Assume the cost of attending Providence College is currently $$74,330($including tuition, fees, room & board$).$ Since college costs tend to increase at a higher rate than the overall cost of living, assume average future college cost increases of $5\%$ per year. As the parent of a new baby, your hope is your child will attend Providence College in $18$ years. As an upper$-$income family you expect your child will be "full$-$pay" $($i$.$e$.,$ there will be no financial aid$)$ and so your objective is to save enough over the $18$ years to cover your child's entire costs for the full four years of college. How much do you need to save each year if you can earn $6\mathrm{.}5\%$ on your investments?

Hint #$1-$ what will one year at PC cost in $18$ years?

Hint #$2-$ what will be the cost of Years two, three and four $($Years $19,20$ & $21)?$

Hint #$3-$ what will be the present value $($as of age $18)$ for the cost of four years at PC$?$

Hint #$4-$ what do you need to save each year over the next $18$ years to reach this goal?