When an inventor? died, he left the majority of his estate to fund five? prizes, each to be awarded annually in perpetuity starting one year after he died. a. If he wanted the cash award of each of the five prizes to be ?$50 comma 000 and his estate could earn 8?% per? year, how much would he need to fund his? prizes? b. If he wanted the value of each prize to grow by 4?% per year? (perhaps to keep up with? inflation), how much would he need to? leave? Assume that the first amount was still ?$50 comma 000. c. His heirs were surprised by his will and fought it. If they had been able to keep the amount of money you calculated in? (b), and had invested it at 8?% per? year, how much would they have 17 years after he? died?