Suppose that you are deciding whether to buy a $1 lottery ticket. The jackpot is

Question

Suppose that you are deciding whether to buy a $1 lottery ticket. The jackpot is 1.2 million and there is a 1/1,000,000 chance of winning. You have just learned that the jackpot will be paid in increments rather than one lump sum. At the end of each of the next 10 years, the winner will receive a payment of $120,000. The interest rate is 6% per year.

1.What is the present value of the jackpot (i.e., today)?

2.What is the expected value of buying the ticket (using present value)?

3.What decision should you make according to the expected value decision rule (using present value)?

Explanation / Answer

ANSWER:

1) I = 6%

yearly payment = $120,000

n = 10 years

pv = yearly payment(p/a,i,n)

pv = 120,000(p/a,6%,10)

pv = 120,000 * 7.36

pv = $883,200

2) expected value = chance of winning * present value

ev = (1 / 1,000,000) * 883,200

ev = $0.8832

3) since the expected value is less then the lottery ticket , therefore we will not purchase the ticket.

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