Question

(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?

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