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## The Rule-of-78s : The Formula and How It Works

Outside of banking circles, the Rule-of-78′s is little understood, even though it is commonly applied to many consumer and business loans. For the borrower, it tends to have a pernicious effect in the nature of a hidden prepayment penalty. The borrower’s disadvantage is heightened by the fact that the operation of the Rule-of-78′s is often referred to as a "Rebate of the Finance Charge." Any consumer who heard the word "rebate" is always tempted to say, "Where do I sign?"

### Not so fast!

Here’s how it works: The name comes from the sum of the numbers one through 12, there being 12 months in a year. Yes, that adds to 78.

The theory of the Rule-of-78′s is that at the moment a borrower signs the Note, the borrower is immediately obligated to pay back all of the principal and ALL of the interest that will accrue in the future over the agreed term of the loan.

Now, if the borrower prepays, the lender "generously" forgives some of the interest EVEN THOUGH at the time for it to accrue has not yet elapsed and so that additional interest has not been earned. That’s the so-called "Rebate." Lenders argue that the uncertainty created about an early payoff entitles them to some compensation for being at the borrower’s whim for payoff. In a time of falling interest rates, that argument may have more merit than when interest rates are rising as the lender gets to put the money back to work at a higher rate and earn more.

In any event, the Rebate is calculated by summing the number of payments elapsed in inverse order as a numerator for the fraction in which the sum of the term is the denominator. That fraction times all interest over the life of the loan is the amount earned by the lender.

### Watch this example:

Assume a two-year loan (so we’ll assume the numbers 1 through 24) for \$10,000 with interest at 12% per year. Using our online amortization schedule calculator, we know the monthly payment is \$470.73. The amortization schedule’s "Running Totals" also tells us that over the life of the loan the total amount of aggregate interest to be paid would be \$1,297.56 (when the "1st payment date" is one month after the "loan date").

After the fourth month, our borrower reaps a windfall and wants to prepay the whole loan. The fraction of the total interest earned by the lender is:

(Sum 24 to 21) over (Sum 1 through Sum 24)

90/300 = 30%

Now, let’s compare that to the interest actually paid to date to see what the penalty will be. From running the "Loan Table" module, we found the total interest to be \$1,297.65 and the interest paid after four payments is \$377.61, so the penalty is:

Earned Interest Per Rule: (30%) (\$1,297.65) = \$389.30

Interest Paid to Payoff: \$377.61

Maybe that doesn’t look like too big a number, but it’s an additional 3.1% interest. Had this been a \$100,000 loan, the increased penalty works out to ten times as much, \$116.84.

Paying off at different times for different maturities and different interest rates produces differing penalty sizes. Two general rules of thumb can be deduced:

1. The higher the interest rate, the greater the penalty amount.

2. The earlier the prepayment in relation to the term, the greater the penalty amount.

So if you’re a lender, you should love using the Rule-of-78′s. If you’re a borrower, you should try to avoid it. A caution for lenders: Some states have usury and other laws that may limit use of the Rule-of-78′s.