Once you reach above $20,000 + 0.8 . $20,000 = $36,000 in expected value, you fall into the third piece of the function, where you receive only 60% on the dollar. Thus, you can set Formula 6.1 on page 163 equal to

$38,500 and solve for “Loan”:

E(Payoff Given Loan Promise = $45,000) =

$38,500 = $20,000 + 80% . ($40,000 − $20,000) + 60% . (x − $40,000)

The correct answer is indeed x ≈ $44,166.67.