# Annual Percentage Rate: Actuarial vs. U.S. Rule Method

Appendix J to Regulation Z states that the annual percentage rate shall be determined in accordance with either the Actuarial or United Sates (U.S.) Rule methods.

## Actuarial method

Appendix J provides an explanation of the actuarial method, along with equations, instructions, and several sample calculations. The calendar method used by the actuarial method (which we call the Federal Calendar) is well defined in the regulation.

Note that since lenders do not generally use the Actuarial method and Federal Calendar to compute loan payments, we cannot expect the disclosed actuarial APR to match the interest rate used in a given loan calculation, for the vast majority of loans.

## United States (U.S.) Rule method

Regulation Z also allows the lender to disclose an APR computed according to the U.S. Rule. This rule forbids the capitalization of interest during the amortization of a loan, but does not specify the calendar method to be used in counting time between cash flows.

Many lenders use the U.S. Rule method to accrue interest during the amortization of a loan, however there are many different calendar methods for counting time between events (i.e Actual/365, Unit Period/360, etc.). If a lender discloses a U.S. Rule APR and uses the same calendar method to compute interest, then the APR and interest rate used should be extremely close, providing there are no contributions to the Finance Charge other than interest.

## Recommendations

J. L. Sherman and Associates, Inc. recommends the actuarial APR method as the default choice in the United States for the following reasons:

1. As mentioned above, Appendix J to Regulation Z provides equations, instructions, and samples for the actuarial method. The calendar method used by the actuarial method (which we call the Federal Calendar) is well defined in the regulation.

2. The FFIEC provides the APR Tool on-line and free of charge to calculate and verify actuarial APRs. This tool is commonly used by examiners to verify APRs. Note that the APR Tool does not support the United States Rule method.

3. In our experience, the United States Rule method is used much less frequently in the lending marketplace. Those institutions that do choose to employ this method are typically large with dedicated compliance departments which can understand and verify APRs computed using the United States Rule method when examiners request information.

4. Because equations, methods and samples are provided for the Actuarial Method, disputes are much more easily resolved with the Actuarial method.

## United States Rule Use Case

The United States Rule method was added as an option when Regulation Z was drafted at the behest of some of the larger lending institutions in the United States. These institutions noted that even when a loan was computed with no other contributions to the Finance Charge besides interest, the computed Regulation Z actuarial APR was not the same as the entered rate, due to differences between the calendar used to accrue interest and the Federal Calendar used in the actuarial method. To mollify these concerns, Regulation Z allows the APR to be disclosed using the United States Rule method. Instead of defining one or more calendars to use for this method (which would create the same potential problem of returning a non-matching rate), the United States Rule method was left without definitions or equations.

If you or your client wishes to disclose the Regulation Z annual percentage rate via the United States Rule method, J. L. Sherman and Associates, Inc. recommends the following:

1. Since the purpose of the United States Rule method is to match the entered interest rate in the absence of contributions to the Finance Charge other than interest, then the interest accrual calendar used for the loan calculation should match the United States Rule calendar requested.

Example 1: The lender has selected an interest accrual method of “Actual/365 U.S. Rule”. Though the Actuarial method is always the default method recommended by J. L. Sherman and Associates, if, however, the lender wishes to disclose the Regulation Z APR using the U.S. Rule method, the APR Code should be set to “Actual/365 U.S. Rule” to match the interest accrual calendar.

Example 2: The lender has selected an interest accrual method of “Unit Period/360 Simple”. Though there is nothing in the regulation that disallows the disclosure of a U.S. Rule APR method, we recommend that in order to honor the spirit for which the U.S. Rule method was created, that the usage of the actuarial method is more appropriate and industry standard. Note, however, that the Sherman Calculation Engine (SCE) will allow you to specify any APR Code that you wish.

Example 3: The lender has elected to accrue interest in a unit period simple manner for part of the loan term, switching to an actual day U.S. Rule method for the remainder. For similar reasons expressed in Example 2 above, we would recommend that the actuarial APR method is more appropriate and industry standard.

2. Note that even in the absence of contributions to the Finance Charge other than interest, the United State Rule APR method may return a value which differs slightly from the entered interest rate, due to payment rounding. The SCE does offer a “U.S. Rule APR exception” which will ensure that in these instances, the returned U.S. Rule APR will be set equal to the entered rate.

## Summary

To summarize — for the majority of lenders that disclose an APR computed by the actuarial method, it will be extremely rare, in fact only coincidental, for the APR to match the interest rate. But those lenders that accrue interest by the U.S. Rule method, and who choose to compute the APR by the same method, will have agreement between interest rate and APR for those loans where the entire finance charge is due to interest.

Of course, all of our products support the calculation of both the Actuarial and U.S. Rule methods of Regulation Z APR calculation. Please contact us for further information.

We hope this analysis clarifies the use of the Actuarial and U.S. Rule APR methods. These explanations reflect our understanding gained in servicing the lending community for approximately forth (40) years, but should not be understood as legal advice.