When Alfred Nobel 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 $48,000 and his estate could earn 11% per year, how much would he need to fund his prizes? (b) If he wanted the value of each prize to grow by 5% per year (perhaps to keep up with inflation), how much would he need to leave? Assume that the first amount was still $48,000. (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 11% per year, how much would they have in 2014, 118 years after his death?

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Kasen Tapia

3 July, 16:10

When Alfred Nobel 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 $48,000 and his estate could earn 11% per year, how much would he need to fund his prizes? (b) If he wanted the value of each prize to grow by 5% per year (perhaps to keep up with inflation), how much would he need to leave? Assume that the first amount was still $48,000. (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 11% per year, how much would they have in 2014, 118 years after his death?

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Akira · Answer 1

a)

a Annual cash flow 48,000 * 5 = 240,000

b Rate of interest 11%

c = a/b present value 2,181,818.18

Amount he need to fund his prizes = 2,181,818.18

b)

a Annual cash flow 240,000

b Rate of interest 11%

c growth rate 5%

d = a / (b-c) Present value 4,000,000

Amount required to fund prizes = 4,000,000

c)

Future value FV = PV * (1+r) ^N

Present value PV = 4,000,000

Rate of interest r = 11.00%

Number of years N = 118

Future value FV = 4000000 * (1+0.11) ^118

FV = 891,602,932,376.1

Value of amount today = 891,602,932,376.1