%.$ How large must the annual payment at t$=5,6,7$ to cover taylors anticipated college?