## What Is Annual Percentage Rate – APR?

An annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment. APR is expressed as a percentage 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 but does not take compounding into account.

As 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 lenders.

#### Annual Percentage Rate (APR)

## APR Formula and Calculation

$\begin{aligned} &\text{APR} = \left ( \left ( \frac{ \frac{ \text{Fees} + \text{Interest} }{ \text {Principal} } }{ n } \right ) \times 365 \right ) \times 100 \\ &\textbf{where:} \\ &\text{Interest} = \text{Total interest paid over life of the loan} \\ &\text{Principal} = \text{Loan amount} \\ &n = \text{Number of days in loan term} \\ \end{aligned}$

APR is most often expressed in terms of an interest rate (%). Annual percentage rate (APR) is a measure that attempts to calculate what percentage of the principal you’ll pay per period (in this case a year), taking every charge from monthly payments over the course of the loan, upfront fees, etc. into account.

APR is the annual rate of interest that is paid on an investment, without taking into account the compounding of interest within that year. APR is calculated by multiplying the periodic interest rate by the number of periods in a year in which the periodic rate is applied. It does not indicate how many times the rate is applied to the balance.

- An annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment.
- APR does not take into account compounding, while annual percentage yield (APY) does.
- Borrowers often see APR figures when they compare credit cards or mortgage rates. APR rolls in any up-front fees and charges.

## What the APR Tells You

The APR, by law, must be shown to customers by credit card companies and loan issuers to facilitate a clear understanding of the actual rates applicable to their agreements. Credit card companies are allowed to advertise interest rates on a monthly basis, but they are also required to clearly state the APR to customers before any agreement is signed. For example, a credit card may charge 1% a month, and its APR is 1% x 12 months, or 12%.

Loans are offered with either fixed or variable APRs. A fixed APR loan has an interest rate that is guaranteed not to change during the life of the loan or credit facility. A variable APR loan has an interest rate that may change at any time.

## APR vs. Nominal Interest Rate

An interest rate, or a nominal interest rate, refers only to the interest charged on a loan, and it does not take any other expenses into account. In contrast, APR is the combination of the nominal interest rate and any other costs or fees involved in procuring the loan. As a result, an APR tends to be higher than a loan's nominal interest rate.

For example, if you were considering a mortgage for $200,000 with a 6% interest rate, your annual interest expense would amount to $12,000, or a monthly payment of $1,000. But say your home purchase also requires closing costs, mortgage insurance, and loan origination fees in the amount of $5,000.

In order to determine your mortgage loan's APR, these fees are added to the original loan amount to create a new loan amount of $205,000. The 6% interest rate is then used to calculate a new annual payment of $12,300. Divide the annual payment of $12,300 by the original loan amount of $200,000 to get an APR of 6.15%.

The federal Truth in Lending Act requires that every consumer loan agreement list the APR along with the nominal interest rate. The scenario most confusing to borrowers is when two lenders are offering the same nominal rate and monthly payments but different APRs. In a case like this, the lender with the lower APR is requiring fewer upfront fees and offering a better deal.

## APR vs. Annual Percentage Yield

An APR takes only simple interest into account. In contrast, the annual percentage yield (APY), also known as the effective annual rate (EAR), takes compound interest into account. As a result, an APY tends to be larger than an APR on the same loan. The higher the interest rate, and to a lesser extent the smaller the compounding periods, the greater the difference between APR and APY.

Imagine the APR of a loan is 12%, and the loan compounds once per month. If an individual has borrowed $10,000, his interest for one month is 1% of his balance or $100. That effectively increases his balance to $10,100. The following month, 1% interest is assessed on this amount, and the interest payment is $101, slightly higher than it was the previous month. If you carry that balance for the year, your effective interest rate becomes 12.68%. APY includes these small shifts in interest expenses due to compounding, while APR does not.

Or say you compare an investment that pays 5% per year with one that pays 5% monthly. For the first, the APY equals 5%, the same as the APR. But for the second, the APY IS 5.12%, reflecting the monthly compounding.

### Advisor Insight

Dann Ryan, CFP®

Sincerus Advisory, *New York, NY*

In a rising interest rate environment, the difference between APR and APY gets amplified. In addition to the disparity between the two becoming greater at higher interest rates, the compounding period also becomes more significant. Loans that compound more frequently are thereby less attractive. For instance, some margin loans against brokerage accounts may compound as often as daily.

Comparing APRs is not always as simple as comparing apples to apples, so spending the time to do an APY calculation and consider all costs is generally worthwhile.

## APR vs. Daily Periodic Rate

The daily periodic rate is the interest rate charged on a loan's balance on a daily basis. It is the APR divided by 365, the number of days in a year. Similarly, the monthly periodic rate is the APR divided by 12. Lenders and credit card providers are allowed to represent APR on a monthly basis as long as the full 12-month APR is listed somewhere before the agreement is signed.

## Varying Definitions

Given the different types of APR and the possibilities for confusion between them, it may come as no surprise that there are multiple legal definitions to sort out when considering this type of interest calculation. Effective annual percentage rate, for instance, can be computed in multiple ways, including by adding origination fees to the balance due and before calculating compound interest, or by compounding the interest rate each year exclusive of fees, or by amortizing the origination fees as a short-term loan.

In the United States, APR is typically presented as the periodic interest rate multiplied by the number of compounding periods per year. Per the Truth in Lending Act, enacted in 1968, APR reporting was transformed throughout the 1970s.

However, a loophole in the act allowed some unscrupulous automakers and others to reduce the "finance charge" to present a lower APR than what would be realistic for customers to expect. The Truth in Lending Act has had a difficult time addressing these concerns, and "zero-percent APR" auto loans have been a misleading phenomenon since that time. Over the years, however, the act has been transferred to various other administrations, where it can be revised and updated.

Definitions of APR outside of the United States may be quite different. The European Union (EU), for instance, focuses on consumer rights and financial transparency in defining this term. A single method for calculating interest rate was established for all EU member nations, although individual countries have some leeway over determining the exact situations in which this formula is to be adopted above and beyond EU-stipulated cases.

## How APR can Be Misleading

As all of the above illustrates, APR can be a misleading indicator of actual costs. Some experts feel the APR is best used to compare long-term loans. Even with shorter-term debt, such as a seven-year note, the APR actually understates the cost of the loan. This is because APR calculations assume long-term repayment schedules. For loans that are repaid faster or have shorter repayment periods, the costs and fees are spread too thin with APR calculations. The average annual impact of closing costs is much smaller when those costs are assumed to have been spread over 30 years instead of seven to 10 years.

APR also runs into some trouble with adjustable-rate mortgages (ARMs). APR estimates always assume a constant rate of interest, and even though APR takes rate caps into consideration, the final number you are presented with is still based on fixed rates. Because the interest rate on an ARM is uncertain once the fixed-rate period is over, APR estimates can severely understate the actual borrowing costs if mortgage rates rise in the future.

## How Credit Card Companies Set APR

Most credit cards have floating APRs, commonly called variable APRs. These feature floating interest rates that move up and down along with the market or an index or the U.S. prime rate. They are set by taking this variable feature and adding the bank's margin to it. For example, if the bank charges a 10% margin and the prime rate is 5%, the borrower pays a 15% interest rate.

Though they are few and far between, there are also some fixed interest rate credit cards available. With credit cards (unlike other types of loans), a fixed APR actually means that the rate remains locked until the lender decides to change it. However, it cannot be changed without written notice, and the adjustment only applies going forward on the loan, not retroactively.

In some cases, credit card companies offer different APRs for different types of charges. For example, a card may charge one APR for purchases, another for cash advances, and third for balance transfers from another card. Similarly, banks charge high-rate penalty APRs to customers who have made late payments or violated other terms of the cardholder agreement and offer low-rate introductory APRs to entice new customers – preferably, those who tend to carry a balance on their cards.

Introductory APRs can have positive effects on personal finance if they are managed carefully. A $2,000 loan balance that carries a 12% APR incurs a $20 interest charge each month. Transferring that balance to a credit card with an introductory APR of 0% for 12 months allows you to apply that same $20 to the principal, paying off the balance much sooner.

## Issues with APR

APR does bring its own bag of limitations and difficulties to the financing arena. From comparing apples to apples to fees that seem to materialize from nowhere, APR—while useful—is not an end-all solution.

### Difficult to Compare

APR calculations could potentially include a host of one-time fees. Regulators in the U.S. have had a difficult time specifying exactly which of these fees must be included or excluded from the APR assessment. As a result, the lender has a fair amount of authority to determine how to calculate the APR, and the APR can thus vary, depending on how that lender decides to include fees or not.

There may be many fees, depending upon the type of borrowing taking place. For instance, in a mortgage situation, fees for appraisal, title, credit report, applications, life insurance, attorneys and notaries, document preparation and more all may or may not be included in the APR calculation. In order to accurately compare multiple offers, a potential borrower thus has to determine which of these fees are included and, to be thorough, calculate APR using the nominal interest rate and other cost information.

### Fees Left Out

Beyond the fees that are left to the lender's discretion in the calculation of APR, there are other fees that are deliberately excluded from the determination. Critics of the APR system suggest that, as a result, APR does not accurately reflect the total cost of borrowing. These excluded fees could include penalties like late fees and other one-time fees as mentioned above.

In many cases, it comes down to a question of terminology. Lenders consider certain fees to be pass-through costs which are not directly related to the cost of lending. To many borrowers, though, these fees seem to act similarly to others that are included in APR calculations.

### Issues With Nominal APR

As discussed above, most credit card companies list the nominal APR, compounded monthly. This is effectively different from the EAR. As a result of the exponential nature of interest, even small differences between the nominal APR and the EAR can actually have a dramatic impact on the amount of interest to be paid, particularly over the lifetime of a long loan.

## Limitations of the APR

Because the time period in question is a crucial component in the calculation of APR, it is not possible to compare APRs for multiple loans of different durations. However, APR may be effective at showing how different payment schedules can impact total cost to the borrower, although this can be difficult to calculate as well.

APR cost calculators are generally not particularly effective at calculating effective interest rates for loans that are paid off early. In these cases, the effective interest rate is likely to be higher than the initial APR. This situation arises quite frequently, particularly in the case of mortgage loans. These loans are often set for durations of 30 years, but many mortgage borrowers either refinance their loans or move before the loan period is complete. In these cases, the APR calculation can be difficult to assess.

## An Example of APR vs. APY

In another example, XYZ Corp. offers a credit card that levies interest of 0.06273% daily. Multiply that by 365, and that’s 22.9% per year, which is the advertised APR. Now, if you were to charge a different $1,000 item to your card every day and waited until the day after the due date (when the issuer started levying interest) to start making payments, you’d owe $1,000.6273 for each thing you bought.

To calculate the APY or EAR (the more typical term on credit cards), add 1 (which represents the principal) and take that number to the *power* of the number of compounding periods in a year; subtract 1 from the result to get the percentage:

$\begin{aligned} &\text{APY} = (1 + \text{Periodic Rate} ) ^ n - 1 \\ &\textbf{where:} \\ &n = \text{Number of compounding periods per year} \\ \end{aligned}$

In this case, your APY or EAR would be 25.7%:

$\begin{aligned} &( ( 1 + .0006273 ) ^ {365} ) - 1 = .257 \\ \end{aligned}$

If you only carry a balance on your credit card for one month's period you will be charged the equivalent yearly rate of 22.9%. However, if you carry that balance for the year, your effective interest rate becomes 25.7% as a result of compounding each day.

Given that an APR and a different APY can be used to represent the same interest rate, it stands to reason that lenders and borrowers will emphasize the more flattering number to state their case (the Truth in Savings Act of 1991 mandated that both APR and APY be disclosed in ads, contracts, and agreements).

A bank will advertise a savings account’s APY in a large font and its corresponding APR in a smaller one, given that the former features a superficially larger number. The opposite happens when the bank acts as the lender and tries to convince its borrowers that it’s charging a low rate. A great resource for comparing both APR and APY rates on a mortgage is a mortgage calculator.