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.

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.

where PMT is the periodic payment

               i is the required rate of return per period

              n is the number of periods

= $31,047,749.

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

YearCash flowPV 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