# The Actuarial Method - Beware the Compounding

During a recent training session for a group of newer employees (fairly new by Carleton standards, since our average tenure is approximately 18 years of service), we began discussing the parameters integral to computing a loan payment. I then asked:

"Ok, so now we agree on the parameters that will drive the payment calculation. If we're a new company and I give you the task to program this into a viable computing routine, where do you go to find out* how to compute a loan payment*? An extremely quiet 30 second impasse filled with blank stares and embarrassed smiles ensued, followed by a collective shrug of the shoulders "we're really not sure".

It is a true statement in this business of creating consumer lending calculations that there is no granular level standard text book for computing loan payments. Yes, you can start with the PV of an annuity formula. But that is incredibly generic and limited for today's lending industry and its ever expanding "exotic financing" outlook. For instance, you can't compute daily simple interest by formula. It is the broadening and refining of that basic equation that is the key to the payment computing kingdom.

So, it's no wonder that we regularly see loan transactions from systems (LOS and DMS) that incorporate payment calculation routines where interest accrues by the "actuarial method".

In this context, the statutory definition for the term "actuarial method" is usually something like "as defined by the Federal Reserve Board in Regulation Z 12 C.F.R. Sec. 266 that implements the Truth in Lending Act."

Since the Truth in Lending Act requires an APR to be computed for nearly every consumer credit transaction, what safer way to build a compliant payment computing routine than to manipulate the Appendix J algorithm, for computing a Reg. Z APR, from finding a rate to finding a payment? "If I just follow that same template, how can I go wrong?" Or so the thought process goes.

One major stumbling block to that solution is that the Appendix J algorithm incorporates the inherent compounding of interest. Nowhere in the definitions, variables, or other explanations is that fact stated, but it's there in the math.

Given that the compounding of interest is generally held to be against public policy in many jurisdictions and the fact that compounding increases the effective yield of the transaction, it can be a precarious practice at best. Very often compounding must be both expressly allowed by statute and clearly agreed to by the parties involved.

I often wonder what percentage of programmers, loan officers and compliance officers are even aware it's there, inherent in the math of the method itself anytime a first interval is longer than a regular period.

Even though a few states, like Louisiana, expressly allow compounding by authorizing the actuarial method of interest accrual in their statutes, the real question for lenders should be "how well will this play in front of Judge Wapner at six o'clock?"

One phrase regarding compliance that I have come to embrace over the years is** “ The Greatest Risk come from those things that have no history of problems”.**

Posted on Apr 24, 2014