8. When Alfred Nobel died, he left the majority of his estate to fund 5 annual prizes starting one year after he died (the 6th one, in economics, was added later). The winner of the 2017 Nobel Prize in Economics was Richard Thaler, who studies behavioral economics and finance. (a) If Nobel wanted the cash award of each of the 5 prizes to be $25,000 and his estate could earn 7% per year, how much would he need to fund his prizes (assuming that they are awarded forever)? in year 10? year, how much would he need to leave? Assume that the award of $25,000 for (b) How much would he need to fund his prizes today if the first cash award started (c) If he wanted the value of each prize to keep up with inflation by growing 3% per each prize starts next year, as in part (a). (d) If the awards ended after 50 years (instead of lasting forever) and he wanted the value to keep up with inflation by growing at 3% per year, how much would he need to leave now? (e) His heirs were surprised by his will and fought it. If they had been able to keep the amount of money you calculated in part (c) until today, 122 years after he died, and had invested it at 7% per year, how much would they have now