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Annual Percentage Rate (APR) is an expression of the effective interest rate that will be paid on a loan, taking into account one-time fees and standardizing the way the rate is expressed. In other words the APR is the total cost of credit to the consumer expressed as an annual percentage of the amount of credit granted. 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. The concept of APR can be generalized. For example lenders use the same concept to calculate their total earnings on loans and for determining their margin on the loan. Consumers can use the APR concept to compare savings accounts and calculate the earnings on a savings account, taking transaction costs into account.

In the US and the UK, lenders are required to disclose the APR before the loan (or credit application) is finalized. APR is a term used with regards to deposit accounts as well. However, when dealing with deposit accounts, Annual Percentage Yield APY or Annual Equivalent Rate AER is the number to be quoted to consumers for comparison purposes.

Rate format

An effective annual interest rate of 10% can also be expressed in several ways:

• 0.7974% effective monthly interest rate
• 9.569% annual interest rate compounded monthly
• 9.091% annual rate in advance.

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 also takes into account when a loan is paid back. Suppose a loan of $100,000 is paid back in 12 monthly terms of $8771.56. Then at the end of the year a total of $105,258.72 has been paid. The APR is not, however, 5.26% but 10% because the principal amount has been paid back earlier: throughout the year instead of at the end of the year.

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.

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.

Does not represent the total cost of borrowing

Credit card holders should be aware that most US 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 EAR=((1+APR/n)^n)-1, where n represents the number of compounding periods of the APR per EAR period. E.g., for a common credit card quoted at 12.99% APR compounded monthly, the one year EAR is (1+.129949/12)^12-1, or 13.7975% (see Credit card interest for the .000049 addition to the 12.99% APR). Note that a high US APR of 29.99% carries an effective annual rate of 34.48%.

While the difference between APR and EAR may seem trivial, because of the exponential nature of interest these small difference can have a large effect over the life of a loan. For example, consider a 30-year loan of $200,000 with a stated APR of 10.00%, i.e., 10.0049% APR or the EAR equivalent of 10.4767%. The monthly payments, using APR, would be $1755.80. However, using an EAR of 10.00% the monthly payment would be $1691.78. The difference between the EAR and APR amounts to a difference of $64.09 per month. Over the life of a 30-year loan, this amounts to $23,070.90, which is over 11% of the original loan amount.

Some classes of fees are deliberately not included in the calculation of APR. Because these fees are not included, some consumer advocates claim that the APR does not represent the total cost of borrowing. Excluded fees may include:

• routine one-time fees which are paid to someone other than the lender (such as a real estate attorney's fee)
• penalties such as late fees or service reinstatement fees without regard for the size of the penalty or the likelihood that it will be imposed.

Lenders argue that the real estate attorney's fee, for example, is a pass-through cost, not a cost of the lending. In effect, they are arguing that the attorney's fee is a separate transaction and not a part of the loan. Consumer advocates argue that this would be true if the customer is free to select which attorney is used. If the lender insists on using a specific attorney however, then the cost should be looked at as a component of the total cost of doing business with that lender. This area is made more complicated by the practice of contingency fees - for example, when the lender receives money from the attorney and other agents to be the one used by the lender. Because of this, US regulators require all lenders to produce an affiliated business disclosure form which shows the amounts paid between the lender and the appraisal firms, attorneys, etc.

Lenders argue that including late fees and other conditional charges would require them to make assumptions about the consumer's behavior — assumptions which would bias the resulting calculation and create more confusion than clarity.

Not a comparable standard

Even beyond the non-included cost components listed above, regulators have been unable to completely define which one-time fees must be included and which excluded from the calculation. This leaves the lender with some discretion to determine which fees will be included (or not) in the calculation.

Consumers can, of course, use the Nominal interest rate and any costs on the loan (or savings account) and compute the APR themselves, for instance using one of the calculators on the internet.

In the example of a mortgage loan, the following kinds of fees are:

The discretion that is illustrated in the "sometimes included" column even in the highly regulated US home mortgage environment makes it difficult to simply compare the APRs of two lenders. Note: US regulators generally require a lender to use the same assumptions and definitions in their calculation of APR for each of their products even though they cannot force consistency across lenders.

With respect to items that may be sold with vendor financing, for example, automobile leasing, the notional cost of the good may effectively be hidden and the APR subsequently rendered meaningless. An example is a case where an automobile is leased to a customer based on a "manufacturer's suggested retail price" with a low APR: the vendor may be accepting a lower lease rate as a trade-off against a higher sale price. Had the customer self-financed, a discounted sales price may have been accepted by the vendor; in other words, the customer has received cheap financing in exchange for paying a higher purchase price, and the quoted APR understates the true cost of the financing. In this case, the only meaningful way to establish the "true" APR would involve arranging financing through other sources, determining the lowest-acceptable cash price and comparing the financing terms (which may not be feasible in all circumstances). For leases where the lessee has a purchase option at the end of the lease term, the cost of the APR is further complicated by this option. In effect, the lease includes a put option back to the manufacturer (or, alternatively, a call option for the consumer), and the value (or cost) of this option to the consumer is not transparent.

Dependence on loan period

APR is dependent on the time period for which the loan is calculated. That is, the APR for one loan with a 30 year duration loan cannot be compared to the APR for another loan with a 20 year loan duration. APR can be used to show the relative impact of different payment schedules (such as balloon payments or bi-weekly payments instead of straight monthly payments), but most standard APR calculators have difficulty with those calculations.

Furthermore, most APR calculators assume that an individual will keep a particular loan until it is completely paid off resulting in the up-front fixed closing costs being amortized over the full term of the loan. If the consumer pays the loan off early, the effective interest rate achieved will be significantly higher than the APR initially calculated. This is especially problematic for mortgage loans where typical loan durations are 15 or 30 years but where many borrowers move or refinance before the loan period runs out.

In theory, this factor should not affect any individual consumer's ability to compare the APR of the same product (same duration loan) across vendors. APR may not, however, be particularly helpful when attempting to compare different products.

Non-repeatable

Two lenders with identical information may still calculate different APRs. The calculations can be quite complex and are poorly understood even by most financial professionals. Most users depend on software packages to calculate APR and are therefore dependent on the assumptions in that particular software package. While differences between software packages will not result in large variations, there are several acceptable methods of calculating APR, each of which returns a slightly different result.

Region-specific details

USA

In the US, the calculation and disclosure of APR is governed by the Truth in Lending Act (also known as Regulation Z). The calculation for "close-ended credit" (such as a home mortgage or auto loan) can be found here. The calculation for "open-ended credit" (such as a credit card, home equity loan or other line of credit) can be found here.

• Office of the Comptroller of the Currency APR Calculation Software

European Union

In the EU, the focus of APR standardization is heavily on the standardization of the time-value of the interest calculation. As of Oct 2005, the EU still allows Member States to determine the specific cost-components to be included in the APR calculation. A single method of calculating the APR was introduced in directive 98/7/EC and is required to be published for the major part of loans. The basic equation for calculation of APR in the EU is:

${\displaystyle \sum _{l=1}^{M}S_{l}(1+APR/100)^{-t_{l}}=\sum _{k=1}^{N}A_{k}(1+APR/100)^{-t_{k}}}$

where:

${\displaystyle M}$ is the number of cash flows paid by the lender

${\displaystyle l}$ is the sequence number for the cash flows paid by the lender (draw down)

${\displaystyle S_{l}}$ is the cash flow (drawdown) in period ${\displaystyle l}$

${\displaystyle N}$ is the total number of cash flows paid by the borrower

${\displaystyle k}$ is the sequence number of the cash flows paid by the borrower (repayment)

${\displaystyle A_{k}}$ is the cash flow (repayment) of period ${\displaystyle k}$, and

${\displaystyle t_{l}}$ and ${\displaystyle t_{k}}$ is the interval, expressed in years and fractions of a year between the date of the first cash flow and the date of cash flow ${\displaystyle l}$ or ${\displaystyle k}$. (${\displaystyle t_{1}}$ = 0.)

In this equation the left side is the present value (PV) of the draw downs 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.

Note that neither the amounts nor the periods between transactions are necessarily equal. For the purposes of this calculation, a year is presumed to have 365 days (366 days for leap years), 52 weeks or 12 equal months. An equal month is presumed to have 30.41666 days regardless of whether or not it is a leap year. The result is to be expressed to at least one decimal place. This algorithm for APR is required for some but not all forms of consumer debt in the EU. For example, this EU directive is limited to agreements of €50,000 and below and excludes all mortgages.

In the Netherlands the formula above is also used for mortgages. In many cases the mortgage is not always paid back completely at the end of period ${\displaystyle N}$, but for instance when the borrower sells his house or dies. In addition there is usually only one payment of the lender to the borrower: in the beginning of the loan. In that case the formula becomes:

${\displaystyle S-A=R(1+APR/100)^{-t_{N}}+\sum _{k=1}^{N}A_{k}(1+APR/100)^{-t_{k}}}$

where:

${\displaystyle S}$ is the borrowed amount

${\displaystyle A}$ is the prepaid onetime fee

${\displaystyle R}$ the rest debt, the amount that remains as an interest-only loan after the last cash flow.

If the length of the periods are equal (monthly payments) then the summations can be simplified using the formula for a geometric series. Either way the APR can only be solved iteratively from the formulas above, apart from trivial cases such as ${\displaystyle N=1}$.

UK

APR was introduced under the Consumer Credit Act 1974, to ensure comparability of loans - and is required to be published for all regulated loans.

• The leaflet Credit charges and APR from the Office of Fair Trading
• The APR and rebate calculator from the Office of Fair Trading

The method used to calculate APRs in the EU and UK is different from that used in the US and will often produce different (higher) results. This is because the US method (regulation 'Zee') produces what would, in the UK, be called a nominal annual rate whereas the UK/EU method results in an effective annual rate.

See also

• Nominal interest rate
• Compound interest

External links

• Interest Rates: An Introduction. Federal Reserve Bank of New York.

• Banking
• Personal finance
• Interest rates
• Mathematical finance