Question

When an inventor​ 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 ​$35,000 and his estate could earn 9​% per​ year, how much would he need to fund his​ prizes?

b. If he wanted the value of each prize to grow by 4​% per year​ (perhaps to keep up with​ inflation), how much would he need to​ leave? Assume that the first amount was still ​$35,000.

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 9​% per​ year, how much would they have 13 years after he​ died?

Answer 1

Please like the answer or comment if you need any clarifications

A. Discounting the value using perpetuity would be by using formula
=(Prize Amount * Number of Prizes) / Interest Rate
= ($35,000*5) / 0.09 =$ 19,44,444.44

B. Amount will be calculated using Growth Model where we will use below formula:
= (Prize in first year) / (Interest Rate - Growth Rate)
=($35,000*5) / (9%-4%)
=$3,500,000

C. Amount calculated in Part B X ((100%+Interest Rate ) ^ Number of years)
=$3,500,000 X(1.09^13)
= $10,730,316.14