To calculate the present value of the lottery winnings, we need to discount each future payment back to the present value.
The formula to calculate the present value of an annuity is:
PV = C / (1 + r)^n
Where:
PV = Present value
C = Cash flow per period
r = Interest rate per period
n = Number of periods
In this case, the cash flow per period is $200,000, the interest rate is 7% (or 0.07 in decimal form), and the number of periods is 3.
Let's calculate the present value:
PV = $200,000 / (1 + 0.07)^1 + $200,000 / (1 + 0.07)^2 + $200,000 / (1 + 0.07)^3
Now, let's solve this equation step by step:
PV = $200,000 / 1.07^1 + $200,000 / 1.07^2 + $200,000 / 1.07^3
PV = $200,000 / 1.07 + $200,000 / (1.07)^2 + $200,000 / (1.07)^3
PV = $186,915.89 + $174,863.39 + $163,851.86
PV = $525,631.14
Therefore, the present value of this lottery is approximately $525,631.14.