## General

While APR does stand for annual percentage rate, it can mean different things in different circumstances. Some people think that APR only means the annual interest rate charged on a loan while others know it to be a calculated value that is disclosed with the loan numbers. This article will go over what APR is and roughly how it’s calculated. It will also give references to other resources that provide information about APR and what it is.

## What Is APR?

APR is a number devised by the US government in an attempt to give consumers a more accurate way to compare loan rates between lenders. The original APR calculation (now called the actuarial method) can be found in Appendix J of Regulation Z. The value of APR as a means to compare two loans was greatly diminished when the US rules accepted other methods for calculating APR.

### Actuarial Method

AutoPal uses the actuarial method to calculate APR.

The rules for computing an Actuarial APR are specified in Appendix J to Regulation Z, along with numerous samples. These rules include a special calendar method, commonly called the “Federal Calendar”, for counting time between cash flows, as well as how loans are to amortize. We could calculate payments for a given loan using Actuarial APR as the interest rate, following the calendar and amortization rules that define the method. Even so, these payments would still differ from those computed by the standard interest methods in use today. You see lenders do not generally use the Actuarial method in computing loan payments. It is for this reason that we cannot expect the disclosed actuarial APR to match the interest rate, for the vast majority of loans.** Please note: Nominal Interest Rate does not equal APR.**

### 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 employ the U.S. Rule method to calculate their interest accrual, but different lenders can use different calendar methods for counting time. If a lender discloses a U.S. Rule APR and uses the same calendar method to compute interest, the APR and interest rate should be the same, providing there are no contributions to finance charge other than interest.

The US Rule method of calculating APR is not outlined in appendix J because there isn’t a single calculation that will compute an accurate APR in all scenarios.

### Actuarial Method Calculation Basics

The actuarial method calculates APR as the interest rate that will cause the present value of future cash flows (payments) on a loan to equal the loan amount. The interest rate is calculated using an iterative method, because there isn’t an easy way to calculate exactly what it should be. Because of this, AutoPal has to guess at the the APR and then raise or lower it in order to make the sum of the present value of future cash flows equal the loan amount.

This causes the calculation of truth in lending (TIL) numbers to take longer than you might expect because sometimes it takes many iterations to arrive at the correct APR.

Our amortization software calculations match that of APRWin as published by the Department of the Treasury.

**Details in Calculating APR**

- Irregular First Period – If the difference between the contract date and the first due date is not equal to a standard unit period then the loan has an irregular first period. This will result in needing to calculate the number of unit periods in the term of the loan and the number of odd days in the first period in order to calculate APR. This will have an impact on the disclosed APR.

**APR Unit Periods & Odd Days Calculations Explained**

- Count Number of Days – The number of unit periods and odd days is really easy to calculate when the unit period is a number of days, such as: Weekly (7), BiWeekly (14), Any Custom Frequency (X). Simply take the number of days between the first due date and the contract date, then divide that by the number of days in a unit period. For example if you have a contract date of 12/15/2015 and a first due date of 01/17/2016 and payments come due on a biweekly frequency, number of days between the contract and first payment dates is 33. Divide 33 by the number of days in the given frequency (14). In this case we get 33/14 = 2 with a remainder of 5 or 2 Unit Periods and 5 odd days.
- Monthly – Calculating unit periods and odd days can be done by taking the day of the month from the first due date and working backwards in full unit periods until you reach or cross the contract date. That will equal the number of unit periods. So, if you have a first due date of 12/7 and a contract date of 11/5, work backwards from 12/7 by whole months. There is one whole month between 11/7 and 12/7, so that is one unit period. There are an additional two days to get to 11/5 from 11/7, so there at two odd days.
- If the payment falls on the last day of the month, you can calculate whole unit periods by moving back through last days of the month even the first payment falls on the 31st and there is no 31st of the previous month.

- SemiMonthly – Calculating unit periods and odd day should be done in this way:
- Step 1 – Calculate the number of full months between the contract date and the first due date. For example, if the contract date is 12/15/2015 and the first due date is 01/17/2016:
- Start on 01/17/2016 and go back in one-month increments until you get as close to the contract date as you can without going past it. The date we get to is 12/17/2015.
- Find the number of days between the date you went back to and the contract date. In our case our date was 12/17/2016 and the contract date is 12/15/2016. The number of days between those dates is 2.
- Multiply the number of full months between the contract date and the first payment date 30. We had only one full month, so the number will be 30.
- Add together the (number of full months * 30) + (count of days) to get the APR Days in first Period. In our case, that is (1 x 30) + 2 = 32 APR Days.
**Note:**This CAN be different then the ACTUAL number of days in the calendar between the two dates. - Take the APR Days in first period and divide by 15. This will give 32/15 or 2 remainder 2. This means we have two unit periods and two odd days.

- Step 1 – Calculate the number of full months between the contract date and the first due date. For example, if the contract date is 12/15/2015 and the first due date is 01/17/2016:

**Resources**

- https://www.fdic.gov/regulations/laws/rules/6500-3550.html
- http://www.consumerfinance.gov/eregulations/1026-J/2013-30108_20150718#1026-J-a
- http://www.consumerfinance.gov/eregulations/1026-J/2013-30108_20150718#1026-J-b-4-i
- http://www.gpo.gov/fdsys/pkg/CFR-2015-title12-vol3/pdf/CFR-2015-title12-vol3-part226-appJ.pdf
- https://en.wikipedia.org/wiki/Truth_in_Lending_Act
- http://www.occ.gov/publications/publications-by-type/comptrollers-handbook/truth-in-lending-handbook.pdf
- APRWIN Download – http://www.occ.gov/tools-forms/tools/compliance-bsa/aprwin-software.html

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