The terms annual percentage of rate (APR) , nominal APR , and effective APR (EAR) describe the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loan, mortgage, credit 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 general:
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 in short, 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).
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. When not using the term "effective APR", the use of "APR" is an early term for nominal APR . 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. APR is intended to make it easier to compare lenders and loan options. The APR is likely to differ from the "note rate" or "headline rate" advertised by the lender, due to the addition of other fees that may need to be included in the APR. APRs can be found by asking the lender or by reading the appropriate section in the contract.
In the U.S. and the UK, lenders are required to disclose the APR before the loan (or credit application) is finalized (although the definition of "APR" is not the same in the two countries-–see below). Credit card companies can advertise monthly interest rates, but they are required to clearly state the annual percentage rate before an agreement is signed. APR is a term used with regard to deposit accounts as well. However, when dealing with deposit accounts, the annual percentage yield (APY) or annual equivalent rate (AER) is quoted to consumers for comparison purposes.
Multiple definitions of effective APR
There are at least three ways of computing effective APR:
- 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, at 5% interest, plus a $10 fee. If the fee is neglected, this loan has a (year-long) effective APR of approximately 79% (1.05^12 =~1.7958). If the $10 fee were considered, the interest increases by 10% ($10/$100) for the month, with the effective APR being approximately 435% (1.15^12 =~5.3502, as 535%-100%=435%). Hence there are at least two possible "effective APRs": 79% and 435%.
Additional considerations
Confusion is possible in that if the word "effective" is used separately as meaning "influential" or having a "long-range effect", then the term effective APR will vary as being an expression, rather than a strict legal definition.
More confusion is possible in that when APR is treated as an abbreviation for the word "April" (4th month), then the term "effective APR" means "going into effect in April" (as a very common legal definition for the separate word "effective").
Still more confusion is possible in that the compound period affects the calculation of effective APR: for example, monthly compounding is different from daily compounding. Some credit cards compound interest daily even though payments are due monthly. (See "Dependence on loan period", below.)
Rate format
An effective annual interest rate of 10% can also be expressed in several ways:
- 0.7974% effective monthly interest rate, because 1.007974^12=1.1
- 9.569% annual interest rate compounded monthly, because 12*0.7974=9.569
- 9.091% annual rate in advance, because 1/1.1=1-0.091
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. This can be expressed mathematically by
This also explains why a 15 year mortgage and a 30 year mortgage with the same APR would have different monthly payments and a different total amount of interest paid. There are many more periods over which to spread the principal, which makes the payment smaller, but there are just as many periods over which to charge interest at the same rate, which makes the total amount of interest paid much greater. For example, $100,000 mortgaged (without fees, since they add into the calculation in a different way) over 15 years costs a total of $193,429.80 (interest is 93.430% of principal), but over 30 years, costs a total of $315,925.20 (interest is 215.925% of principal).
In addition the APR takes costs into account. Suppose for instance that $100,000 is borrowed with $1000 one-time fees paid in advance. If, in the second case, equal monthly payments are made of $946.01 against 9.569% compounded monthly then it takes 240 months to pay the loan back. If the $1000 one-time fees are taken into account then the yearly interest rate paid is effectively equal to 10.31%.
The APR concept can also be applied to savings accounts: imagine a savings account with 1% costs at each withdrawal and again 9.569% interest compounded monthly. Suppose that the complete amount including the interest is withdrawn after exactly one year. Then, taking this 1% fee into account, the savings effectively earned 8.9% interest that year.
Money factor
The APR can also be represented by a money factor (also known as the lease factor, lease rate, or factor). The money factor is usually given as a decimal, for example .0030 . To find the equivalent APR, the money factor is multiplied by 2400. A money factor of .0030 is equivalent to a monthly interest rate of 0.6% and an APR of 7.2%.
For a leasing arrangement with an initial capital cost of C , a residual value at the end of the lease of F and a monthly interest rate of r , monthly interest starts at Cr and decreases almost linearly during the term of the lease to a final value of Fr . The total amount of interest paid over the lease term of N months is therefore
and the average interest amount per month is
This amount is called the "monthly finance fee". The factor r /2 is called the "money factor"
Failings
Despite repeated attempts by regulators to establish usable and consistent standards, APR does not represent the total cost of borrowing nor does it really create a comparable standard. Nevertheless, it is considered a reasonable starting point for an ad-hoc comparison of lenders.
Nominal APR does not reflect the true cost
Credit card holders should be aware that most U.S. credit cards are quoted in terms of nominal APR compounded monthly, which is not the same as the effective annual rate (EAR). Despite the “Annual” in APR, it is not necessarily a direct reference for the interest rate paid on a stable balance over one year. The more direct reference for the one-year rate of interest is EAR. The general conversion factor for APR to EAR is
, where n represents the number of compounding periods of the APR per EAR period. As an example, for a common credit card quoted at 12.99% APR compounded monthly, the one year EAR is
, or 13.7975%. For 12.99% APR compounded daily, the EAR paid on a stable balance over one year becomes 13.87% (see credit card interest for the .000
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