How can I calculate the annual percentage rate of a loan?

Problem

Sometimes the annual percentage rate (APR) of a loan needs to be calculated to compare different alternatives.

The APR is meant to be a common measure so that consumers can compare different loans effectively. However, depending on where you live, legislators have defined the APR in different ways. FinFlow allows APR calculations according to European legislation, and in some cases, according to U.S. legislation.

Section 226.14 of the Truth in Lending Act (Regulation Z) defines the annual percentage rate as a measure of the cost of credit, expressed as a yearly rate. Furthermore Appendix J—Annual Percentage Rate Computations For Closed-End Credit Transactions of the Truth in Lending Act describes methods to calculate the APR in a variety of cases.

The Office of the Comptroller of the Currency (OCC) has provided a Windows based program that lets you calculate the APR using the formulas defined in the Truth in Lending Act.

In most cases, it's possible to calculate the APR using FinFlow:

When there are regular or irregular payments at regular intervals or at intervals that are a multiple of the smallest interval (unit period), it's possible to obtain the same results as the OCC calculator, provided that you switch to the compounding frequency that corresponds with the payment frequency (annually, monthly, etc.).

When there are odd days (e.g. with a short or long first period), results remain are the same as with the OCC calculator, als long as the interval is monthly or less. For bimonthly up to annually (or more) results differ due to a different way of treating stub periods of more than a month.

Europe

The APR is calculated using methods described in Directive 98/7/EC (click to download) of the European Parliament and of the Council of 16 February 1998 amending Directive 87/102/EEC for the approximation of the laws, regulations and administrative provisions of the Member States concerning consumer credit.

These methods determine the APR as the annually compounded rate, which equalizes the present values of all commitments agreed upon by the creditor and the borrower.

To calculate the APR using FinFlow, all you need to do is set up the cash flow with the actual loan and payment amounts and their respective dates, then switch to annual compounding: the IRR result will indicate the APR of the loan.

Settings

To calculate the APR according to U.S. legislation, set the compute method to Actuarial interest and the payment frequency to the frequency that occurs most frequently.

Set the year length so that it corresponds with the payment frequency in order to ensure that odd days are calculated correctly: for weekly or biweekly intervals, use 364 as the year lenghth, for month based frequencies and day based frequencies, use 365. If there are no odd days then 360 usually produces the same results as the 365 day setting.

To calculate the APR according to European legislation, set the compute method to Compound interest and always set the payment frequency to annually regardless of the actual payment frequency.

Please note that "Calendar basis" corresponds with FinFlow's act/act day count and "Standard year" basis corresponds with the 30/360 day count.

Note: for maximum accuracy, set the rounding for amounts to "no rounding" and the rounding for percentages to four digits.

Examples

Included with the FinFlow download are a few examples that show you how you would calculate the examples given in the Directive 98/7/EC (Europe) and in Section 226.14 of the Truth in Lending Act.

Please note that the examples that produce different results have intervals of more than a month (e.g. US examples 4_2, 5_3 and 7_2)

Comment

The European approach enables any situation to be compared on the same base, i.e. the annually compounded rate that makes all outflows equal the inflows. As the U.S. method produces nominal annual rates that correspond to the payment frequencies, you may still need to convert them to the corresponding annual rate to be able to compare them effectively.