When Alfred Nobel died, he left most of his estate to fund five prizes, each to be awarded annually in perpetuity starting one year after he died (the sixth one, in economics, was added later).

a) If he wanted the cash award of each of the five prizes to be $45,000 and his estate could earn 5% per year, how much would he need to fund his prizes?

b) If he wanted the value of each prize to grow by 3% per year (perhaps to keep up with inflation), how much would he need to leave? Assume that the first prize paid was still $45,000