Suppose last year the race had $4,500$ contestants each paying $$50$ to enter. Suppose the fixed$-$

cost for running the race is $$50,000($and will be constant over time$)$ and the variable cost will

remain flat at $$3\mathrm{.}75$ per racer. Organizers expect the race grow $3\%$ annually. Looking at the

next five years, what charitable award amount could race organizers promise $($in present value

terms$)$ if the discount rate were $7\mathrm{.}5\%?$

What is the value if we assume the race will occur each year under these terms perpetually