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

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). If he wanted the cash award of each of the five prizes to be $55,000 and his estate could earn 10% per year, how much would be need to fund his prizes? 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 $55,000. His heirs were surprised by his will and fought it. If they had been able to keep the amount of money you calculated in, and had invested it at 10% per year, how much would they have in 2014, 118 years after his death?

Explanation / Answer

Answer:a The total award is 5 * $55,000 = $275 , 000. To endow a perpetuity of $275,000 per year that earns 10% per year, Alfred Nobel would need

PV=C/r=$275000/0.10=$2750000

Answer:b Using the perpetuity formula when the cash ow grows, he would need

PV=C/(r-g)=$275000/(0.10-0.05)=$55,00000

Answer:c The amount from part (b) is $5,500,000. Then, today they would have

PV0=PV118/(1+r)118

=$5500000*(1.10)118

=$4214048.5826 million

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