Madeleine is a high school graduate deciding whether to go to university. She (like everyone else) lives for two periods after high school. In the first period, she can work (without university) for a salary of YH, or she can attend university. If she attends university, she must pay $5,000 in fees (tuition, books), but she will also earn $5,000 from a summer job. In the second period, she will continue to earn YH if she did not attend university, or she will earn YU if she went to university. The interest rate at which money can be borrowed or invested is r.

a) Show that she will attend university if YU > (2 + r) YH

b) Explain how an increase in the interest rate would affect her decision to attend university.