At first, Berkeley psychology professor Geoffrey Keppel rejected out of hand his Toyota dealer's offer of financing: He had saved up the price of a new Corolla and, like many people, didn't want a loan because "that's the way I'd been brought up." The dealer even told him he could earn more on the same $8,300 in an 8% certificate of deposit than he'd pay out on a 14.2% car loan, "but you just don't believe it," he says. "It's counter-intuitive: anyone can see 14 is bigger than 8."
He's not unusual. Many people who spend their adult lives avoiding debt have heard from (usually richer) friends that it's generally better to spend borrowed money than savings, but they can never clearly see why, particularly when loan rates are higher than investment yields. What's more, Keppel says, "when you've just spent several hours nickel-and-diming with an auto dealer, you're not inclined to jump when they say they have another good deal for you."
That night, however, Keppel awoke and went to his computer to "work it out for myself, month by month." Calculating different investment yields and weighing them against the total interest that he'd pay on the 14.2% loan, he saw that he'd break even with only a 7% investment, and, if he could earn 10%, he'd make almost $1,500. The trick, as he figured it out, was that "the 14% is applied to a declining balance, and the 8% is on an increasing balance." Thus, he'd really be borrowing $8,239.05 only the first month, zero the last, and over four years, the average outstanding balance of the loan would actually be about half the total amount borrowed. Total interest paid out would be $2,607.62. His investment, on the other hand, would be left in for the term and compounded monthly, yielding interest of $3,095.06 and a profit of $487.44.
Assume, based on the information given in article that the cost of car is $8,239.05, that the loan is given for 48 months at 14.2% APR, and that the savings rate is 8% APR. Note that this loan, as most consumer loans (mortgages, car loans), has equal payments over the life of the loan.
Questions
1. What is the monthly payment Keppel will need to make on his car loan?
2. What is the "Total Interest Paid" (total payments minus the price) on the
loan?
3. How much interest will he earn on his savings?
4. What is the right decision? Why?