Question

Who Wants to Be a Millionaire? 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%. What is the amount you will receive today with the lump sum option? Which option would you select? How would you present your argument for your decision in a debate? 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%. How much will you have in the account when you retire at age 65? What would be different if you started this plan later in your life? Your submitted assignment must include the following: Submit a double-spaced Word document of 1–2 pages t

Answer 1

Winning a lottery,

a) Lump sum option = $600,000;

b) Yearly option = $772,173.49

Not winning a lottery,

Grand savings will be = $86,322.50

Step-by-step explanation:

Requirement 1) Winning a Lottery -

a) If I take the lump sum option, I will get the tax-deducted amount. Since the tax rate is 40%, I will get -

= $1,000,000 x (1 - 0.40)

= $1,000,000 x 0.60

= $600,000

b) If I choose the second option, I might get -

PV = PMT x [{1 - (1+r)^(-n)}/r]

PV = $100,000 x [{1 - (1+0.05)^(-10)}/0.05]

PV = $100,000 x 7.7217

PV = $772,173.49

From the above calculation, I will accept the yearly payment as it provides more earnings than the lump sum amount.

Requirement 2) Not Winning a Lottery -

Every day earnings = $5

Yearly earnings = $5 x 365 = $1,825

If I retire at the age of 65 years, therefore, I will save for (65 - 22) = 43 years.

Therefore, the savings will be = 43 x $1,825 = $78,475

If the savings for the average interest rate 10%, the total will be =

$78,475 x (1 + 0.10) = $86,322.50

Therefore, I will have $86,322.50 when I retire at age 65.

Requirement 3) If I started this plan later in my life, I would lose savings for how many years I wait for the started savings. For example, If I began at the age of 30, I would lose eight years of savings. Therefore, I would lose 7*$1,825 = $12,775 savings. I would also lose the grand savings of $12,775 x (1 + 0.10) = $14,052.50.

Therefore, for each year's of delay would lose $1,825.00 amounts.