Question $5,6,$ and $7$

You prepare yourself for the high costs of college tuition for your daughter. You expect her to

start college in $18$ years $(t=18)$ and expect her to be in college for $4$ years. Today's tuition is

$$28,000$ per year and tuition has increased historically at $6\%$ per year and is expected to continue

to grow at the same rate in the future.

You want to make an initial deposit of $$15,000$ in a savings account, which is guaranteed to return

$1\mathrm{.}982\%$ per year $($APR$)$ in interest, compounded monthly. Each year, until your daughter starts

college you plan on depositing an equal amount that is precisely gets you to to make the tuition

payments during the time your daughter attends college. Hence, your first deposit $($not including

the initial $$15,000)$ takes place at $t=1$ and your final deposit takes place at $t=17.$ Your first tuition

payment occurs in $t=18.$

If you could write one single check to payoff all the tuition at the time your daughter starts college

$(t=18),$ what is the correct amount for this check? $[$Question $5]$

Assuming you could pay all the tuition right now for your daughter's college education with a

$$350,000$ check, would you do this $($all else equal$)?$ Explain your answer $[$Question $6]$

Following your original plan to make yearly equal deposits in years $1$ through $17,$ which will pay

exactly for your daughter's college education, what is the amount of the deposit each year?

$[$Question $7]$