Question

suppose you win a raffle held at a minor league baseball game 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 $2,800 today. if you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. at an interest rate of 7% per year, the winner would be better off accepting the , since that choice has the greater present value. at an interest rate of 10% 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?

Answer 1

The best choice depends on the interest rate. If the interest rate is 7% per year, the series of payments is better, but if the interest rate rises to 10%, the lump sum is more advantageous. The friend should calculate the present value using the current interest rate to decide.

Step-by-step explanation:

To decide whether to accept the lump sum or the series of payments from the baseball game raffle win, we need to calculate the present value of each option using the given interest rates. At 7% per year, the series of future payments would have a present discounted value calculated as follows: $1,000 (received today) + $1,000 / (1+0.07) + $1,000 / (1+0.07)^2. At 10% per year, for the same series of payments, we would calculate the present value as: $1,000 (received today) + $1,000 / (1+0.10) + $1,000 / (1+0.10)^2.

For the first case (7% interest), the calculation yields: $1,000 + $934.58 + $873.44 = $2,808.02, which is slightly greater than the lump sum of $2,800. Therefore, at 7%, it's better to accept the series of payments. However, at 10%, the present value of the series is $1,000 + $909.09 + $826.45 = $2,735.54, which is less than the lump sum. So, at 10%, the lump sum is the superior choice.

The most helpful advice for your friend would be to perform these present value calculations with the current interest rate to see which option has a higher present value and make a decision accordingly.