Adam Rust looked at his mechanic in automobile repair shop... and sighed. The mechanic had just pronounced a death sentence on his road-weary used car. The car had served him well - at a cost of just $500, it had lasted through four years of college with minimal repairs. Now, he desperately needs new wheels. Adam has just graduated, and has a good job with a decent starting salary. He hopes to purchase his first new car. The car dealer seems very optimistic about his ability to get a loan and afford the car payments - another first for him. The car Adam is considering has a price of $35,000. The dealer has given him 3 payment options: 1. Zero percent financing. Make a $4,000 down payment from his savings and finance the remainder with a 0% APR loan for 48 months. Adam has more than enough cash for the down payment, thanks to generous graduation gifts from his family. 2. Rebate with no money down. Receive a $4,000 rebate, which he would then use for the down payment (and leave his savings intact), and finance the rest with a standard 48- month loan, with an 8% APR. He likes this option, as he could think of many other uses for his savings. 3. Pay cash. Get the $4,000 rebate on the original purchase price and pay the rest with cash. While Adam doesn't have sufficient amount of cash, he wants to evaluate this option. His parents always paid cash when they bought a family car; Adam wonders if this really was a good idea.

Adam's fellow graduate, Jenna Hawthorne, was lucky. Her parents gave her a car for graduation. It was a little Hyundai, and definitely not her dream car, but it was serviceable, and Jenna didn't have to worry about buying a new car. In fact, Jenna has been trying to decide how much of her new salary she could save. Adam knows that with a hefty car payment, saving for retirement would be very low on his priority list. Jenna believes she could easily set aside $3,000 annually of her $45,000 salary. She is considering putting her savings in a stock fund. She just turned 22 and has a long way to go until retirement at age 65, and she considers this risk level reasonable. The stock fund she is looking at has earned an average of 9% annual return over the past 15 years and could be expected to continue earning this amount, on average. While she has no current retirement savings, five years ago Jenna's grandparents gave her a new 30-year U.S. Treasury bond with a $10,000 face value. Jenna wants to know her retirement income if she both (i) sells her Treasury bond at its current market value and invests the proceeds in the stock fund and (ii) saves $3,000 at the end of each year and invests it in the stock fund (from now until she turns 65). Once she retires, Jenna wants those savings to last for 25 years until she is 90. Both Adam and Jenna need to determine their best options.

1. In fact, Adam doesn't have sufficient cash to cover all his debts, including his substantial student loans. The loans have a 10% APR, and any money spent on the car could not be used to pay down the loans. What is the best option for Adam now? ( HINT: Note that having an extra $1 today saves Adam roughly $1.10 next year because he can pay down the student loans. So, 10% is Adam's time value of money in this case.)

2. Suppose instead that Adam has a lot of credit card debt, with an 18% APR, and he doubts he will pay off this debt completely before he pays off the car. What is Adam's best option now?

3. Suppose Jenna's Treasury bond has coupon interest rate of 6.5%, paid semi-annually, while current Treasury bonds with the same maturity date have a yield to maturity of 5.4435% (expressed as an APR with semi-annual compounding). If she has just received the bond's 10th coupon, for how much can Jenna sell her Treasury bond?

4. Jenna expects her salary to grow regularly. While there are no guarantees, she believes an increase of 4% a year is reasonable. She plans to save $3,000 the first year, and then increase the amount she saves by 4% each year as her salary grows. Unfortunately, prices will also grow due to inflation. Suppose Jenna assumes that there will be 3% inflation every year. In retirement, she will need to increase her withdrawals each year to keep up with inflation. In this case, how much can she withdraw at the end of the first year of her retirement? What amount does this correspond to in today's dollars? ( HINT: Build a spreadsheet in which you track the amount in her retirement account each year.)

9. Should Jenna sell her Treasury bond and invest the proceeds in the stock fund? Give at least one reason for and against this plan.