Jenny$$s grandparents want to start a college fund for her newborn baby. They would like to provide four years of college when their grandchild reaches age $18.$ The current cost of a high quality education at Texas State University is $$15,000$ annually and is expected to increase at a rate of $9\%$ per year indefinitely. The general inflation rate is expected to be $4\mathrm{.}5\%.$ Assuming all payments occur at the beginning of the year and they can earn $8\mathrm{.}5\%$ on their investments annually, a$.$ How much would they need to invest in a single sum to accomplish their goal? b$.$ How much would they need to invest annually? c$.$ How much would they need to invest annually if they wanted the investment to be level in real dollars?