A young man receives a new car and an unusual financial contract as a gift for his

Question:

A young man receives a new car and an unusual financial contract as a gift for his 16th birthday. If the car is worth $11,000 and the contract promises to pay $10,000 if he survives to his 20th birthday, estimate the financial value of the gift.

You should assume that, 

• His 1-year survival function is given by px = 0.8 + 0.006 × (x − 20)2 for ages x = 16, 17, . . . , 19,

• If paid, the $10,000 would be received on his 20th birthday,

• The effective rate of interest is 5% per annum.

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