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 ​$30000 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 ​$30000. 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?In 2014,118 years after his death ,his heir would have _ $million (round to the nearest million doller) (a)ans is 1363636 (b)2500000 i just need the ans c in 2014,118 years after his death .his heir would have_$ million.

Answer 1

a) Value of perpetuity = Annual cash flow / Rate = 30,000 x 5 / 11% = $1,363,636

b) Value of growing perpetuity = CF / (r - g) =30,000 x 5 / (11% - 5%) = $2,500,000

c) Value in 2014 = PV x (1 + r)^n = 2,500,000 x (1 + 11%)^118 = $557,252 million