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"A woman wins the lottery worth $2.38 million. The woman receives an immediate check for $357,000,...

"A woman wins the lottery worth $2.38 million. The woman receives an immediate check for $357,000, and she plans to receive 19 annual checks of $106,474, with the first check coming exactly one year from now. A buyer offers to purchase the 19 remaining checks of $106,474. If the woman can deposit the money from that sale (which she would receive immediately) in an account that earns 8% interest, what would be the least amount of money she should accept to sell the forthcoming 19 checks?"

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Answer #1

The objective is to find the single future sum (F) of the initial payment (P) made at time 0 after n periods at an interest rate i compounded every period.

F = P(1 + i)n

F = P(F/P, i, n)

In the above

F = Future amount at the end of year n

P = Principal amount

n = Number of interest periods

i = Interest rate

P = $106,474

n = 19

i = 8% or 0.08

F = 106,474(1 + 0.08)19

F = 106,474(F/P, 8%, 19)

F = 106,474(1.08)19

F = 106,474 × 4.316

F = $459,509.95

The maturity value of $106,474 invested now at 8% interest rate compounded yearly is equal to $459,509.95 after 19 years. So, this is the least amount of money she should accept to sell the forthcoming 19 checks.

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