Jack and Diane are lottery winners. They hold the ticket to the Grand Prize in the “Set for Life” Prize that makes 20 consecutive annual payments of $50,000 starting immediately. There is one hitch: the eleventh payment (to be received at the end of year 10) is not $50,000 but only $20,000 (that is, this payment is $30,000 LESS than the other 20). Which of the following comes closest to the present value of the prize if interest rates are 6%?
a. 
$ 635,849 

b. 
$ 743,867 

c. 
$ 591,154 

d. 
$ 551,529 

e. 
$ 686,430 
Present value of annuity due concept
Here 11 th payment is 20,000 only.
Here we should calculate 50,000 for 11th payment and cakculate present value of 50,000 for 20 payments. Later present value of 30,000 amount deducted from above calculation.
Present value = 50,000 * PVADF(6% ,20 years)  30,000 * PVF( 6%,10Years)
Present value = 50,000 * 12.15811649  30,000 / (1.06)10
Present value = $ 607,905.824583959  16,751.84331
Present value = $ 591,153.98
Present value = $ 591,154
Option c is correct.
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