is saving for his son's college tuiton. His son is currently $11$ years old and will begin college in $7$ years. Robert has an index fund investment worth $6150$ that is arning $9\mathrm{.}5\%$ annually. Total expenses at the university of Maryland, where his son says he plans to go$,$ currently total $15600$ per year but are expected to grow at roughly $6\%$ each year. Robert plans t invest in a mutual f$-$und that will earn $11\%$ annually to make up the difference between the college expenses and his current savings. In total, robert will make seven equal investments with the first starting today and the last being made a year before his son begins college. What will be the present value of the four years of college expenses at the time that Robert's son starts college? Assume a discountt rate of $5\mathrm{.}5\%.$ Assume that the tuiton payments are made at the end of the year.