A professor has two daughters that he hopes will one day go to college. Currently, in$-$state students at the local University pay about $$20,731\mathrm{.}41$ per year $($all expenses included$).$ Tuition will increase by $3\mathrm{.}88\%$ per year going forward. The professor's oldest daughter, Sam, will start college in $16$ years, while his youngest daughter, Ellie, will begin in $18$ years. The professor is saving for their college by putting money in a mutual fund that pays about $8\mathrm{.}15\%$ per year. Tuition payments are at the beginning of the year and college will take $4$ years for each girl. $($Sam$\text{'}$s first tuition payment will be in exactly $16$ years$)$

The professor has no illusion that the state lottery funded scholarship will still be around for his girls, so how much does he need to deposit each year in this mutual fund to successfully put each daughter through college. $($ASSUME that the money stays invested during college and the professor will make his last deposit in the account when Sam, the OLDEST daughter, starts college.$)$