Winners of the Georgia Lotto drawing are given the choice of receiving the winning amount divided equally over 2222 years or as a lump-sum cash option amount. The cash option amount is determined by discounting the annual winning payment at 66 % over 2222 years. This week the lottery is worth $1919 million to a single winner. What would the cash option payout be?

0 i. e. zero

Explanation:

The formula we will us to calculate the cash option payout for formula for calculating the present value (PV).

Present value (PV) can simply be described as the current value of a future amount or future stream of cash flows given a certain return rate.

To calculate the PV of a future cash flow, we will discount it by using the discount rate.

The formula is provided as follows:

PV = FV / (1 + r) ^n ... (1)

Where,

PV = Present Value = ?

r = discount rate = 66% = 0.66

FV = annual future value = $863,636.36

n = number of years = 2222 years

Note that the annual future value calculated by diving the $1919 million by 2222 years and this give us $863,636.36 (i. e. 1,919,000,000 : 2222 = $863,636.36).

Substituting the figures above into equation (1), we obtain:

PV = 863,636.36 / (1 + 0.66) ^2222

= 863,636.36 / (1.66) ^2222

= 863,636.36/∞

PV = 0

This is because, the division of any number by infinity is equal to zero. And if we multiply by zero by 2222, it will still give us zero PV.

Therefore, the cash option payout will be zero. It is better the winner take the option of collecting $863,636.36.