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Suppose that you win the Lottery. The stated prize is $402 million. If you agree to...

Suppose that you win the Lottery. The stated prize is $402 million. If you agree to take the payout over 30 years in the form of an annuity due, then each payment equals the stated prize divided by 30. The first payment will be made to you immediately, and the remaining 29 future payments will be paid out annually (beginning one year from today). Alternatively, you can take the lump sum payout. This payout is calculated as the present value of the annuity due described above. The annual rate of return used in this calculation is the estimated rate of return that the sponsor (the Multi-State Lottery Association, or MUSL) forecasts that it can earn by investing the funds necessary to support the annuity payout. For the sake of this example, suppose that the projected annual rate of return is 4.71% per year. What is the lump sum payout (before taxes, of course)

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Expert Solution

Lumpsum Payment =  PV of Annuity + Today's Installment = P*[1-{(1+i)^-n}]/i + Today's Installment

Where, P = Annuity = 402000000/30 = 13400000, i = Interest Rate = 0.0471, n = Number of Periods = 30-1 = 29

Therefore, Present Value = PV of next 29 Installments + Today’s Installment = [13400000*{1-((1+0.0471)^-29)}/0.0471]+13400000 = 209610469.66+13400000= $223010469.66 = $223.01 Million

jeff jeffy answered 2 years ago
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