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Investment Dictionary:

Annual Percentage Rate - APR

The annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number that represents the actual yearly cost of funds over the term of a loan. This includes any fees or additional costs associated with the transaction.

Investopedia Says:
Loans or credit agreements can vary in terms of interest-rate structure, transaction fees, late penalties and other factors. A standardized computation such as the APR provides borrowers with a bottom-line number they can easily compare to rates charged by other potential lenders.

By law, credit card companies and loan issuers must show customers the APR to facilitate a clear understanding of the actual rates applicable to their agreements. Credit card companies are allowed advertise interest rates on a monthly basis (e.g. 2% per month), but are also required to clearly state the APR to customers before any agreement is signed. For example, a credit card company might charge 1% a month, but the APR is 1% x 12 months = 12%. This differs from annual percentage yield, which also takes compound interest into account.

Related Links:
Find out why time really is money by learning to calculate present and future value. Understanding The Time Value Of Money
Learn and ensure the different rates quoted to you by banks and institutions are what they claim to be. APR vs. APY: How the Distinction Affects You
Learn the factors to consider when comparing the different programs offered by various lenders. Home-Equity Loans: The Costs


 
 
Banking Dictionary: Annual Percentage Rate (APR)

Effective cost of credit in consumer loans and real estate loans expressed as a percentage rate. The annual percentage rate is the finance charge the borrower actually pays, including loan Interest points, and origination fees.

The Federal Truth in Lending Act of 1968 requires lenders to calculate the cost of credit as an annual percentage and disclose the APR in large bold type in loan application documents. APR rates and the dollar amount (principal and interest) for various fixed-rate amortizing loans can be found in APR tables available from the Federal Reserve Board. See alsoAdd-on Interest; Effective Rate; Nominal Interest Rate; Simple Interest.

 
Real Estate Dictionary: Annual Percentage Rate

The effective rate of interest for a loan per year, disclosure of which is required by the Truth-In-Lending Law. See Yield to Maturity, Regulation Z.
Example: Abel gets a loan for $50,000 at 8% interest plus 2 Discount Points payable over 30 years. Because of the discount points $49,000 has been effectively borrowed but $50,000 must be repaid with 8% interest on $50,000. Considering the effective amount borrowed, the annual percentage rate is 8.21%.

 
Small Business Encyclopedia: Annual Percentage Rate (APR)

The annual percentage rate (APR) is the effective rate of interest that is charged on an installment loan, such as those provided by banks, retail stores, and other lenders. Since the enactment of the Truth in Lending Act in 1969, lenders have been required to report the APR in boldface type on the first page of all loan contracts. The truth in lending law "requires lenders to disclose in great detail the terms and conditions that apply to consumers when they borrow," according to an article in United States Banker. "Its purpose was to allow consumers to shop for credit by comparing the fine print." In the absence of such requirements, it would conceivably be possible for a lender to misrepresent a loan with a 20 percent effective interest rate as a 10 percent loan. However, the APR can be calculated in different ways and can sometimes cause rather than eliminate confusion.

Loans and Interest Rates

A loan is the purchase of the present use of money with the promise to repay the amount in the future according to a pre-arranged schedule and at a specified rate of interest. Loan contracts formally spell out the terms and obligations between the lender and borrower. Loans are by far the most common type of debt financing used by small businesses. The interest rate charged on the borrowed funds reflects the level of risk that the lender undertakes by providing the money. For example, a lender might charge a startup company a higher interest rate than it would a company that had shown a profit for several years. The interest rate also tends to be higher on smaller loans, since lenders must be able to cover the fixed costs involved in making the loans.

The lowest interest rate charged by lenders—which is offered only to firms that qualify on the basis of their size and financial strength—is known as the prime rate. All other types of loans feature interest rates that are scaled upward from the prime rate. Interest rates vary greatly over time, depending on the policies set forth by the Federal Reserve Board as well as prevailing economic conditions in the nation. For all but the simplest of loans, the nominal or stated rate of interest may differ from the annual percentage rate or effective rate of interest. These differences occur because loans take many forms and cover various time periods. The effect of compounding and the addition of fees may also affect the APR of a loan.

Calculating the Apr

The effective rate of interest on a loan can be defined as the total interest paid divided by the amount of money received. For simple interest loans—in which the borrower receives the face value of the loan and repays the principal plus interest at maturity—the effective rate and the nominal rate are usually the same. As an example, say that a small business owner borrows $10,000 at 12 percent for 1 year. The effective rate would thus be $1,200 /$10,000 12 percent, the same as the stated rate.

But the effective rate would be slightly different for a discount interest loan, wherein the interest is deducted in advance so the borrower actually receives less than the face value. Using the same example, the small business owner would pay the $1,200 interest up front and receive $8,800 upon signing the loan contract. In this case, the effective interest rate would be $1,200 /$8,800 13.64 percent.

The most problematic differences between the nominal and effective rates of interest occur with installment loans. In this type of loan, the interest is calculated based on the nominal rate and added back in to get the face value of the loan. The loan amount is then repaid in equal installments during the loan period. Using the same example, the small business owner would sign for a loan with a face value of $11,200 and would receive $10,000. Since the loan is repaid in monthly installments, however, the business owner would not actually have use of the full loan amount over the course of the year. Instead, assuming 12 equal installments, the business owner would actually have average usable funds from the loan of $5,000. The effective rate of the loan is thus $1,200 /$5,000 24 percent, twice the stated rate of the loan.

True APR calculations should also include any up-front fees or penalties that are applied to a loan. These amounts are totaled and added to the interest figure. In the case of mortgage loans, such charges can be significant. They might include a mortgage insurance premium, points, lost interest earnings on escrow accounts, and prepayment penalties, for example.

Further Reading:

Brigham, Eugene F. Fundamentals of Financial Management. Dryden Press, 1989.

Eaglesham, Jean. "APRs Daze and Confuse." Financial Times. April 16, 1997.

Heath, Gibson. Doing Business with Banks: A Common Sense Guide for Small Business Borrowers. Lakewood, CO: DBA/USA Press, 1991.

Lee, Jinkook, and Jeanne M. Hogarth. "The Price of Money: Consumers' Understanding of APRs and Contract Interest Rates." Journal of Public Policy and Marketing. Spring 1999.

"Preparing for Truth in Savings." United States Banker. November 1992.

 
Law Encyclopedia: Annual Percentage Rate
This entry contains information applicable to United States law only.

The actual cost of borrowing money, expressed in the form of a yearly measure to allow consumers to compare the cost of borrowing money among several lenders.

The Federal Truth-in-Lending Act (15 U.S.C.A. § 1601 et seq. [1968]) mandates the complete disclosure of this rate in addition to other credit terms.

See: truth-in-lending act.

 
Wikipedia: annual percentage rate

Annual Percentage Rate (APR) is an expression of the effective interest rate that the borrower will pay 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, due to the addition of other fees that may need to be included in the APR.

In the US and the UK, lenders are required to disclose the APR before the loan (or credit application) is finalized. 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 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 does not necessarily convey the total amount of interest paid over the course of a year. APR, in the simple case of a loan with no fees (or, say, a credit card), is the monthly interest rate multiplied by 12.

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


p = \cfrac{P_0*r^{(n+1)}}{\sum_{l=1}^n r^n}
where:
P0 is the initial principal
r is the percentage rate used each payment
n is the number of payments


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.

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:

Generally included:

Sometimes included:

Generally not included:

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.

Interest-only loans

Since the principal loan balance is not paid down during the interest-only term, the total interest paid over the lifetime of the loan is increased and the APR is higher than a loan without an interest-only payment period.

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). In general, APR in the United States is expressed as the periodic interest rate times the number of compounding periods in a year[1] (also known as the nominal interest rate); since the APR must include certain non-interest charges and fees, however, requiring more detailed calculation.

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.

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:

\sum_{l=1}^M S_l (1 + APR/100)^{-t_l} = \sum_{k=1}^N A_k (1 + APR/100)^{-t_k}
where:
M is the number of cash flows paid by the lender
l is the sequence number for the cash flows paid by the lender (draw down)
Sl is the cash flow (drawdown) in period l
N is the total number of cash flows paid by the borrower
k is the sequence number of the cash flows paid by the borrower (repayment)
Ak is the cash flow (repayment) of period k, and
tl and tk 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 l or k. (t1 = 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.[1]

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 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:

S -A = R (1 + APR/100)^{-t_N} + \sum_{k=1}^N A_k (1 + APR/100)^{-t_k}
where:
S is the borrowed amount
A is the prepaid onetime fee
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 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 APR must be more prominent than any other rate or charge.

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 'Z') 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

References

  1. ^ http://www.uncdf.org/mfdl/readings/EIR_Tucker.pdf Tucker, William R. "Effective Interest Rate," Paper, Bankakademie Micro Banking Competence Center, 5-6 September 2000.

External links


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Investment Dictionary. Copyright ©2000, Investopedia.com - Owned and Operated by Investopedia Inc. All rights reserved.  Read more
Banking Dictionary. Dictionary of Banking Terms. Copyright © 2006 by Barron's Educational Series, Inc. All rights reserved.  Read more
Real Estate Dictionary. Dictionary of Real Estate Terms. Copyright © 2004 by Barron's Educational Series, Inc. All rights reserved.  Read more
Small Business Encyclopedia. Encyclopedia of Small Business. Copyright © 2002 by The Gale Group, Inc. All rights reserved.  Read more
Law Encyclopedia. West's Encyclopedia of American Law. Copyright © 1998 by The Gale Group, Inc. All rights reserved.  Read more
Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Annual percentage rate".  Read more

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