You are the proud winner of the multistate Sour Ball Lottery. You're to receive $2,000,000 at the end of each year for the next 20 years. While the Lottery Commission refers to this as a $40,000,000 jackpot, if you choose the "cash option" they will give you much less than that; you can receive a lump sum payment today equal to the present value of the ordinary annuity instead of the 20 annual payments. If the discount rate that the Lottery Commission uses to determine the lump sum payoff is 7%, what is your pay-off if you select the cash option?

Question

Business

Lexie Orozco

20 January, 10:11

You are the proud winner of the multistate Sour Ball Lottery. You're to receive $2,000,000 at the end of each year for the next 20 years. While the Lottery Commission refers to this as a $40,000,000 jackpot, if you choose the "cash option" they will give you much less than that; you can receive a lump sum payment today equal to the present value of the ordinary annuity instead of the 20 annual payments. If the discount rate that the Lottery Commission uses to determine the lump sum payoff is 7%, what is your pay-off if you select the cash option?

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Answers (1)

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Shania Pennington · Answer 1

PV = $21,188,028.49

Explanation:

Giving the following information:

Cash flow = $2,000,000 at the end of each year for the next 20 years.

Interest rate = 7%

We need to calculate the present value of the annuity. First, we need to calculate the future value of the annuity:

FV = {A*[ (1+i) ^n-1]}/i

A = cash flow

FV = {2,00,000*[ (1.07^20) - 1]/0.07

FV = $81,990,984.64

Now, we can calculate the present value:

PV = FV / (1+i) ^n

PV = 81,990,984.64 / (1.07^20)

PV = $21,188,028.49