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 Audit?

The term audit usually refers to a financial statement audit. A financial audit is an objective examination and evaluation of the financial statements of an organization to make sure that the financial records are a fair and accurate representation of the transactions they claim to represent. The audit can be conducted internally by employees of the organization or externally by an outside Certified Public Accountant (CPA) firm.

Understanding Audits

Almost all companies receive a yearly audit of their financial statements, such as the income statement, balance sheet, and cash flow statement. Lenders often require the results of an external audit annually as part of their debt covenants. For some companies, audits are a legal requirement due to the compelling incentives to intentionally misstate financial information in an attempt to commit fraud. As a result of the Sarbanes-Oxley Act (SOX) of 2002, publicly traded companies must also receive an evaluation of the effectiveness of their internal controls.

Standards for external audits performed in the United States, called the generally accepted auditing standards (GAAS), are set out by Auditing Standards Board (ASB) of the American Institute of Certified Public Accountants (AICPA). Additional rules for the audits of publicly traded companies are made by the Public Company Accounting Oversight Board (PCAOB), which was established as a result of SOX in 2002. A separate set of international standards, called the International Standards on Auditing (ISA), were set up by the International Auditing and Assurance Standards Board (IAASB).

Types of Audits

External Audits

Audits performed by outside parties can be extremely helpful in removing any bias in reviewing the state of a company’s financials. Financial audits seek to identify if there are any material misstatements in the financial statements. An unqualified, or clean, auditor’s opinion provides financial statement users with confidence that the financials are both accurate and complete. External audits, therefore, allow stakeholders to make better, more informed decisions related to the company being audited.

External auditors follow a set of standards different from that of the company or organization hiring them to do the work. The biggest difference between an internal and external audit is the concept of independence of the external auditor. When audits are performed by third parties, the resulting auditor’s opinion expressed on items being audited (a company’s financials, internal controls, or a system) can be candid and honest without it affecting daily work relationships within the company.

Internal Audits

Internal auditors are employed by the company or organization for whom they are performing an audit, and the resulting audit report is given directly to management and the board of directors. Consultant auditors, while not employed internally, use the standards of the company they are auditing as opposed to a separate set of standards. These types of auditors are used when an organization doesn’t have the in-house resources to audit certain parts of their own operations.

The results of the internal audit are used to make managerial changes and improvements to internal controls. The purpose of an internal audit is to ensure compliance with laws and regulations and to help maintain accurate and timely financial reporting and data collection. It also provides a benefit to management by identifying flaws in internal control or financial reporting prior to its review by external auditors.

Internal Revenue Service (IRS) Audits

The Internal Revenue Service (IRS) also routinely performs audits to verify the accuracy of a taxpayer’s return and specific transactions. When the IRS audits a person or company, it usually carries a negative connotation and is seen as evidence of some type of wrongdoing by the taxpayer. However, being selected for an audit is not necessarily indicative of any wrongdoing.

IRS audit selection is usually made by random statistical formulas that analyze a taxpayer’s return and compare it to similar returns. A taxpayer may also be selected for an audit if they have any dealings with another person or company who was found to have tax errors on their audit.

There are three possible IRS audit outcomes available: no change to the tax return, a change that is accepted by the taxpayer, or a change that the taxpayer disagrees with. If the change is accepted, the taxpayer may owe additional taxes or penalties. If the taxpayer disagrees, there is a process to follow that may include mediation or an appeal.

What Is Alpha?

Alpha (α) is a term used in investing to describe an investment strategy’s ability to beat the market, or its “edge.” Alpha is thus also often referred to as “excess return” or “abnormal rate of return,” which refers to the idea that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole. Alpha is often used in conjunction with beta (the Greek letter β), which measures the broad market’s overall volatility or risk, known as systematic market risk.

Alpha is used in finance as a measure of performance, indicating when a strategy, trader, or portfolio manager has managed to beat the market return over some period. Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index or benchmark that is considered to represent the market’s movement as a whole.

The excess return of an investment relative to the return of a benchmark index is the investment’s alpha. Alpha may be positive or negative and is the result of active investing. Beta, on the other hand, can be earned through passive index investing.

Understanding Alpha

Alpha is one of five popular technical investment risk ratios. The others are beta, standard deviation, R-squared, and the Sharpe ratio. These are all statistical measurements used in modern portfolio theory (MPT). All of these indicators are intended to help investors determine the risk-return profile of an investment.

Active portfolio managers seek to generate alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk. Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund’s return.

In other words, alpha is the return on an investment that is not a result of a general movement in the greater market. As such, an alpha of zero would indicate that the portfolio or fund is tracking perfectly with the benchmark index and that the manager has not added or lost any additional value compared to the broad market.

The concept of alpha became more popular with the advent of smart beta index funds tied to indexes like the Standard & Poor’s 500 index and the Wilshire 5000 Total Market Index. These funds attempt to enhance the performance of a portfolio that tracks a targeted subset of the market.

Despite the considerable desirability of alpha in a portfolio, many index benchmarks manage to beat asset managers the vast majority of the time. Due in part to a growing lack of faith in traditional financial advising brought about by this trend, more and more investors are switching to low-cost, passive online advisors (often called roboadvisors​) who exclusively or almost exclusively invest clients’ capital into index-tracking funds, the rationale being that if they cannot beat the market they may as well join it.

Moreover, because most “traditional” financial advisors charge a fee, when one manages a portfolio and nets an alpha of zero, it actually represents a slight net loss for the investor. For example, suppose that Jim, a financial advisor, charges 1% of a portfolio’s value for his services and that during a 12-month period Jim managed to produce an alpha of 0.75 for the portfolio of one of his clients, Frank. While Jim has indeed helped the performance of Frank’s portfolio, the fee that Jim charges is in excess of the alpha he has generated, so Frank’s portfolio has experienced a net loss. For investors, the example highlights the importance of considering fees in conjunction with performance returns and alpha.

The Efficient Market Hypothesis (EMH) postulates that market prices incorporate all available information at all times, and so securities are always properly priced (the market is efficient.) Therefore, according to the EMH, there is no way to systematically identify and take advantage of mispricings in the market because they do not exist.

If mispricings are identified, they are quickly arbitraged away and so persistent patterns of market anomalies that can be taken advantage of tend to be few and far between.

Empirical evidence comparing historical returns of active mutual funds relative to their passive benchmarks indicates that fewer than 10% of all active funds are able to earn a positive alpha over a 10-plus year time period, and this percentage falls once taxes and fees are taken into consideration. In other words, alpha is hard to come by, especially after taxes and fees.

Because beta risk can be isolated by diversifying and hedging various risks (which comes with various transaction costs), some have proposed that alpha does not really exist, but that it simply represents the compensation for taking some un-hedged risk that hadn’t been identified or was overlooked.

Seeking Investment Alpha

Alpha is commonly used to rank active mutual funds as well as all other types of investments. It is often represented as a single number (like +3.0 or -5.0), and this typically refers to a percentage measuring how the portfolio or fund performed compared to the referenced benchmark index (i.e., 3% better or 5% worse).

Deeper analysis of alpha may also include “Jensen’s alpha.” Jensen’s alpha takes into consideration the capital asset pricing model (CAPM) market theory and includes a risk-adjusted component in its calculation. Beta (or the beta coefficient) is used in the CAPM, which calculates the expected return of an asset based on its own particular beta and the expected market returns. Alpha and beta are used together by investment managers to calculate, compare, and analyze returns.

The entire investing universe offers a broad range of securities, investment products, and advisory options for investors to consider. Different market cycles also have an influence on the alpha of investments across different asset classes. This is why risk-return metrics are important to consider in conjunction with alpha.

Examples

This is illustrated in the following two historical examples for a fixed income ETF and an equity ETF:

The iShares Convertible Bond ETF (ICVT) is a fixed income investment with low risk. It tracks a customized index called the Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index. The 3-year standard deviation was 18.94%, as of Feb. 28, 2022. The year-to-date return, as of Feb. 28, 2022, was -6.67%. The Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index had a return of -13.17% over the same period. Therefore, the alpha for ICVT was -0 12% in comparison to the Bloomberg U.S. Aggregate Index and a 3-year standard deviation of 18.97%.

However, since the aggregate bond index is not the proper benchmark for ICVT (it should be the Bloomberg Convertible index), this alpha may not be as large as initially thought; and in fact, may be misattributed since convertible bonds have far riskier profiles than plain vanilla bonds.

The WisdomTree U.S. Quality Dividend Growth Fund (DGRW) is an equity investment with higher market risk that seeks to invest in dividend growth equities. Its holdings track a customized index called the WisdomTree U.S. Quality Dividend Growth Index. It had a three-year annualized standard deviation of 10.58%, higher than ICVT.

As of Feb. 28, 2022, DGRW annualized return was 18.1%, which was also higher than the S&P 500 at 16.4%, so it had an alpha of 1.7% in comparison to the S&P 500. But again, the S&P 500 may not be the correct benchmark for this ETF, since dividend-paying growth stocks are a very particular subset of the overall stock market, and may not even be inclusive of the 500 most valuable stocks in America.

Alpha Considerations

While alpha has been called the “holy grail” of investing, and as such, receives a lot of attention from investors and advisors alike, there are a couple of important considerations that one should take into account when using alpha.

1. A basic calculation of alpha subtracts the total return of an investment from a comparable benchmark in its asset category. This alpha calculation is primarily only used against a comparable asset category benchmark, as noted in the examples above. Therefore, it does not measure the outperformance of an equity ETF versus a fixed income benchmark. This alpha is also best used when comparing the performance of similar asset investments. Thus, the alpha of the equity ETF, DGRW, is not relatively comparable to the alpha of the fixed income ETF, ICVT.
2. Some references to alpha may refer to a more advanced technique. Jensen’s alpha takes into consideration CAPM theory and risk-adjusted measures by utilizing the risk-free rate and beta.

When using a generated alpha calculation it is important to understand the calculations involved. Alpha can be calculated using various different index benchmarks within an asset class. In some cases, there might not be a suitable pre-existing index, in which case advisors may use algorithms and other models to simulate an index for comparative alpha calculation purposes.

Alpha can also refer to the abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like CAPM. In this instance, a CAPM model might aim to estimate returns for investors at various points along an efficient frontier. The CAPM analysis might estimate that a portfolio should earn 10% based on the portfolio’s risk profile. If the portfolio actually earns 15%, the portfolio’s alpha would be 5.0, or +5% over what was predicted in the CAPM model.

DEFINITION of 90-Day Letter

90-Day Letter is an IRS notice stating that there was a discrepancy or error within an individual’s taxes and they will be assessed unless petitioned. The taxpayer has 90 days to respond, otherwise the audit deficiencies will result in reassessment. Also known as a Notice of Deficiency. 

BREAKING DOWN 90-Day Letter

Once you receive your notice, you have 90 days (150 days if the notice is addressed to a person who is outside the country) from the date of the notice to file a petition with the Tax Court, if you want to challenge the tax the IRS proposed, according to the agency. These notices are usually sent after or audit, in the case of people who fail to file a tax return or who have unreported income.

What The Notice Means

If you don’t dispute the accuracy of the assessment the Internal Revenue Service has made, you won’t need to amend your tax return unless you have additional income, expenses, or credits that you want to report. In that case, all you need to do is sign Form 5564, Notice of Deficiency and return it to the IRS with a check attached to avoid additional interest and or penalties.

If you agree with the findings but have additional income, expenses, or credits to claim, it will be necessary to amend your original tax return with Form 1040-X. You can do this through your online tax prep service or your tax professional or fill out the form yourself.

It gets more complicated if you disagree with the IRS findings. If you think the IRS notice is incorrect, incomplete or otherwise mistaken, you can contact them with additional information that will shed light on the case. You have 90 days from the date of the notice to dispute the claim. You can ask the Tax Court to reassess or correct or eliminate the liability proposed by the deficiency notice. During the 90 days and any period the case is being reconsidered the IRS by law can’t assess or put your account into collection.

Many taxpayers use a tax professional or attorney to handle the dispute process if the amount in question is significant. 

If you lose the appeal and don’t or can’t pay, the government can file a federal tax lien against your wages, personal property, or your bank account. This is a claim against the assets, not the seizure of them. That happens when a federal tax levy occurs and the IRS actually seizes your property. Payment plans can also be worked out to avoid liens and seizure.