Overview

In some areas, the annual percentage rate (APR) is the simplified counterpart to the effective interest rate that the borrower will pay on a loan. In many countries and jurisdictions, lenders (such as banks) are required to disclose the "cost" of borrowing in some standardized way as a form of consumer protection. The (effective) APR has been intended to make it easier to compare lenders and loan options.

Multiple definitions of effective APR

The nominal APR is calculated by multiplying the interest rate for a payment period by the number of payment periods in a year. However, the exact legal definition of "effective APR", or EAR, can vary greatly in each jurisdiction, depending on the type of fees included, such as participation fees, loan origination fees, monthly service charges, or late fees. The effective APR has been called the "mathematically-true" interest rate for each year.

The computation for the effective APR, as the fee + compound interest rate, can also vary depending on whether the up-front fees, such as origination or participation fees, are added to the entire amount, or treated as a short-term loan due in the first payment. When start-up fees are paid as first payment(s), the balance due might accrue more interest, as being delayed by the extra payment period(s).

For example, consider a $100 loan which must be repaid after one month, plus 5%, plus a $10 fee. If the fee is not considered, this loan has an effective APR of approximately 80% (1.05^(12) = 1.7959, which is approximately an 80% increase). If the $10 fee were considered, the monthly interest increases by 10% ($10/$100), and the effective APR becomes approximately 435% (1.15^(12) = 5.3503, which equals a 435% increase). Hence there are at least two possible "effective APRs": 80% and 435%. Laws vary as to whether fees must be included in APR calculations.

United States

In the United States, the Truth in Lending Act governs the calculation and disclosure of APR, implemented by the Consumer Financial Protection Bureau (CFPB) through Regulation Z. In general, APR in the United States is expressed as the periodic (for instance, monthly) interest rate times the number of compounding periods in a year (also known as the nominal interest rate); since the APR must include certain non-interest charges and fees, it requires more detailed calculation. The APR must be disclosed to the borrower within 3 days of applying for a mortgage.

This information is typically mailed to the borrower and the APR is found on the truth in lending disclosure statement, which also includes an amortization schedule.

On July 30, 2009, provisions of the Mortgage Disclosure Improvement Act of 2008 (MDIA) came into effect. A specific clause of this act refers directly to APR disclosure on mortgages. It states, if the final annual percentage rate APR is off by more than 0.125% from the initial GFE disclosure, then the lender must re-disclose and wait another three business days before closing on the transaction.

The calculation for "close-ended credit" (such as a home mortgage or auto loan) can be found here. For a fixed-rate mortgage, the APR is thus equal to its internal rate of return (or yield) under an assumption of zero prepayment and zero default. For an adjustable-rate mortgage the APR will also depend on the particular assumption regarding the prospective trajectory of the index rate.

European Union

The European Union's APR standardization focuses on transparency and consumer rights: «a comprehensible set of information to be given to consumers in good time before the contract is concluded and also as part of the credit agreement [...] every creditor has to use this form when marketing a consumer credit in any Member State» so marketing different figures is not allowed.

The EU regulations were reinforced with directives 2008/48/EC and 2011/90/EU, fully in force in all member states since 2013. However, in the UK the EU directive has been interpreted as the Representative APR.

In this equation the left side is the present value of the drawdowns made by the lender and the right side is the present value of the repayments made by the borrower. In both cases the present value is defined given the APR as the interest rate. So the present value of the drawdowns is equal to the present value of the repayments, given the APR as the interest rate.

Rate format

These rates are all equivalent, but to a consumer who is not trained in the mathematics of finance, this can be confusing. APR helps to standardize how interest rates are compared, so that a 10% loan is not made to look cheaper by calling it a loan at "9.1% annually in advance".

The APR does not necessarily convey the total amount of interest paid over the course of a year: if one pays part of the interest prior to the end of the year, the total amount of interest paid is less.

In the case of a loan with no fees, the amortization schedule would be worked out by taking the principal left at the end of each month, multiplying by the monthly rate and then subtracting the monthly payment.