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**

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