Income Optimization: FSA Accounts Employees of the University are permitted to contribute a portion of their paychecks to a flexible spending account (FSA) to cover healthcare expenses that are not covered by their primary insurance plan (deductibles, dental work, eyeglasses, etc.). These contributions are tax-deductible (that is, paid with pre-tax dollars), but any amounts not spent in the plan year are forfeited; use it or lose it. The maximum contribution in any year is $3,500. Suppose an employee is subject to a total (federal + state) marginal tax rate of 32%. The employee estimates that for her family, eligible medical expenses will be somewhere between $500 and $4,000, with a most likely value of $2,500. Assume these amounts will not be tax-deductible unless paid out of the FSA, and that they follow a triangular distribution.

1. Build a spreadsheet model and simulate 1,000 years (one year, 1,000 times) to determine the amount that she should contribute to the FSA to minimize the amount of money she will have to spend on medical expenses.

2. With that contribution amount, what is the probability that there will be leftover funds in the account that will be forfeited? Suppose she thinks that a uniform distribution (with the min and max values as above) is a more accurate representation of reality.

3. What would be the revised value for the optimum contribution? Now what is the probability that funds will be forfeited?