1. How do you work the problem in the description using present and future value?

Question

1. You just won $1 million dollars in the lottery! They offer you two options for your winnings: a lump sum payment right now, or $100,000 a year over the next 10 years. Current 10-year interest rates are at 5%, and the current tax on lottery winnings is 40%. o What is the amount you will receive today with the lump sum option? o Which option would you select? How would you present your argument for your decision in a debate?

Answer 1

Since the tax rates are 40%, the $100,000 per year is really $60,000 per year.

We are looking for the present value of a 10 year annuity with payments of $60,000 at an interest rate of 5%

 

The formula is Present Value = PMT * (1/i)*(1-1/(1+i)^n = $60,000(1/.05)(1-1/1.05^10) = $463,304.10

 

The lump sum after tax payment is $463,304

 

The decision will be to take the lump sum payment if you can earn above 5% on the money. For example, if you can earn 6%, the annual payments increase from $60,000 to $62,948.18