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 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.

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 and fees 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 mandates 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 is actually applied to the balance.

$\begin{aligned} &\text{APR} = \left ( \left ( \frac{ \frac{ \text{Fees} + \text{Interest} }{ \text {Principal} } }{ n } \right ) \times 365 \right ) \times 100 \\ &\textbf{where:} \\ &\text{Interest} = \text{Total interest paid over life of the loan} \\ &\text{Principal} = \text{Loan amount} \\ &n = \text{Number of days in loan term} \\ \end{aligned}$​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—with which many credit card companies try 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 those offered to those with bad credit.

APR vs. Annual Percentage Yield (APY)

Though 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 the 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 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 both APR and APY disclosure 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.

APR vs. APY Example

Let’s say that 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—the more typical term for credit cards—add one (that 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:

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

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

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

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 when 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.

The Bottom Line

The APR is the basic theoretical cost or benefit of money loaned or borrowed. By calculating only the simple interest without periodic compounding, the APR gives borrowers and lenders a snapshot of how much interest they are earning or paying within a certain period of time. If someone is borrowing money, such as by using a credit card or applying for a mortgage, the APR can be misleading because it only presents the base number of what they are paying without taking time into the equation. Conversely, if someone is looking at the APR on a savings account, it doesn’t illustrate the full impact of interest earned over time.

APRs are often a selling point for different financial instruments, such as mortgages or credit cards. When choosing a tool with an APR, be careful to also take into account the APY because it will prove a more accurate number for what you will pay or earn over time. Though the formula for your APR may stay the same, different financial institutions will include different fees in the principal balance. Be aware of what is included in your APR when signing any agreement.

What Is an Auditor’s Report?

An auditor’s report is a written letter from the auditor containing their opinion on whether a company’s financial statements comply with generally accepted accounting principles (GAAP) and are free from material misstatement.

The independent and external audit report is typically published with the company’s annual report. The auditor’s report is important because banks and creditors require an audit of a company’s financial statements before lending to them.

How an Auditor’s Report Works

An auditor’s report is a written letter attached to a company’s financial statements that expresses its opinion on a company’s compliance with standard accounting practices. The auditor’s report is required to be filed with a public company’s financial statements when reporting earnings to the Securities and Exchange Commission (SEC).

However, an auditor’s report is not an evaluation of whether a company is a good investment. Also, the audit report is not an analysis of the company’s earnings performance for the period. Instead, the report is merely a measure of the reliability of the financial statements.

The Components of an Auditor’s Report

The auditor’s letter follows a standard format, as established by generally accepted auditing standards (GAAS). A report usually consists of three paragraphs.

• The first paragraph states the responsibilities of the auditor and directors.
• The second paragraph contains the scope, stating that a set of standard accounting practices was the guide.
• The third paragraph contains the auditor’s opinion.

An additional paragraph may inform the investor of the results of a separate audit on another function of the entity. The investor will key in on the third paragraph, where the opinion is stated.

The type of report issued will be dependent on the findings by the auditor. Below are the most common types of reports issued for companies.

Clean or Unqualified Report

A clean report means that the company’s financial records are free from material misstatement and conform to the guidelines set by GAAP. A majority of audits end in unqualified, or clean, opinions.

Qualified Opinion

A qualified opinion may be issued in one of two situations: first, if the financial statements contain material misstatements that are not pervasive; or second, if the auditor is unable to obtain sufficient appropriate audit evidence on which to base an opinion, but the possible effects of any material misstatements are not pervasive. For example, a mistake might have been made in calculating operating expenses or profit. Auditors typically state the specific reasons and areas where the issues are present so that the company can fix them.

Adverse Opinion

An adverse opinion means that the auditor has obtained sufficient audit evidence and concludes that misstatements in the financial statements are both material and pervasive. An adverse opinion is the worst possible outcome for a company and can have a lasting impact and legal ramifications if not corrected.

Disclaimer of Opinion

A disclaimer of opinion means that, for some reason, the auditor is unable to obtain sufficient audit evidence on which to base the opinion, and the possible effects on the financial statements of undetected misstatements, if any, could be both material and pervasive. Examples can include when an auditor can’t be impartial or wasn’t allowed access to certain financial information.

Example of an Auditor’s Report

Excerpts from the audit report by Deloitte & Touche LLP for Starbucks Corporation, dated Nov. 15, 2019, follow.

Paragraph 1: Opinion on the Financial Statements

“We have audited the accompanying consolidated balance sheets of Starbucks Corporation and subsidiaries (the ‘Company’) as of September 29, 2019, and September 30, 2018, the related consolidated statements of earnings, comprehensive income, equity, and cash flows, for each of the three years in the period ended September 29, 2019, and the related notes (collectively referred to as the ‘financial statements’).

In our opinion, the financial statements present fairly, in all material respects, the financial position of the Company as of September 29, 2019, and September 30, 2018, and the results of its operations and its cash flows for each of the three years in the period ended September 29, 2019, in conformity with accounting principles generally accepted in the United States of America.”

Paragraph 2: Basis for Opinion

“We conducted our audits in accordance with the standards of the Public Company Accounting Oversight Board (PCAOB). Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements are free of material misstatement, whether due to error or fraud. Our audits included performing procedures to assess the risks of material misstatement of the financial statements, whether due to error or fraud, and performing procedures that respond to those risks.

Such procedures included examining, on a test basis, evidence regarding the amounts and disclosures in the financial statements. Our audits also included evaluating the accounting principles used and significant estimates made by management, as well as evaluating the overall presentation of the financial statements. We believe that our audits provide a reasonable basis for our opinion.”

What Is Adverse Selection?

Adverse selection refers generally to a situation in which sellers have information that buyers do not have, or vice versa, about some aspect of product quality. In other words, it is a case where asymmetric information is exploited. Asymmetric information, also called information failure, happens when one party to a transaction has greater material knowledge than the other party.

Typically, the more knowledgeable party is the seller. Symmetric information is when both parties have equal knowledge.

In the case of insurance, adverse selection is the tendency of those in dangerous jobs or high-risk lifestyles to purchase products like life insurance. In these cases, it is the buyer who actually has more knowledge (i.e., about their health). To fight adverse selection, insurance companies reduce exposure to large claims by limiting coverage or raising premiums.

Understanding Adverse Selection

Adverse selection occurs when one party in a negotiation has relevant information the other party lacks. The asymmetry of information often leads to making bad decisions, such as doing more business with less profitable or riskier market segments.

In the case of insurance, avoiding adverse selection requires identifying groups of people more at risk than the general population and charging them more money. For example, life insurance companies go through underwriting when evaluating whether to give an applicant a policy and what premium to charge.

Underwriters typically evaluate an applicant’s height, weight, current health, medical history, family history, occupation, hobbies, driving record, and lifestyle risks such as smoking; all these issues impact an applicant’s health and the company’s potential for paying a claim. The insurance company then determines whether to give the applicant a policy and what premium to charge for taking on that risk.

Consequences of Adverse Selection

A seller may have better information than a buyer about products and services being offered, putting the buyer at a disadvantage in the transaction. For example, a company’s managers may more willingly issue shares when they know the share price is overvalued compared to the real value; buyers can end up buying overvalued shares and lose money. In the secondhand car market, a seller may know about a vehicle’s defect and charge the buyer more without disclosing the issue.

The general consequence of adverse selection is that it increases costs since consumers lack information held by sellers or producers, creating an asymmetry in the market. This can also lower consumption as buyers may be wary of the quality of the products that are offered for sale. Or, it may exclude certain consumers that do not have access to or cannot afford to obtain information that could lead them to make better buying decisions.

One indirect effect of this is a negative impact on consumers’ health and well-being. If you buy a faulty product or dangerous medication because you don’t have good information, consuming these products can cause physical harm. Or, by refraining from buying certain healthcare products (e.g., vaccines), consumers may wrongly judge a safe intervention as overly risky.

Adverse Selection in Insurance

Because of adverse selection, insurers find that high-risk people are more willing to take out and pay greater premiums for policies. If the company charges an average price but only high-risk consumers buy, the company takes a financial loss by paying out more benefits or claims.

However, by increasing premiums for high-risk policyholders, the company has more money with which to pay those benefits. For example, a life insurance company charges higher premiums for race car drivers. A car insurance company charges more for customers living in high-crime areas. A health insurance company charges higher premiums for customers who smoke. In contrast, customers who do not engage in risky behaviors are less likely to pay for insurance due to increasing policy costs.

A prime example of adverse selection in regard to life or health insurance coverage is a smoker who successfully manages to obtain insurance coverage as a nonsmoker. Smoking is a key identified risk factor for life insurance or health insurance, so a smoker must pay higher premiums to obtain the same coverage level as a nonsmoker. By concealing their behavioral choice to smoke, an applicant is leading the insurance company to make decisions on coverage or premium costs that are adverse to the insurance company’s management of financial risk.

Another example of adverse selection in the case of auto insurance would be a situation where the applicant obtains insurance coverage based on providing a residence address in an area with a very low crime rate when the applicant actually lives in an area with a very high crime rate. Obviously, the risk of the applicant’s vehicle being stolen, vandalized, or otherwise damaged when regularly parked in a high-crime area is substantially greater than if the vehicle was regularly parked in a low-crime area.

How to Minimize Adverse Selection

Adverse selection by increasing access to information, thus minimizing asymmetries. For consumers, the internet has greatly increased access while reducing costs. Crowdsourced information in the form of user reviews along with more formal reviews by bloggers or specialist websites are often free and warn potential buyers about otherwise obscure issues around quality.

Warranties and guarantees offered by sellers can also help, allowing consumers to use a product risk-free for a certain period to see if it has flaws or quality issues and the ability to return them without consequence if there are issues. Laws and regulations can also help, such as Lemon Laws in the used car industry. Federal regulatory authorities such as the FDA also help ensure that products are safe and effective for consumers.

Insurers reduce adverse selection by requesting medical information from applicants in the form of requiring paramedical examinations, querying doctors’ offices for medical records, and looking at one’s family history. This gives the insurance company more information that an applicant may fail to disclose on their own.

Moral Hazard vs. Adverse Selection

Like adverse selection, moral hazard occurs when there is asymmetric information between two parties, but where a change in the behavior of one party is exposed after a deal is struck. Adverse selection occurs when there’s a lack of symmetric information prior to a deal between a buyer and a seller.

Moral hazard is the risk that one party has not entered into the contract in good faith or has provided false details about its assets, liabilities, or credit capacity. For instance, in the investment banking sector, it may become known that government regulatory bodies will bail out failing banks; as a result, bank employees may take on excessive amounts of risk to score lucrative bonuses knowing that if their risky bets do not pan out, the bank will be saved anyhow.

The Lemons Problem

The lemons problem refers to issues that arise regarding the value of an investment or product due to asymmetric information possessed by the buyer and the seller.

The lemons problem was put forward in a research paper, “The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism,” written in the late 1960s by George A. Akerlof, an economist and professor at the University of California, Berkeley. The tag phrase identifying the problem came from the example of used cars Akerlof used to illustrate the concept of asymmetric information, as defective used cars are commonly referred to as lemons. The takeaway is that due to adverse selection, the only used cars left on the market will ultimately be lemons.

The lemons problem exists in the marketplace for both consumer and business products, and also in the arena of investing, related to the disparity in the perceived value of an investment between buyers and sellers. The lemons problem is also prevalent in financial sector areas, including insurance and credit markets. For example, in the realm of corporate finance, a lender has asymmetrical and less-than-ideal information regarding the actual creditworthiness of a borrower.

The Bottom Line

Contrary to assumptions made by mainstream economic and financial models, information is not symmetrically accessible and available to all actors in a market. In particular, sellers and producers often have far more information about what they are selling than do buyers. This information asymmetry can lead to market inefficiencies via what is known as adverse selection. In insurance markets, applicants have more information about themselves than do insurers, meaning that they withhold key information about being higher-risk.

What Is After-Hours Trading?

After-hours trading is securities trading that starts at 4 p.m. U.S. Eastern Time after the major U.S. stock exchanges close. The after-hours trading session can run as late as 8 p.m., though volume typically thins out much earlier in the session. Trading in the after hours is conducted through electronic communication networks (ECNs).

Understanding After-Hours Trading

Traders and investors engage in after-hours trading for a variety of reasons. They may prefer trading with fewer market participants or their schedules may require it. They may want to take positions as a result of news that breaks after the close of the stock exchange. Or, they may want to close out a position before they leave on vacation.

Generally, after-hours trading refers to trading that takes place after normal market hours and up until about 8 pm. Premarket trading refers to trading that takes place before the start of normal market hours, generally from 7 a.m. until 9:25 a.m. Together, after-hours trading and premarket trading are referred to as extended-hours trading.

The precise times of extended-hours trading can depend on the ECN an investor uses or the financial institution where they place their orders. For instance, Wells Fargo allows after-hours trading from 4:05 p.m. ET until just 5 p.m.

Electronic markets (or ECNs) used in after-hours trading automatically attempt to match up buy and sell orders. If they can do so, trades are completed. If they can’t, trades remain unfilled.

After-hours trading typically only allows limit orders to buy, sell, or short, although a particular brokerage may be less restrictive. No stop, stop-limit, or orders with special instructions (such as fill or kill or all or none) are accepted. Moreover, orders are normally only good for the after-hours trading session in which they’re placed.

The maximum share amount per order is 25,000.

Quotes provided are limited to those available through the electronic market used. Investors may have access to other participating ECNs but it isn’t guaranteed.

Volume

In after-hours trading, the trading volume for a stock may spike on the initial release of news but most of the time thins out as the session progresses. The growth of volume generally slows significantly by 6 p.m. So, there is a substantial risk that investors will be trading illiquid stocks after-hours. 

Price

Not only does volume sometimes come at a premium in the after-hours trading sessions, so does price. It is not unusual for the spreads to be wide in the after-hours. The spread is the difference between the bid and the ask prices. Due to fewer shares trading, the spread may be significantly wider than during the normal trading session.

Participation

If liquidity and prices weren’t enough to make after-hours trading risky, the lack of participants may do the trick. That’s why certain investors and institutions may choose not to participate in after-hours trading, regardless of news or events.

It’s quite possible for a stock to fall sharply in the after hours only to rise once the regular trading session resumes the next day at 9:30 a.m. Many big institutional investors have a certain view of price action during after-hours trading sessions and express that view with their trades once the regular market re-opens.

Since volume is thin and spreads are wide in after-hours trading, it is much easier to push prices higher or lower. Fewer shares and trades are needed to make a substantial impact on a stock’s price. That’s why after-hours orders usually are restricted to limit orders. If your brokerage doesn’t restrict them, consider them anyway as a means to protect yourself from unexpected price swings and order fills.

Standard Trading vs. After-Hours Trading