(Related to Checkpoint 6.2) (Present value of annuity payments) The state lottery's million-dollar payout provides for
$1.11.1
million to be paid in
2525
installments of
$44 comma 00044,000
per payment. The first
$44 comma 00044,000
payment is made immediately, and the
2424
remaining
$44 comma 00044,000
payments occur at the end of each of the next
2424
years. If
77
percent is the discount rate, what is the present value of this stream of cash flows? If
1414
percent is the discount rate, what is the present value of the cash flows?
a. If
77
percent is the discount rate, the present value of the annuity due is
$nothing.
(Round to the nearest cent.)
Solution a:
Present value of cash flows at 7% discount rate = $44,000 * Cumulative PV factor at 7% for 25 periods of annuity due
= $44,000 * 12.46933 = $548,650.52
Solution b:
Present value of cash flows at 7% discount rate = $44,000 * Cumulative PV factor at 14% for 25 periods of annuity due
= $44,000 * 7.83514 = $344,746.16
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