You have a winning $1,000,000 ticket in the state lottery. You hurry down to the

Question

You have a winning $1,000,000 ticket in the state lottery. You hurry down to the lottery office and ask for your million dollars. Somewhat surprised you are told that your winnings will be paid out over 20 years at $50,000 per year.You complain that your health is not good, and you may not live 20 years to collect. As an option you are told an immediate lump sum settlement can be paid. Assuming an interest rate of 5%, what is the amount of lump sum settlement that should be paid?

Hint: This problem is the same as what amount must be deposited in a bank so as to withdraw $50,000 a year for 20 years, and the account will be 0 at the end of the 20 years.

Do you think the lottery is guilty of false advertising?

Explanation / Answer

The present value of annuity of $50000 received every for 20 years at an discount rate of 5% =

= $50000 * PVIFA(5%,20years) = $50000 * 12.462 = $623100.

the amount of lump sum settlement that should be paid = $623100

Yes, the lottery is guilty of false advertising because they have concelled the fact that winnings lottery will be paid out over 20 years at $50,000 per year.

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