Question

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​ (the sixth​ one, in​ economics, was added​ later). a. If he wanted the cash award of each of the five prizes to be ​$42 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 2​% per year​ (perhaps to keep up with​ inflation), how much would he need to​ leave? Assume that the first amount was still ​$42 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 in​ 2014, 118 years after his​ death?

Answer 1

Solution

Amount of each cash prize=42000

Amount of 5 prizes=42000*5=210000

a. If he wanted to give 210000 as perpetutiy

PV of perpetuity= Perpetuity amount/Intrest rate

=210000/.08=2625000(Money needed to fund the prizes)

b. If he wanted the prizes to grow by 2%

PV of perpetuity= First payment of perpetuity/(Intrest rate-growth rate)

=210000/(.08-.02)=3500000(Money needed to fund the prizes)

c. If the fund 3500000 is invested for 118 years @8%

Amount after 118 years will be= Amount invested*(1+r)^n

Here

r=intrest rate=8%

n=number of periods=118

Amount after 118 years will be=3500000*(1+.08)^118=30766011058.620

If you are satisfied with the answer,please give a thumbs up