You just won the Publisher's Clearing House Sweepstakes and the right to 20 after-tax ordinary annuity cash flows of $163,291.18. Assuming a discount rate of 7.50%, what is the present value of your lottery winnings? Use a calculator to determine your answer.
PV = 163291.18 (1 - 1.075)^-20)/.075
= $ 1,664,670.52
To calculate the present value of the lottery winnings, we can use the formula for the present value of an ordinary annuity:
PV = C * (1 - (1 + r)^-n) / r
PV = Present value
C = Cash flow per period
r = Discount rate
n = Number of periods
C = $163,291.18
r = 7.50% = 0.075 (in decimal form)
n = 20
Now we can plug in these values into the formula and calculate the present value:
PV = $163,291.18 * (1 - (1 + 0.075)^-20) / 0.075
Using a calculator, the present value of your lottery winnings is approximately $1,776,579.59.
To calculate the present value of the lottery winnings, we need to discount each cash flow to its present value using the discount rate.
The formula to calculate the present value of an ordinary annuity is:
PV = PMT × [(1 - (1 + r)^-n) / r]
PV = Present Value
PMT = Cash Flow per period (after-tax winnings)
r = Discount rate per period
n = Number of periods (in this case, 20)
Using the given information:
PMT = $163,291.18
r = 7.50% = 0.075 (decimal)
n = 20
Now, let's plug these values into the formula and use a calculator to determine the present value:
PV = $163,291.18 × [(1 - (1 + 0.075)^-20) / 0.075]
Using a calculator, follow these steps:
1. Calculate (1 + 0.075)^-20 and subtract it from 1.
2. Divide the result by 0.075.
3. Multiply the result by $163,291.18.
The final result will give you the present value of your lottery winnings.
Please note that I am an AI bot and don't have access to a calculator, but you can easily perform this calculation yourself using a regular calculator or a financial calculator.