Winners of the Georgia Lotto drawing are given the choice of receiving the winning amount divided equally over 19 years or as a lump-sum cash option amount. The cash option amount is determined by discounting the annual winning payment at 8% over 19 years. This week the lottery is worth $3 million to a single winner. What would the cash option payout be?

In order to solve this, we need to use the compound interest formula to calculate the final amount after deducting the 8% for 19 years. The formula is the following...

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Now we plug in the values and solve for A

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

[tex]A = 3000000(1 + \frac{-0.08}{1} )^{(1)(19)}[/tex]

[tex]A = 3000000(0.92 )^{19}[/tex]

[tex]A = 3000000 * 0.2051[/tex]

[tex]A = 615,304.33[/tex]

Therefore, the final lump sum payout would be $615,304.33