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When Alfred Nobel died, he left the majority of his estate to fund five prizes, each to be awarded annually in perpetulty 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 8% 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 amount was still $45,000. 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 in 2008 , 112 years after he died? a. He would need $2812500 to fund his prizes. (Round to the nearest dollar.) b. He would need $4500000 to fund his prizes. (Round to the nearest dollar.) c. His heirs would have $ million. (Round to the nearest million.)