Question

# (Related to Checkpoint​ 6.2)  ​(Present value of annuity​ payments)  The state​ lottery's million-dollar payout provides for...

(Related to Checkpoint​ 6.2)  ​(Present value of annuity​ payments)  The state​ lottery's million-dollar payout provides for

​\$1.5 million to be paid in

20

installments of

​\$75,000

per payment. The first

​\$75,000

payment is made​ immediately, and the

19

remaining

​\$75,000

payments occur at the end of each of the next

19

years. If

8

percent is the discount​ rate, what is the present value of this stream of cash​ flows? If

16

percent is the discount​ rate, what is the present value of the cash​ flows?

#### Homework Answers

Answer #1

8%:

Present value of annuity due = ( 1 + r) * Annuity * [ 1 - 1 / ( 1 + r)n] / r

Present value of annuity due = ( 1 + 0.08) * 75,000 * [ 1 - 1 / ( 1 + 0.08)20] / 0.08

Present value of annuity due = 1.08 * 75,000 * 9.818147

Present value of annuity due = \$795,269.9

16%:

Present value of annuity due = ( 1 + r) * Annuity * [ 1 - 1 / ( 1 + r)n] / r

Present value of annuity due = ( 1 + 0.16) * 75,000 * [ 1 - 1 / ( 1 + 0.16)20] / 0.16

Present value of annuity due = 1.16 * 75,000 * 5.928841

Present value of annuity due = \$515,809.2

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