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On January 1 you win $50,000,000 in the state lottery. The $50,000,000 prize will be paid in equal installments of $6,250,000 over eight years. The payments will be made on December 31 of each year, beginning on December 31 of this year. If the current interest rate is 12%, determine the present value of your winnings. Use the present value tables in Exhibit 7. Round to the nearest whole dollar.

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Answer:

Present Value = $31,047,749

Explanation:

The question is describing an ordinary annuity i.e equal payments made in equal intervals over eight years, with the 1st payment received at the end of year 1 and the last payment being received at the end of the 8th year.

[tex]PV = \frac{PMT[1-(1+i)^{-n} ] }{i}[/tex]

where PMT is the periodic payment

               i is the required rate of return per period

              n is the number of periods

[tex]PV = \frac{$6,250,000[1-(1+0.12)^{-8}]}{0.12} [/tex] = $31,047,749.

Alternatively, use the present value tables to calculate the present value of the winnings as follows:

Year Cash flow PV factor at 12% Present value

1             6,250,000.00       0.8929                  5,580,357.14  

2            6,250,000.00       0.7972                   4,982,461.73  

3            6,250,000.00       0.7118                    4,448,626.55  

4            6,250,000.00       0.6355                  3,971,987.99  

5           6,250,000.00        0.5674                  3, 546,417.85  

6            6,250,000.00       0.5066                   3,166,444.51  

7            6,250,000.00        0.4523                  2,827,182.60  

8            6,250,000.00        0.4039                  2,524,270.17  

               NPV                                                   31,047,748.54  

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