Round and Round With Rule of 78s

Question: My agreement to buy a motor vehicle says: “Any refund of unearned finance charges due upon prepayment or acceleration shall be calculated by the method indicated: the rule of 78’s.”

I tried to find out more about the Rule of 78s. Unfortunately, nobody seems to know anything about it. Please try to explain to me and your other readers the Rule of 78s.--M.K.

Answer: Hoo boy! Wouldn’t you prefer a quick rundown on the quantum theory instead?

The what-it-is, unfortunately, is the only simple part of the explanation: It’s a method of computing rebates on installment loans by using the “sum-of-the-year’s-digits” basis. And it gets its catchy name, the Rule of 78s, from the fact that if you add up all of the digits beginning with Month No. 1 through Month No. 12 you come up with a total of 78 (1 plus 2 plus 3 plus 4 and so forth).

What the lender is really telling you, however, is that under the Rule of 78s, if you pay off a one-year installment loan in six months you are not --repeat not --going to save half the year’s interest on that loan. The logic of it to the contrary.

As Howard DeWeiss, corporate compliance officer for First Interstate Bank, puts it: “The Rule of 78s means that at the end of the first month of a one-year loan, the lender has earned 12/78ths of the total finance charge, because the balance is higher at the beginning of the year.”

At the end of the second month, he’s earned 23/78ths of the finance charge, and at the end of the third month he’s earned 33/78ths of the total (12/78ths plus 11/78ths plus 10/78ths).

Considerably More

“So,” DeWeiss continues, “at the end of the year he’s earned 78/78ths of the total finance charge. But, at about the half-way point, six months, he’s earned roughly 74% of the total interest.” And the borrower, paying off such a loan after six months, finds that he still owes considerably more on the principal than he thinks he does--not half, but closer to three-fourths.

The whole subject of interest rates on installment loans is an enigma wrapped in confusion, and the approach least explainable to the average consumer (and some bankers, as well) is the installment loan written under the Rule of 78s, which, by its very nature, is also defined as an add-on loan. Most California bankers don’t like the add-on loan, DeWeiss adds, not only because it’s difficult to impossible to explain to the layman, but because it also distorts the actual interest that can be paid. While car dealers in California prefer it, he says, the majority of bankers--given their druthers--would stick strictly to “simple interest,” both for personal loans and car loans.

“Some time ago,” DeWeiss adds, “Arizona lenders apparently banded together and simply told the car dealers that they would write simple-interest car loans exclusively and that was that. We’ve tried to get legislation here along the same lines, but the end result was a stipulation still permitting the add-on loan for anything under 62 months--a hair over five years. Which, of course, covers most of your car loans.”

What’s the difference between the two--the add-on (Rule of 78s) loan and the simple-interest loan? With a simple-interest loan, what you see is what you get--a one-year, $1,000 loan at 10% means that you will repay the lender $1,100. A one-year, 10% loan under the Rule of 78s, the add-on, means that the interest, $100, is added on at the time the loan is made and monthly payments are computed on the total.

“That means, with the add-on,” DeWeiss says, “you can’t say how much is going to principal and how much is going to interest. You’re just lumping the whole thing together and dividing it by the number of months. You’re paying interest on your interest.”

With a simple-interest loan, the lender merely takes the annual percentage rate and divides it by 365 to arrive at the daily rate. Thus, with a one-year, 10% loan on $1,000, the daily rate works out to .000274%, and so your first month’s payment reflects a monthly interest rate of .00849% (31 x .000274%) of your balance. Under a standard amortization schedule, though, how does this work out?

On the $1,000, one-year, 10% note mentioned above, DeWeiss continues, payments of $87.88 a month (based on standard schedules) are called for, of which $8.22 goes toward the lender’s interest and $79.66 goes to reduce the principal. The second month--assuming, once again, that it is 31 days between payments--the payment is, also again, .00849% of the principal, but now your balance has dropped to $920.34 ($1,000 less $79.66). So the amount of your payment diverted to interest has also dropped to $7.82 (with $80.06 now going to the reduction of principal), and so on until the entire $1,000 principal and the $100 interest has been paid off.

The only real distortion built into the simple-interest loan is in the fact that life isn’t so neat and clean that the monthly payments are exactly 31 days apart. Weekends and holidays get in the way, and the borrower is sometimes a few days late, or sometimes a few days early, in making his payment. The amount going to interest, however, is based entirely on the actual number of days since the last payment. Thus, if the payment is made 28 days since the last one, the multiplier would be 28 x .00027% or, in the case of a late payment coming in 44 (instead of 31) days since the last one, the multiplier would be 44 x .00027%.

Exactly the Same

Ironically, DeWeiss adds, the actual interest on a loan (let’s say a loan of $1,000 for one year) works out exactly the same, $100, whether its an add-on loan or a simple interest loan-- as long as it runs to maturity. The distortion in the add-on comes into play only when payments are accelerated or paid off early.

“When you prepay a simple-interest loan,” DeWeiss adds, “you save a tremendous amount of interest. But, when you prepay an add-on loan--paying, for instance, three months ahead--you don’t gain anything. It just prepays your loan for three months and, in effect, makes the actual interest on what you do pay much higher. On an 11.33% add-on loan, for instance, the distortion can be converted to an actual rate of about 20.53%.

“Under Truth in Lending legislation,” he continues, “the add-on rate has to be converted to an annual rate, and so the car buyer gets home, finally reads his disclosure statement and is shocked by a figure like 20.53%. But that’s only if he accelerates his payment. Now, how do you explain that in a way that makes sense to anyone? The car buyer is assured by the dealer that there’s no ‘prepayment penalty.’ And, technically, there isn’t. But, in actuality, there certainly is. “

How do you avoid this?

“Never, never,” DeWeiss emphasizes, “go along with an add-on loan unless you fully intend to ride it out to maturity. And, certainly, never sign the purchase agreement and drive off the lot until you’ve read the disclosure statement fully and see what the interest rate is if you do pay it off early.”

This is obviously far more than anyone in his right mind would ever want to know about the Rule of 78s. But, once into it, knowing where to stop--like knowing when to stop sawing a chair’s legs to make them even--is the real trick.

Don G. Campbell cannot answer mail personally but will respond in this column to consumer questions of general interest. Write to Consumer VIEWS, You section, The Times, Times Mirror Square, Los Angeles 90053.