Business
Annual Percentage Rate (APR)
The Annual Percentage Rate (APR) represents the annual cost of borrowing, including interest and fees, expressed as a percentage. It is a standardized way of comparing the cost of loans or credit cards. Lenders are required to disclose the APR to borrowers, providing transparency and enabling them to make informed financial decisions.
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6 Key excerpts on "Annual Percentage Rate (APR)"
eBook - ePubMultiple Interest Rate Analysis
Theory and Applications
- M. Osborne(Author)
- 2014(Publication Date)
- Palgrave Pivot(Publisher)
... What distinguishes the APR from other cost measures is that it puts the credit, its costs and time together, thus recognizing that these three elements are relevant in determining a comparable and uniform measure of the cost of the credit. In this way, the APR presents significant advantages over other measures of cost.... Compared to a simple rate, ... [APR] ... has in its favour the primacy of compound interest in finance and economics, a greater interpretability and a higher adaptation to situations where the amount of the credit varies, and the payments might adopt different and diverse patterns, as happens in consumer credit agreements. (Directorate General for Health and Consumer Protection (2009, p. 8)2It is argued below that this conventional interpretation is not entirely correct. The relative merits of the simple rate of interest and APR are most effectively compared within a single equation containing both rates of interest. To the author’s knowledge no equation containing both rates has been identified in the financial literature. The remainder of this chapter derives and analyzes such an equation. The equation demonstrates that the connection between APR and the simple rate is more subtle and powerful than conventional financial theory allows and that the simple rate of interest is a superior policy variable to APR.4.3 A deeper analysis of APR and the FCWhen comparing loans of different amounts and terms, the FC normalized by loan amount and term is more meaningful than the FC alone. When both sides of the expression for the FC are divided by the principal amount(C 0
eBook - PDF- Mary Jane Sterling, Benjamin Schultz(Authors)
- 2008(Publication Date)
- For Dummies(Publisher)
If you aren’t in the position to pay cash or borrow more money from a bank, the installment plan allows you the use of the mer-chandise immediately. Calculating the annual percentage rate The APR isn’t something that’s widely broadcast on many installment loan contracts; you’ll see the stated interest amount, but the APR takes a little more figuring. It takes into account the effects of compounding and any fees and extra charges. If you’ve ever tried to find a formula for determining APR, you’ve probably discovered that it’s difficult to find one. Most Web sites just want to do the calculations for you. It must be assumed that you really don’t want to tackle a formula or that it’s beyond your capabilities. Well, I know better than that! Of course you want to do the math! The best formula I’ve found is a variation on Steve Slavin’s formula in Business Math (Wiley). Here it is: APR P n m P n m Prt n mrt 1 2 1 2 1 2 finance charge = + = + = + ^ _ ^ ^ h i h h where m is the number of payments made each year, P is the principal or amount borrowed, r is the interest rate, t is the number of years involved, and n is the total number of payments to be made. After you determine your vari-ables, you’re all set to plug in and solve. Try out an example. 174 Part III: Discovering the Math of Finance and Investments What’s the APR of a loan for $6,000 for 2 years at 10.125% interest with monthly payments? The number of payments per year, m , is 12; the interest rate, r , is 10.125, or 0.10125; the amount of time, t , is 2; and the number of payments, n , is 2 × 12 = 24. Plugging these numbers into the formula for APR and solving gives you an answer: . . . APR n mrt 1 2 24 1 2 12 0 10125 2 25 4 86 0 1944 = + = + = = ^ ^ ^ h h h The APR of 19.44% is much higher than the stated interest rate of 10.125%. You don’t have any choice on the rate — the APR is what’s used in the com-putations. You just need to know what you’re getting into when you agree to a particular stated rate.
- James Deitz, James Southam(Authors)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
The most recent major protection legislation is the Wall Street Reform and Consumer Protection Act of 2010 (the Dodd-Frank bill) which has established the Consumer Financial Protection Bureau (CFPB). It is an independent bureau within the Federal Reserve System, officially started in mid-2011, and is expected to consolidate the regulatory responsibilities and some employees of several agencies, including those mentioned. A major objective is to have all the important consumer protection functions controlled from one powerful, independent agency. Our study in Chapter 14 is an introduction to calculating the costs of borrowing on in-stallment purchases. One part of the earliest legislation still has particular significance for us. Title 1 of the original 1968 act is known as the Truth in Lending Act (TILA) . Among several mandates, TILA requires creditors (lenders) to tell consumers (borrowers) these three things: 1. The total of all finance charges, including interest, carrying charges, insurance, and special fees 2. The annual percentage rate (APR) of the total finance charge 3. The method by which they compute the finance charge As noted in the previous section, an annual interest rate is a monthly interest rate multiplied by 12. However, as the term is used in TILA, the annual percentage rate (APR) is a specific, defined term that must include all finance charges, not just interest. Furthermore, under TILA, lenders are permitted to use more than one method to compute the APR. Lenders may even use either a 360-day year or a 365-day year. TILA does not set limits on rates. Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.
- Pamela Peterson Drake, Frank J. Fabozzi(Authors)
- 2009(Publication Date)
- Wiley(Publisher)
The basic concept underlying the time value of money is that when you invest, you are compensated for the time value of money and risk, and when you borrow, you must pay enough to compensate the lender for the time value of money and risk. Situations arise often in which we wish to determine the interest rate that is implied from an advertised or stated rate. There are also cases in which we wish to determine the rate of interest implied from a set of payments in a loan arrangement.ANNUALIZED RATES OF INTEREST
A common problem in finance is comparing alternative financing or investment opportunities when the interest rates are stated in a way that makes it difficult to compare terms. One lending source may offer terms that specify 9.25% annual percentage rate (APR), with interest compounding annually, whereas another lending source may offer terms of 9% APR with interest compounding continuously. How do you begin to compare these rates to determine which is a lower cost of borrowing? Ideally, we would like to translate these interest rates into some comparable form.One obvious way to represent rates stated in various time intervals on a common basis is to express them in the same unit of time—so we annualize them. To annualize a rate is to put it on an annual basis. Supposedly, if you put all the terms on the same, annual basis, they should be comparable. Right? Wrong.There are two approaches to annualizing rates: the simple way, resulting in an APR, and the more complex way, resulting in an effective annual rate (EAR). These are both annualized rates, but they provide different information.Annual Percentage Rate
In Chapters 1 and 2, we showed you how we use the APR for compounding and discounting when interest compounds more frequently than annually. We look at the APR here to set the stage for determining the EAR, the effective annual rate.Suppose a bank is willing to lend to you at the rate of 12% APR, with interest compounded monthly. What does this really mean in terms of what you end up paying? It means that you are paying 12% ÷ 12 = 1% each month and that interest compounds 12 times a year. Let’s put this into an equation. Let i be the rate of interest per period and let n be the number of compounding periods in a year. The annualized rate, also referred to as the nominal interest rate
eBook - ePubEssential Personal Finance
A Practical Guide for Students
- Lien Luu, Jonquil Lowe, Jason Butler, Tony Byrne(Authors)
- 2017(Publication Date)
- Routledge(Publisher)
The rates above assume that the borrower has a good credit history. Those with a poor credit history will pay a higher rate, and interest rates of 20–30 per cent or more are not uncommon. This is why debts can spiral out of control when payments start being missed. At an interest rate of 24 per cent a credit card balance will on average double every three years assuming you did not have to make any repayments!Also bear in mind that this example is based on the best rates available from a comparison website. The disparities would be far wider if the borrower did not shop around.Figure 5.6 Costs of borrowingsSource: The Money Charity (2016b).In comparison to unsecured debt, secured debt such as a mortgage is a cheaper form of lending because the lender has more security. If you do not pay your mortgage, the lender can repossess the house and sell it to get back the money. However, a mortgage is long-term lending and borrowed over many years.Besides understanding the interest rate, the borrower needs to know the annual percentage rate (APR). All lenders have to disclose the APR as well as the headline interest rate. The APR is the true rate of interest calculated on a yearly basis including all fees and costs. It is in effect the real cost of credit. It is vital to understand this because otherwise one could be fooled into thinking that a mortgage or a loan with a particularly tempting low initial interest rate is a real bargain, whereas over the borrowing term it may not be good at all if the APR is high (see Chapter 8 , Box 8.2 ).Activity 5.2 Read the following case study and answer the question that follows:Case study: Martin is aged 24 and is employed as a landscape gardener. He lives at home with his parents. He earns £20,000 a year. He has a deposit of £1,000 but needs to borrow £5,000 to buy a second-hand Volkswagen Golf for £6,000. The maximum term he wants to borrow the money is over three years. He would like to pay by monthly instalments and would like the flexibility to be able to repay his borrowing early. He has asked his parents to lend him the money and they were unable to do so. He doesn’t know any individual who could lend him the money he needs. He has a good credit record. He has two credit cards with combined limits of £7,000 and pays back in full what he borrows monthly. He has no debts.
eBook - PDF- John A. White, Kenneth E. Case, David B. Pratt(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
Generally, the assumptions behind Web-based calculators are not specified on the Web site. Hence, we do not recommend that the APR values obtained from such calculators be used to evaluate alternative mortgage vehicles. Instead, we recommend using the effective annual interest rate as the basis for evaluating mortgage alternatives. In solving problems at the end of the chapter, unless instructed otherwise, use the additive approach. EXAMPLE 3.7 Imputing Administrative Costs from the APR Suppose a lending institution approved Ms. Lopez for a 30-year conventional 5 percent fixed rate loan, which would include 0.157 in points plus other administrative costs, and the APR on the loan would be 5.095 percent. Excluding points and other closing costs, her monthly payment would be $5.366 per $1,000 borrowed. How much were they charging her in administrative costs? 132 CHAPTER 3 / BORROWING, LENDING, AND INVESTING Since she knew that the lending institution computed the APR by deducting closing costs from the amount borrowed, she used Excel’s PV function to calculate the present value on which the APR was calculated. Letting BASE denote the base amount on which the APR is calculated, she obtained the following results: BASE ¼ $5:366ð$225;000ÞðPjA 5:095=12%;360Þ=$1;000 ¼ $222;494:52 =PV(0.05095/12,360,-5.366)*225000/1000 = $222,494.52 Therefore, administrative costs plus points equal the difference in $225,000 and $222,494.52, or $2,505.48. Assuming points do not apply to other closing costs, since 0.157 points on a $225,000 loan equals $353.25, the administrative costs totaled $2,505.48 $353.25, or $2,152.23. EXAMPLE 3.8 Selecting a Mortgage Plan A professional couple has decided to purchase a house for $450,000. They made a down payment of $100,000. After meeting with representatives of several banks and mortgage brokers, they narrowed the choice of mortgages to the following: a 30-year fixed rate mortgage; a 30-year ARM; and a 5-year interest-only loan.
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