Who wants to be a millionaire?

Question

Who Wants to Be a Millionaire? 

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%.   
2. What is the amount you will receive today with the lump sum option? 
3. Which option would you select? How would you present your argument for your decision in a debate?
4. Sorry, you didn’t win the lottery, but here’s a way you can still be a millionaire! Starting at age 22, every night you take $5 out of your pocket and put it in a manila envelope (title it “Lottery Winnings”). At the end of the year, you place the money from the envelope in a stock fund with an average interest rate of 10%.  
5. How much will you have in the account when you retire at age 65? 
6. What would be different if you started this plan later in your life?

Answer 1

1.

a) 1,000,000 * (1-0.4) = $600,000

b) In order to calculate other payment option, use annuity formula: 100,000 * [(1-(1.05)^-10)]/.05 = $772,173.5

Thus, you should choose to be paid in installments versus a lump sum. https://www.annuity.org/annuities/types/lottery/ --> here's a good explanation

2)

a) Time = 65 years old - 22 years old = 43 years

r = 10%

$5 a day x 365 days a year = $1,825 a year

value at age 65 = 1825 * (1.1)^43 = $109,938.13