You have just graduated, are dead broke, but would still like to buy a new car so that you can show it off on Instagram. Your rich Aunt Amy, who is a retired investment banker at the age of 35 because she knew better, is willing to lend you the money to buy the car, as long as you promise to pay her back in four years. You propose to pay her the rate of interest she would otherwise get by putting the money in the bank, which has deposit and loan rates of 2% and 6%, respectively. Based on your projected income and living expenses, you anticipate that you will be able to pay her $30,000, $40,000, $45,000, and $50,000 at the end of each of the next four years, respectively.

(a) If your aunt accepted your proposal, how much would she be willing to lend you today? (b) How much would your aunt have in four (4) years if she chooses not to lend you the money? (c) How much would your aunt have in four (4) years if she chooses to lend you the money? (d) Based on your calculations in parts (b) and (c), you believe your aunt should be indifferent between lending you the money or putting the money in the bank. Discuss whether she would agree with your assessment. (e) Suppose your aunt proposes to make you indifferent between borrowing from her or borrowing from the bank instead. How much would she be willing to lend you today?

(f) You and your aunt eventually agree to an interest rate of 4%. Explain whether you win, whether your aunt wins, and how such an outcome can be possible.