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 7 percent is the discount rate, what is the present value of this stream of cash flows? if 14 percent is the discount rate, what is the present value of the cash flows?

(a) $850,169.64

(b) $566,277.662

Explanation:

Given that,

Principal amount (P) = $75,000

No. of installments = 20

Period (t) = 19 years

Discount rate (r) = 7%

(a)

                                                     = $75,000 + 75,000 × 10.3355952

                                                     = $75,000 + 775,169.64

                                                     = $850,169.64

(b) When discount rate changes to 14%, then

                                                     = $75,000 + 75,000 × 6.55036883

                                                     = $75,000 + 491,277.662

                                                     = $566,277.662

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