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Math Help - Lotter Winnings Present Value

  1. #1
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    Lotter Winnings Present Value

    Lottery winnings are divided into equal payments given annually. Present value of winnings is worth less then the actual jackpot. Find the present value in dollars using the given conditions:
    Jackpot Amount: $17,000,000
    Interest Rate: 8%
    Equal Annual Payments: 20
    Present Value in Dollars: ?
    I have the answer from the book, but I donít understand how it was found.
    Answer: $8 345 425
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  2. #2
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    Mar 2009
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    For the answer given, You win the lottery today, and receive payment 1 one year from today, payment 2 two years from today.... Up to the 20th payment. Each payment is equal in value, so;
    17,000,000/20=\$ 850,000

    PV=850000\left[\frac{1-(1.08)^{-20}}{0.08}\right]=\$ 8,345,425

    edit; it is a bit confusing, as if I won the lottery, I would want to receive the first payment now, not have to sit and wait for a year after winning the big jackpot! But the question doesn't specify when you receive the first payment..
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