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Annual percentage rate

The term annual percentage rate of charge (APR), corresponding sometimes to a nominal APR and sometimes to an effective APR (EAPR), is the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loanmortgage loancredit card, etc. It is a finance charge expressed as an annual rate. Those terms have formal, legal definitions in some countries or legal jurisdictions, but in the United States:

  • The nominal APR is the simple-interest rate (for a year).
  • The effective APR is the fee+compound interest rate (calculated across a year).

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 as: the rate, for a payment period, multiplied 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.[5][6]

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).

There are at least three ways of computing effective annual percentage rate:

  • by compounding the interest rate for each year, without considering fees;
  • origination fees are added to the balance due, and the total amount is treated as the basis for computing compound interest;
  • the origination fees are amortized as a short-term loan. This loan is due in the first payment(s), and the unpaid balance is amortized as a second long-term loan. The extra first payment(s) is dedicated to primarily paying origination fees and interest charges on that portion.

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% (1.0512 = 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% (1.1512 = 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 U.S., the calculation and disclosure of APR is governed by the Truth in Lending Act (which is implemented by the Consumer Financial Protection Bureau (CFPB) in Regulation Z of the Act). 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.

The calculation for “open-ended credit” (such as a credit card, home equity loan or other line of credit) can be found here.

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