Carleton, Inc.
Consumer Lending Software

The Rule of 78ths

What's in a name?  Often through this blog, and other writings over the years, you have heard me preach clear communication.  The use, and mis-use, of labels, slang, jargon and other esoteric terms not only makes it difficult to communicate in this industry, it can also lead to less than stellar compliance performance when it comes to calculations and disclosures.

Almost everyone in the industry is familiar with the term "Rule of 78ths".  Ever think about how much you really know about this widely used term?

Here are some things that I know after 27  years of dealing with it:

1) It's an allocation method not a "calculation" method.  I can compute monthly payments that will adhere to a Rule of 78ths allocation of the charge and liquidation of the principal, but I cannot "compute a payment by the Rule of 78ths".

In the heyday of add-on and discount interest, the need arose for a way to determine how much interest was to be allocated to a specific period of time.  Both add-on and discount compute interest charges based on the life of the loan and there is no thought to repayment terms.

Creditors needed a way to determine "earned" interest and, thus, "unearned" interest.  This is how the method grew into a popular method for computing refunds when a loan is prepaid in full before maturity.  It was easy and uncomplicated.


2) It's technically only the "Rule of 78" for a 12 month transaction with equal monthly payments.  The "78" refers to the sum of the numbers 1 through 12.  Since the use of Rule of 78ths requires the summing of the number of payments remaining divided by the sum of the original number of payments, the 78 portion is only applicable if there are 12 payments in the loan.


3) The more precise name is "Direct Ratio" method.  Direct Ratio assumes that the portion of the total charge contained in each installment is computed as a direct ratio of the number of remaining unpaid installments to the sum of the original number of installments.

I wish I could claim that I crafted that definition myself but I can't.  It comes from one of the rare textbooks that address lending calculations titled "Neifeld's Guide to Instalment Computations" by Dr. M.R. Neifeld.  It was first published in 1951.  This definition forms the premise of the concept for which we all take the mathematical shortcut of summing remaining and original payments to find the valued "factor".


4) Most statutes authorize The Sum of the Balances method in the language they use to describe refunds of interest and charge.  The statutory language talks about the sum of the "monthly time balances" scheduled for a loan not the number of scheduled payments.  That provides a more accurate description of the Sum of the Balances method, of which Rule of 78ths is a subset, which accounts more properly for irregularities.

5) The Rule of 78ths can provide accurate computations only if there are none of these irregularities in the loan transaction.  Loan characteristics such as balloon payments, irregular payment amounts, irregular first intervals (aka "45 days to the 1st Payment),

skipped payments, non-monthly repayment periods (e.g. quarterly payments) etc. render  a Rule of 78ths calculation imprecise mathematically at best.  The simplistic, traditional Rule of 78ths shortcut cannot properly account for the actual balances and the time they are scheduled to be outstanding.

But when is the last time you had a generic, simple loan transaction with no type of irregularity?  Those transactions seem to be few and far between these days.


6) While Rule of 78ths is  more often used for interest or charge refunds, it can also be used in the proper setting for determining unearned credit insurance premium or ancillary product charges.  The same rules for irregularities, however, continue to apply.

Like a lot things in an ever evolving industry, the intent of "Rule of 78ths" was most likely the concept of the more robust Sum of the Balances method.  As loan products become more complex, the methods we apply to specific operations must adjust also.

Rule of 78ths is still in use today on a regular basis.  However, it is not a "one size fits all" solution and the characteristics of the loan itself determine it's accuracy and viability.

Posted on Oct 20, 2011