Amortization Deep Dive: The Rule of 78s

As we talked about previously, there are many reasons why understanding amortization methods is helpful for financial professionals. Today, we’re taking a deep dive into one such method: the Rule of 78s.

A Brief History Lesson

The Rule of 78s is a sum-of-digits method where the interest is weighted more heavily towards the beginning of the loan term. The method was developed in the 1930s as a kind of compromise between borrowers and lenders for precomputed loans. Traditionally, when a borrower took out a loan, the interest and principal of each payment was calculated at the beginning of the loan term and split into equal amounts, spread out over the entire life of the loan. For example, if a borrower wanted to take out a loan with the following structure:

• Total Principal: $1,200
• Interest Rate: 5%
• Loan Term: 12 Months
• Payment Period: Monthly

For such a loan, the total interest was calculated as $60 over the course of the loan, making the total monthly payment $105 ($1200/12 = $100 + $5 = $105), and the borrower paid the same amount of interest every month.

If the borrower took the full loan term to repay the loan, everything was fine. After all, the lender still got their full $60 of interest. However, lenders would lose out on interest were the borrower able to pay back their loan early. If the borrower paid off their loan in, say, 6 months, they only paid half of the total amount of interest that the lender was anticipating collecting. This new Rule of 78s method was created to favor the borrower with more interest collected in the first months the loan is opened, with less interest collected near the end of the loan’s life cycle. Should the borrower pay the loan off early, then precomputed interest could be refunded in a principal balance reduction for any unearned amount of interest based on this new way of calculating precomputed interest and the refunding of that interest on early payoff.

As a compromise, in 1935 someone (Indiana legislators, to be precise) came up with the idea of having the borrower pay more interest early in the loan life cycle and less interest (and more principal) later. Using the same loan terms as above ($1,200 principal, 12 months, 5% interest rate), they suggested that the precomputed interest amount ($60) should be divided into 78 parts, each approximately $0.77. (Why 78? We’ll get to that in a moment.) During the first month of the 12-month loan period, the borrower would pay 12 parts of the total interest, or $9.24 (= $0.77 x 12). During the second month, the borrower would pay 11 parts of the total interest, or $8.46. During the third month, the interest payment would be $7.69 (10 parts). And so on, until in the final month of the loan term, the borrower would pay only one part of the interest, or $0.77.

Below is a sample payment schedule based on the scenario I’ve just described:

Thus, while the monthly payment remains the same each month ($105), the amount of that payment applied to the interest is much higher in the first month and then gradually decreases with each payment period. If a borrower pays off a 12-month loan in only 6 months, for example, they have already paid nearly three-quarters of the total interest (57 parts out of 78 total parts = 73%), so the lender is still making a nice profit from the situation.

And that 78? Well, that’s the number you come up with if you add all the numbers from 1 to 12—that is, 1 + 2 + 3 … + 12. So technically, if you have a two-year loan, you are using a “rule of 300s” amortization method (1 + 2 + 3 … + 24 = 300). But, since it was commonly used for 12-month loans in the beginning, it simply became known as the “Rule of 78s.”

The Rule of 78s in Today’s Financial Landscape

The Rule of 78s is widely used in certain contexts, especially for small-amount, short-term loans (60 months or less), such as auto loans. Just make sure you check your state’s laws before you decide to use it, as it is no longer allowed in some states.

Calculating the Interest Rebate: An Example

Anytime a borrower pays off a loan early, it’s important to make sure that the interest rebate is correctly calculated. (The interest rebate represents the portion of the total interest amount that the borrower doesn’t have to pay since the loan is paid off early.) Here are the steps to calculate the interest rebate on a Rule of 78s loan:

1. Calculate the total interest for the full loan term.
2. Calculate the total interest paid for the first 6 months.
3. Subtract the interest paid for the first 6 months from the total interest to find the interest rebate.

Now let’s calculate it for a loan with the same structure described earlier ($1,200 at 5% over 12 months) with the borrower paying off the loan after 6 months.

We already know the total interest for the full-term loan is $60. Using the payment schedule from earlier, we can calculate that the interest already paid after 6 months is $43.83. When we subtract the latter from the former, we get $16.17. Therefore, when this Rule of 78s loan is paid off after 6 months, the interest rebate will be $16.17.

Conclusion

Although some might consider the Rule of 78s an outdated method, its legacy lives on in many areas of the lending world. It has been a standard amortization tool in the lender’s toolbox for decades past and is still common in certain industries. Of course, you’ll always want to double-check your state’s lending regulations before adopting it.

Our GOLDPoint Systems lending software regularly uses the Rule of 78s for precomputed loans, although other amortization methods are certainly available. We even have specialized Rule of 78s amortization methods, like “Rule of 78 – Multi Frequency,” which is used to calculate Rule of 78s amortization for loans where the payment frequency is something other than monthly.

If you’d like to learn more about using the Rule of 78s at your institution, you’ll want to speak with your GOLDPoint Systems account manager for details.