4. Consider the problem of a worker(Grace) who is deciding between going back to school or not. Suppose, Grace only cares about the lifetime income when she makes 5 a decision. Assume, she will work for 21 years, t=0,1,2,3,,20. After t=20, Grace will retire. If she remains on her job, she will earn $50,000 each year. If she goes to school, she pays tuition of $40,000 for the first two periods (t=0 and t=1) and has no income during the school period. After she graduates, she earns $80,000 each year. At the start of t=0, she must decide whether she will go to school or not. (Assume she has no savings or debts at t=0, but she can borrow or lend at interest rate r=0.01. (a) What is the present value of Grace's income when she doesn't go to school? (b) What is the present value of Grace's income when she goes to school? (c) According to the previous results, which option gives more benefit to her? (d) Suppose there was a shock to the interest rate, so r=0.05. Should Grace go to school or not? (You should calculate the present value of going to school and not going to school and compare those two with a new interest rate.)