Question

Which lottery payout scheme is better? Suppose you win a raffle held at a county fair and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $2,850 today: If you choose to collect payments over time, you recelve three paymentsi $1,000 today, $1,0001 year from today, and $1,0002 years from today. At an interest rate of 8% per year, the winner would be better off accepting the value. At an interest rate of 11% per year, the winner would be better off accepting , since it has the greater present value. A couple years after you win the raffle, you and your friend are back at the same event, This time, your friend gets lucky and wins the contest, and you both realize the payout schemes are the same as they were back when you won. They now face the decision between collecting their prize as a lump sum or as a series of payments over time. Based on your experience, which piece of advice will be most helpful to your friend?

A. The lump sum is ahways better.
B. The payments over time are always better.
C. It will depend on the interest rate; advise her to get a calculator.
D. None of these answers is good advice.

Answer 1

The decision between accepting a lump sum or payments over time in a lottery payout scheme depends on the interest rate.

Step-by-step explanation:

The question is asking which lottery payout scheme is better: accepting a lump sum immediately or receiving payments over time. To determine which option is more favorable, we need to compare the present values of the two payout schemes based on the given interest rates.

At an interest rate of 8% per year, the lump sum payout of $2,850 has a greater present value compared to the series of payments over time. This means that the winner would be better off accepting the lump sum.

However, at an interest rate of 11% per year, the series of payments over time has a greater present value compared to the lump sum. Therefore, at this interest rate, the winner would be better off choosing the payments over time.

Based on my experience, I would advise your friend that the decision between a lump sum and payments over time will depend on the interest rate. It would be helpful for her to use a calculator to compare the present values and make an informed decision.