Some universities allow an employee to put an amount q into an account at the beginning of each year, to be used for child-care expenses. The amount q is not subject to federal income tax. Assume that...

Some universities allow an employee to put an amount q into an account at the beginning of each year, to be used for child-care expenses. The amount q is not subject to federal income tax. Assume that all other income is taxed by the federal government at a 40% rate. If child-care expenses for the year (call them d) are less than q, the employee in effect loses q - d dollars in before-tax income. If child-care expenses exceed q, the employee must pay the excess out of his or her own pocket but may credit 25% of that as a savings on his or her state income tax. Suppose Professor Muffy Rabbit believes that there is an equal chance that her child-care expenses for the coming year will be $3,000, $4,000, $5,000, $6,000, or $7,000. At the beginning of the year, how much money should she place in the child-care account?