When Alfred Nobel died, he left the majority of his estate to fund five prizes t

Question

When Alfred Nobel died, he left the majority of his estate to fund five prizes to be made annually 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 $60,000 and his estate could earn 10% per year, how much would he need to fund his prizes? b. If he wanted the value of each prize to grow by 6% per year (perhaps to keep up with inflation), how much would he need to leave? a. To fund the five prizes, he would need $. (Round to the nearest cent.) b. He would need to leave $[ ]. (?Round to he nearest cent.)

Explanation / Answer

Solution-a

The total award is 5*$60, 000 = $300,000

Endow a perpetuity of $300,000 per year that earns 10% per year

So, Alfred Nobel would need:

PV = C /r

PV = $300,000 / 0.10

PV = $3,000,000

To fund the five prizes, he would need $3,000,000

Solution-b

Using the growing annuity formula, he would need:

PV = C / r-g (1- (1+r) / (1+g)t )

PV = $300,000 / 0.10 - 0.06 (1- (1+ 0.06) (1+0.10)1)

PV = $272,727.28

He would need to leave $272,727.28

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