Annual Percentage Rate (APR)

What Is Annual Percentage Rate (APR)?

Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment. This includes any fees or additional costs associated with the transaction, but it does not take compounding into account. The APR provides consumers with a bottom-line number they can compare among lenders, credit cards, or investment products.

Key Takeaways

  • An annual percentage rate (APR) is the yearly rate charged for a loan or earned by an investment.
  • Financial institutions must disclose a financial instrument’s APR before any agreement is signed.
  • The APR provides a consistent basis for presenting annual interest rate information, in order to protect consumers from misleading advertising.
  • An APR may not reflect the actual cost of borrowing because lenders have a fair amount of leeway in calculating it, excluding certain fees.
  • APR shouldn't be confused with APY (annual percentage yield), a calculation that takes the compounding of interest into account.
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APR vs. APY: What's the Difference?

How the Annual Percentage Rate (APR) Works

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you’ll pay each year by taking things such as monthly payments into account. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.

The Truth in Lending Act (TILA)of 1968 mandated that lenders disclose the APR they charge to borrowers. Credit card companies are allowed to advertise interest rates on a monthly basis, but they must clearly report the APR to customers before they sign an agreement.

How Is APR Calculated?

APR is calculated by multiplying the periodic interest rate by the number of periods in a year in which it was applied. It does not indicate how many times the rate actually is applied to the balance.

APR = ( ( Fees + Interest Principal n ) × 365 ) × 100 where: Interest = Total interest paid over life of the loan Principal = Loan amount n = Number of days in loan term \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=((nPrincipalFees+Interest)×365)×100where:Interest=Total interest paid over life of the loanPrincipal=Loan amountn=Number of days in loan term

Types of APRs

Credit card APRs vary based on the type of charge. The credit card issuer may charge one APR for purchases, another for cash advances, and yet another for balance transfers from another card. Issuers also charge high-rate penalty APRs to customers for late payments or violating other terms of the cardholder agreement. There’s also the introductory APR—a low or 0% rate—which many credit card companies use to entice new customers to sign up for a card.

Bank loans generally come 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.

The APR borrowers are charged also depends on their credit. The rates offered to those with excellent credit are significantly lower than the ones to those with bad credit.

Compound Interest or Simple Interest?

APR does not take into account the compounding of interest within a specific year: It is based only on simple interest.

APR vs. Annual Percentage Yield (APY)

While an APR only accounts for simple interest, the annual percentage yield (APY) takes compound interest into account. As a result, a loan’s APY is higher than its APR. The higher the interest rate, and to a lesser extent the smaller the compounding periods, the greater the difference between APR and APY.

Imagine that a loan’s APR is 12%, and the loan compounds once a month. If an individual borrows $10,000, their interest for one month is 1% of the balance or $100. That effectively increases the 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.

Here's another way to look at it. Say you compare an investment that pays 5% per year with one that pays 5% monthly. For the first month, the APY equals 5%, the same as the APR. But for the second, the APY is 5.12%, reflecting the monthly compounding.

Given that an APR and a different APY can be used to represent the same interest rate on a loan or financial product, lenders often emphasize the more flattering number, which is why 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.

An Example of APR vs. APY

Say 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 effective annual interest rate (EAR)—the more typical term used for credit cards—add one (which represents the principal) and take that number to the power of the number of compounding periods in a year; subtract one from the result to get the percentage:

APY = ( 1 + Periodic Rate ) n 1 where: n = Number of compounding periods per year \begin{aligned} &\text{APY} = (1 + \text{Periodic Rate} ) ^ n - 1 \\ &\textbf{where:} \\ &n = \text{Number of compounding periods per year} \\ \end{aligned} APY=(1+Periodic Rate)n1where:n=Number of compounding periods per year

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

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

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.

APR vs. Nominal Interest Rate vs. Daily Periodic Rate

An APR tends to be higher than a loan’s nominal interest rate. That’s because the nominal interest rate doesn’t account for any other expense accrued by the borrower. The nominal rate may be lower on your mortgage if you don’t account for closing costs, insurance, and origination fees. If you end up rolling these into your mortgage, your mortgage balance increases, as does your APR.

The daily periodic rate, on the other hand, is the interest charged on a loan’s balance on a daily basis—the APR divided by 365. Lenders and credit card providers are allowed to represent APR on a monthly basis, though, as long as the full 12-month APR is listed somewhere before the agreement is signed.

Disadvantages of Annual Percentage Rate (APR)

The APR isn’t always an accurate reflection of the total cost of borrowing. In fact, it may understate the actual cost of a loan. That’s because the calculations assume long-term repayment schedules. The costs and fees are spread too thin with APR calculations for loans that are repaid faster or have shorter repayment periods. For instance, the average annual impact of mortgage closing costs is much smaller when those costs are assumed to have been spread over 30 years instead of seven to 10 years.

Who Calculates APR?

Lenders have a fair amount of authority to determine how to calculate the APR, including or excluding different fees and charges.

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

Mortgage APRs may or may not include other charges, such as appraisals, titles, credit reports, applications, life insurance, attorneys and notaries, and document preparation. There are other fees that are deliberately excluded, including late fees and other one-time fees.

All this may make it difficult to compare similar products because the fees included or excluded differ from institution to institution. In order to accurately compare multiple offers, a potential borrower must determine which of these fees are included and, to be thorough, calculate APR using the nominal interest rate and other cost information.

Why Is the Annual Percentage Rate (APR) Disclosed?

Consumer protection laws require companies to disclose the APRs associated with their product offerings, in order to prevent companies from misleading customers. For instance, if they were not required to disclose the APR, a company might advertise a low monthly interest rate while implying to customers that it was an annual rate. This could mislead a customer into comparing a seemingly low monthly rate against a seemingly high annual one. By requiring all companies to disclose their APRs, customers are presented with an “apples to apples” comparison.

What Is a Good APR?

What counts as a “good” APR will depend on factors such as the competing rates offered in the market, the prime interest rate set by the central bank, and the borrower’s own credit score. When prime rates are low, companies in competitive industries will sometimes offer very low APRs on their credit products, such as the 0% on car loans or lease options. Although these low rates might seem attractive, customers should verify whether these rates last for the full length of the product’s term, or whether they are simply introductory rates that will revert to a higher APR after a certain period has passed. Moreover, low APRs may only be available to customers with especially high credit scores.

How Do You Calculate APR?

The formula for calculating APR is straightforward. It consists of multiplying the periodic interest rate by the number of periods in a year in which the rate is applied. The exact formula is as follows:

APR=((Fees+InterestPrincipaln)×365)×100where:Interest=Total interest paid over life of the loanPrincipal=Loan amountn=Number of days in loan term\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=((nPrincipalFees+Interest)×365)×100where:Interest=Total interest paid over life of the loanPrincipal=Loan amountn=Number of days in loan term


Article Sources

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  1. Federal Register. "Truth in Lending (Regulation Z)." Accessed Sept. 19, 2021.

  2. Federal Trade Commission. "Truth in Lending Act." Accessed Sept. 19, 2021.

  3. Federal Deposit Insurance Corporation. "Part 1030—Truth in Savings (Regulation DD)." Accessed Sept. 19, 2021.