*The Business Professor*, updated September 5, 2019, last accessed July 11, 2020, https://thebusinessprofessor.com/lesson/annual-percentage-rate-definition/.

Back to: BANKING, LENDING, & CREDIT INDUSTRY

### Annual Percentage Rate Definition

Annual Percentage Rate is a method of calculating how much a lender charges for funds annually, as well as the interest payable on an investment. This system combines the cost of the loan, associated fees, and the interest per annum, and expresses them as a percentage. This model, however, doesn’t calculate the yield on former accumulated interest (i.e., it doesn’t use compound interest). APR provides borrowers with the option to find the best rates by different lenders as it provides a comparison of interest-rate structures, transactions fees, defaulting fees, and other determinants.

### A Little More on What is Annual Percentage Rate (APR)

Annual Percentage (APR) calculates the ratio or percentage of the principal loan that you’ll be able to pay up per annum by measuring every possible charge and fees that you’ll or might pay during the period of the loan. It also analyses upfront fees which are planted in agreements by some lenders.

In a portfolio, the Annual Percentage Rate is the interest rate paid on an investment using simple interest ration. In this case, APR doesn’t make use of compound ratio, which means that interests gotten that year are not added to the main principal when the calculation is done. This measurement is carried out by multiplying the interest rate per period, by the stated number of periods in a year. Say, for example, an investment periodical payment is on a 3-month basis, with 0.80% interest per period. To get the APR, you multiply 0.80% by 4 (three quarters make a year, so 12/3 =4). The answer becomes the APR, which then multiplies the principal investment. Note that the interest is not compounded, as 0.80% multiplies all four quarters once, and not subsequently. It also doesn’t indicate how many times the interest is added to the principal capital. So if John invests $400000, his APR would be 0.80%*4*400000, over and over again.

### How the Annual Percentage Rate Works

As necessitated by law, each potential or existing customer is allowed a preview of the APR by their credit card firms and loan issuers. This gives customers a hint of the rates associated with each agreement. While credit card firms put up ads on their interest rates each month, they are required by law to provide an APR to potential customers before entering into an agreement. They are also required to provide these details to existing customers upon request. For a firm which charges 4% semiannually, the APR would be 4% x 2 periods, which is approximately 8%. Loans, on the other hand, have fixed APRs attached to them, and there is no space for alterations on the interest rates through the duration of the loan. They also have variable APR loans which possess altering interest rates.

**Important Details**

- Annual Percentage Rate (APR) refers to the annual interest on borrowed loans or investments
- In calculating APR, compound interest doesn’t come into play
- APRs can come in the form of upfront fees or charges which borrowers can easily view before entering into an agreement.

### Nominal Interest Rate and Annual Percentage Rate

A nominal interest rate (also known as an interest rate), is the interest charged on loan and does not contain any other expenses which might be charged by the lender. On the other hand, APR is the collection of the nominal interest rate and any other fee which the lender might assign to be paid by the borrower. This, in fact, means that the APR is bigger than the nominal value and can be defined mathematically as:

APR = Nominal Interest Rate + Fees and other charges

As required by the Federal Truth in Lending act, every credit card firm and loan issuer is to provide borrowers and customers the APR and nominal interest rate associated with their loan or investments. In some situations, two lenders might offer the same nominal interest rate and other charges but come up with different annual percentage rates (APR). When this occurs, then the lender with the higher APR is said to require a higher upfront fee, while the one with a lower APR is said to be offering a better loan or investment bargain.

Assume that you want to get a mortgage loan of $100,000 with a 3% interest rate per annum. This will result in a monthly payment of $250, or an annual interest rate of $3000. However, this isn’t the total cost of getting the house as you need to pay $1200 for insurance, property maintenance, loan origination fees, as well as a closing cost.

To measure the annual rate percentage of your mortgage loan, we’ll first add the cost of the extra charges to the mortgage loan amount, thus making it $101,200. Then we’ll calculate the rate using a 3% interest rate on $101,200, and this would give us $3036. Next, we’ll check the percentage value of $3036 in $100,000, which is the original loan amount. This would give us an APR of 3.036%.

### Annual Percentage Rate and Annual Percentage Yield

Just like we stated before, in calculating the annual percentage rate (APR), compound interest is not used. The annual percentage yield (APY), on the other hand, includes the compound interest in its measurement. This makes the APY larger than the APR on the same loan or investment. The difference in size between both concepts may be caused by an increase in the interest rate or a low compounding interest period. The APY is also called the effective annual rate (EAR) in loan issuance.

To better illustrate this difference, let us assume that an investor picks a dividend share that pays 4% annually, and 4% on a monthly basis. At first, the APY and the APR would be equal since that would be their first interest payment. However, when it goes on to the second year, the APY would increase to 4.12% due to compound interest while the APR would sit at 4% due to simple interest.

Now, putting this knowledge in monetary terms, let us assume that a borrower was given a loan with 6% APR, and it compounds on a monthly basis. In a case where this individual borrowed $20,000, his interest for one month would be 0.5%, which is approximately $100. This moves up his balance to $20,100. Now, due to compound interest, the next interest assessment is done on the $20,100 instead of the original $20,000. When this occurs, the new balance would be $20,100.5. When this balance is calculated all throughout the year, the total interest rate will shift from 6% to approximately 6.34%. In the APY, your balance would be the result you get after the last interest period when compounding. In the APR, on the other, your balance would still be $20,000 since you don’t add up the interest to the original balance when calculating for a new interest period.

### An Illustration of Annual Percentage Yield (APY) and Annual Percentage Rate (APR)

APR and APY are also used in calculating interest in credit card companies. Let us assume that a credit card firm CSX has an interest rate of 0.05237% daily, which translates to 19.12% percentage interest on an annual basis (0.05237% * 365 days). According to the federal truth of lending act, the firm must showcase this 19.12% as their annual interest rate (APR) to existing and potential customers. Now, as a customer purchases items worth $100 each day till the due date (when the firm starts applying interest), you’d owe $100.5237 for each day you bought something.

Now, when computing the annual percentage yield (APY) or the EAR, we stick to these instructions:

- Add 1 (the principal) to the interest rate before multiplying it by 365 [i.e. (1
- + 0.0005237) * 365= 1.211]
- Subtract 1 from the result (i.e., 1.211 – 1 = 0.211)

Thus, if you owe a balance for a period of one month on your credit card, you’re expected to pay 19.12% yearly. However, your EAR would be 21.1% due to compound interest, and this is what you’ll be expected to pay if you stall the debt till the end of the year.

Lenders and borrowers analyze the APR and APY before entering into a loan or credit card agreement, as both methods provide different results which benefits both parties in different ways. The Truth in Savings Act of 1991 made it compulsory for APR and APY to be disclosed before the start of a contractual loan agreement, to prevent the possibility of defaulting due to lack of adequate information.

In the financial services sector, a bank acting as a savings party would publish the APY in bigger fonts and the APR in smaller fonts. This is because they want people to be enticed by the total percentage they’d have at the end of the year. In this case, we say that the bank is acting as a borrower by providing deals that no lender might want to reject. When it acts as a lender, on the other hand, the APR would be displayed in bigger fonts and the APY in smaller fonts. This way, they’re trying to tell borrowers that they should take their loans since they’re charging a small sum.

### Annual Percentage Rate and Daily Interest Rate

Mathematically, the daily interest rate is given as:

DIR = APR/365

In standard terms, we define the daily interests rate as a loan’s interest on a daily basis. It is the annual percentage rate divided by 365 (number of days in a year).

Same thing goes for the monthly interest rate; APR/12 (number of months in a year).

Most lenders prefer sticking to the monthly interest rate, but they are required to show the full interest for a period of 12 years before engaging borrowers to sign a loan agreement.

### Other Definitions of Annual Percentage Rate (APR)

There are different definitions of Annual Percentage Rate, and each one seems to be a totally different concept. Their methods of calculation can also make a difference between them, as can be seen from the case of the effective annual percentage rate (EAR).

In the United States, APR is measured as period interest rate multiplying the number of periods in a year. The Truth in Lending Act helped shaped APR reporting into what it is today. Exploitation kicked into the system as some automakers discovered some loopholes in the Lending Act. This way, the present what was known as a 0% APR, which was more misleading than it was true. The Truth in Lending Act has a hard time stitching up these exploits, as it had a negative cost on customers of these firms or entities. However, in modern times, this organization passes the act over to other regulating bodies for revisions and enactment.

Outside the United States, the definition of APR is different from what we normally know. For instance, the European Union defines APR with regards to consumers’ rights and transparency of transactions. Almost all EU member countries have adopted a single method of calculating annual Percentage Rate, although some prefer to make alterations to it depending on the economic situation of the sector in question.

### Controversies and Possible Confusion Associated with the APR

A general misconception and confusion about the APR is associated with its measurement of the actual cost of loans. There are different arguments surrounding its calculation of short term and long term loan costs. While some scholars advise using APR solely for long term investments, this method has been in used for loans with at most seven years repayment duration. When loans are repaid faster, the costs are reduced considerably when calculated with APR. This is because this measurement method assumes that loans will take a longer time to be fully repaid. In other words, it assumes a long-term repayment duration for each loan agreement made. For loans that take up to 30 years to repay, the closing cost per annum seems to be smaller than those repaid in 10 years or less. An example would be paying a loan of $30,000 in 30 years. Extracting the costs and fees out, we can say that the borrower is expected to pay $1,000 per year, which is lesser than paying $6,000 per year in the case of five years.

When used in adjustable-rate mortgages (ARMs), APRs seem to get into a lot of issues, as it calculates mostly the fixed-rate, and doesn’t take into account the variable cost and how they increase on a yearly basis. Even when it takes rate caps into account when computing, results are based on fixed rates. Due to an unstable rise in the prices and cost of mortgages, the APR presented before entering into a loan agreement can understate the real cost to be paid.

### Annual Percentage Rate in Credit Card Companies

Most credit companies make use of variable APRs instead of fixed APR. In this system, the interest rate offered on a transaction depends on the performance of the market, the US prime rate, or an index. APRs in credit companies are determined by adding variable costs to the bank’s margin. Thus, if the prime rate is 3% and the bank charges 8% margin, then the interest rate will be 11%.

Other credit firms can choose to stick to fixed rates which cannot be changed without prior notice to customers and gaining consent from them. Adjustments mostly affect future transactions, where any former transaction would be associated with the interest rate charged at the time of processing. These firms do not make use of the US prime rate, so market or index performance won’t affect them.

Some firms, however, charge different APRs on different transactions and card types. Some credit card can change APR for deposits, others for purchases, while some might just glue it solely to cash advances. Most banks charge penalty APR to customers who delay or default in paying their debts, or to cardholders who violate the terms and agreements associated with the card.

When managed effectively, APRs can help to pay off loans faster. For example, a $4000 loan with a 12% APR incurs an interest of $40 monthly. When this $40 is transferred to a 0% introductory APR of a credit card for a period of 12 months, it allows you to apply the original $40 to the principal, thus help you pay off the balance much sooner.

### Problems of the Annual Percentage Rate (APR)

There are many issues associated with the annual percentage rate, and they’re as follows:

*Comparison Issues*

In calculating APR, many regulators have a hard time determining what fees would be included and disregarded in the APR assessment. This gives different lenders the right to choose whether to calculate APR or not, as well as the opportunity to include whatever fee they want. This causes the difference in APR of different lenders for the same actual cost of a loan.

Fees can pile up to a large amount in an APR, ad this is most likely in mortgage loans. Mortgage loans can include appraisal fees, land title fees, home insurance fees, and maintenance fees. Other fees in different sectors may include attorney fees, life insurance fees, notaries, document preparation and credit report charges, as well as loan or credit card application fees. Borrowers should make it a priority to know the fees included in an APR. It’s best they also calculate it using the nominal interest rate and other cost data to see what they’re paying for each listed fee type.

*Exempted Fees*

Some lenders decide it’d be best to exempt some fees from the APR, thus raising concerns that this is misleading as it doesn’t allow the borrower to know the actual cost of the loan he or she is receiving. An example is the penalty fee mostly charged by credit card companies. These fees are not really specified in the APR before the agreement is signed, although most firms would give a heads up to potential customers.

Lenders exempt these fees because they feel that they’re only incurred on rare events, and as such, they wouldn’t want to charge for something that might not happen. Most borrowers, on the other hand, feel that the APR has already covered the charge in case a one-time event occurs.

*Nominal APR*

Most credit card firms prepare to showcase the nominal APR, which is different from the annual percentage yield or the EAR in this case. Little differences in the EAR and the APR can alter the interest to be paid in the long-run.

### Shortcomings of the Annual Percentage Rate (APR)

Time is a variable which greatly affects a loan’s APR, thus limiting the possibility of calculating investments or loans of varying durations. APR, however, can measure how different payment schedules can greatly benefit a borrower, but this is a complex concept with requires top expertise.

Also, when a loan is paid faster than expected, it provides room for error in APR cost calculators. In situations like this, the effective interest rate (EAR) steps in for the APR. We’ve seen situations like this recently, especially in the real estate sector. When a loan with a duration of 20 years is paid in 2 years, then it’d pose a major problem to APR calculations.

### Reference for “Annual Percentage Rate – APR”

https://www.thebalance.com/annual-percentage-rate-apr-315533

https://www.investopedia.com › Personal Finance › Mortgages

https://www.thebalance.com › Personal Finance › Banking and Loans › Getting a Loan

https://en.wikipedia.org/wiki/Annual_percentage_rate

https://corporatefinanceinstitute.com › Resources › Knowledge › Finance

### Academics research on **“**Annual Percentage Rate **–** APR**”**

Resolving confusion in terminology: annual percentage rate and effective rate of interest, **Chandrasekaran, P. R., Cole, C. S., & Roden, F. (1996). Resolving confusion in terminology: annual percentage rate and effective rate of interest. ***Journal of Financial Education***, 60-64. **This paper examines the confusion surrounding the term annual percentage rate (APR) and effective rate of interest (ERI). Some textbooks use the terms synonymously and some differentiate between the meaning of the terms. The authors note that differentiating between the two terms presents several advantages to borrowers and lenders alike: It permits applying APR as a periodic rate consistent with Regulation Z of the Federal Reserve Act Second, it preserves ERI for use as the effective rate per year compounded annually equivalent to the APR, thus permitting direct comparisons between borrowing and lending rates with different APRs.

Comparing fixed-rate mortgage loans via the annual percentage rate: Cautions and caveats, **McClatchey, C., & de la Torre, C. (2006). Comparing fixed-rate mortgage loans via the annual percentage rate: Cautions and caveats. ***Journal of Financial Service Professionals***, ***60***(1), 16.**

The usefulness of the APR for mortgage marketing in the USA and the UK, **Buch, J., Rhoda, K. L., & Talaga, J. (2002). The usefulness of the APR for mortgage marketing in the USA and the UK. ***International Journal of Bank Marketing***, ***20***(2), 76-85. **Regulators in the UK and the USA recognize the need to assist borrowers that face a huge number of mortgage products with a multitude of fee combinations offered by a large number of lenders. For over 25 years they attempted to make the mortgage selection process more borrower‐friendly but, for many reasons, the efficacy of the chosen comparison tool, the Annual Percentage Rate (APR), is questionable. Because many consumers are either unwilling or unable to make price comparisons between mortgages based on the APR, we suggest replacing the APR with a new measure called the Annual Effective Rate (AER). The AER is based on the actual length of time the borrower expects to maintain the loan and the assumption that all up‐front loan costs are financed. In addition, we suggest that this comparison rate only be presented for true fixed‐rate loans and that all up‐front cost categories that are used in computing the AER be standardized.

Is the Truth in Lending Being Told with the Annual Percentage Rate as the Measure of the Cost of Credit?, **Celec, S. E. (1981). Is the Truth in Lending Being Told with the Annual Percentage Rate as the Measure of the Cost of Credit?. ***Journal of Consumer Affairs***, ***15***(1), 128-135. **This paper demonstrates that the Annual Percentage Rate (APR) measure required under the Federal Reserve System’s Regulation Z is not consistent with the mathematical procedures involved in calculating the interest charges on a loan. The APR is never a correct cardinal measure of the true cost of credit, and it is a correct ordinal measure only under specific restrictive conditions. Since the APR always understates the true cost of credit, and since a correct cardinal measure is already familiar to the finance profession, it is difficult to justify the required disclosure of the APR. The Annual Effective Rate should be required as the summary measure of the true cost of credit for all types of consumer loans.

Some ethical issues in computation and disclosure of interest rate and cost of credit, **Bhandari, S. B. (1997). Some ethical issues in computation and disclosure of interest rate and cost of credit. ***Journal of Business Ethics***, ***16***(5), 531-535. **Although the mathematics of interest is very precise, the practice of charging computing and disclosing interest or cost of credit is full of variations and therefore often questionable on ethical grounds. The purpose of this paper is to examine some of the prevalent practices which are incorrect, illogical, unfair or deceptive. Both utilitarian and formalist schools of ethical theory would find these practices to be inappropriate. The paper will specifically look at unfair practices in the areas of estimation of intrayear rates, use of 360 days in a year, the “rule of 78th”, interest rate (‘APR’) advertising, and computation of unpaid balance by credit card issuers to figure interest costs.