Joe and June Green are planning for their son's college education. Joe would like

his son to attend his alma mater where tuition is currently $$25,000$ per year.

Tuition costs are expected to increase by $4\%$ each year. Joe and June's son,

David, just turned $5$ years old today, September $1,2022.$ David is expected to

begin college the year in which he turns $18$ years old and will complete his

schooling in four years. College tuition must be paid at the beginning of each

school year on August $31.$

Grandma Green invested $$10,000$ in a mutual fund the day David was born. The

mutual fund investment has earned and is expected to continue to earn $8\%$ per

year. Joe and June will now begin adding to this fund every August ${31}^{st}$

$($beginning with August $31,2023$ and ending on August $31,2035)$ to ensure that

there is enough money to send David to college.

$($a$)$ How much money must Joe and June put into the college fund $($mutual fund

started by Grandma Green$)$ each of the next $13$ years if their goal is to have

enough money in the investment account by the time David begins college?

$(3$ Points$)$

$($b$)$ Joe is worried that he and June cannot afford to contribute to the college fund

right away. He suggests waiting a few years before making the equal annual

contributions. If Joe and June begin making deposits on August $31,2026,$

rather than August $31,2023,$ how much higher with their annual deposits have.

to be$?(1$ Points$)$

$($c$)$ If the mutual fund earns $7\mathrm{.}8\%$ compounded quarterly, will the amount

required in part $($a$)$ be higher or lower? Support your answer. $(1$ Points$)*$PLEASE SHOW ALL WORK SO I CAN UNDERSTAND$*$