Question

Winners of the georgia lotto drawing are given the choice of receiving the winning amount divided equally over 2222 years or as a​ lump-sum cash option amount. the cash option amount is determined by discounting the annual winning payment at 44​% over 2222 years. this week the lottery is worth ​$33 million to a single winner. what would the cash option payout​ be?

Answer 1

To calculate the cash option payout, we need to discount the annual payment at a rate of 44% over 2222 years using the present value formula. The cash option payout would be approximately $2,938,624.13.

Step-by-step explanation:

To determine the cash option payout, we need to calculate the present value of the annuity. The annual payment is the total amount of the lottery prize divided by the number of years, which is $33 million / 2222 = $14,808.81. To discount this amount at a rate of 44% over 2222 years, we can use the formula:

PV = Payment / ((1 + r)^n - 1) * (1 - (1 / (1 + r))^n)

where PV is the present value, Payment is the annual payment, r is the discount rate (0.44), and n is the number of years (2222). Plugging in the values, we get:

PV = $14,808.81 / ((1 + 0.44)^2222 - 1) * (1 - (1 / (1 + 0.44))^2222)

Solving this equation gives us the cash option payout, which is approximately $2,938,624.13.

Answer 2

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