Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program.

Ben currently works at the money management firm of Dewey and Louis. His annual salary at the firm is $$69,000$ per year, and his salary is expected to increase at $3$ percent per year until retirement. He is currently $28$ years old and expects to work for $40$ more years. His current job includes a fully paid health insurance plan, and his current average tax rate is $26$ percent. Ben has a savings account with enough money to cover the entire cost of his MBA program. The Ritter College of Business at Wilton University is one of the top MBA programs in the country. The MBA degree requires two years of full$-$time enrollment at the university. The annual tuition is $$75,000,$ payable at the beginning of each school year. Books and other supplies are estimated to cost $$3,600$ per year. Ben expects that after graduation from Wilton, he will receive a job offer for about $$115,000$ per year, with a $$20,000$ signing bonus. The salary at this job will increase at $4$ percent per year. Because of the higher salary, his average income tax rate will increase to $31$ percent.

The Bradley School of Business at Mount Perry College began its MBA program $16$ years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one$-$year program, with a tuition cost of $$90,000$ to be paid upon matriculation. Books and other supplies for the program are expected to cost $$5,400.$ Ben thinks that he will receive an offer of $$96,000$ per year upon graduation, with an $$18,000$ signing bonus. The salary at this job will increase at $3\mathrm{.}5$ percent per year. His average tax rate at this level of income will be $29$ percent. Both schools offer a health insurance plan that will cost $$3,500$ per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $$2,500$ more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is $4\mathrm{.}7$ percent.

$1.$ What initial salary would Ben need to receive to make him indifferent between attending Wilton University and staying in his current position?