Question

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

Answer 1

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.