Albert Einstein reportedly referred to compound interest as the greatest force on earth. Whether you agree or not, you should understand the common financial tools that use compound interest, such as annual percentage rate (APR) and annual percentage yield (APY)*—*and, more specifically, the difference between them. Both are used to calculate interest for investment and credit products. But what are they? Keep reading to find out more about the difference between these two interest calculations and what they mean for both borrowers and lenders.

### Key Takeaways

- An annual percentage rate represents the annual rate charged for earning or borrowing money.
- An annual percentage yield takes into account compounding, but an APR does not.
- Earned annual interest is another definition of how an annual percentage yield is earned.
- Credit card companies are required to disclose the APR on the card to customers.

## What Are APR and APY?

It's easy to understand why people may confuse the terms annual percentage rate and annual percentage yield. Both are applied to investment products and loans and, while they may sound the same, they are, in fact, quite different and are not created equal. In fact, they significantly affect how much you earn or must pay when they're applied to your account balances.

Investment companies generally advertise the APY they pay to attract investors because it seems like they'll earn more on things like certificates of deposit (CDs), individual retirement accounts (IRAs), and savings accounts. But it's a little different when it comes to lenders. Financial institutions often tout their credit products using APR since it seems like borrowers end up paying less in the long run for accounts like loans, mortgages, and credit cards.

APR does not take into account the compounding of interest within a specific year. It 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.

APR is calculated as follows:

$APR=\text{Periodic Rate }\times\text{ Number of Periods in a Year}$

APY, on the other hand, does take into account the frequency with which the interest is applied—the effects of intra-year compounding. This seemingly subtle difference can have important implications for investors and borrowers. APY is calculated by adding 1+ the periodic rate as a decimal and multiplying it by the number of times equal to the number of periods that the rate is applied, then subtracting 1.

Here's how APY is calculated:

$APY=(1+\text{Periodic Rate) }^{\text{ Number of Periods}-1}$

### APR and APY Example

A credit card company might charge 1% interest each month. Therefore, the APR equals 12% (1% x 12 months = 12%). This differs from APY, which takes into account compound interest.

The APY for a 1% rate of interest compounded monthly would be 12.68% [(1 + 0.01)^12 – 1 = 12.68%] a year. If you only carry a balance on your credit card for one month's period, you will be charged the equivalent yearly rate of 12%. However, if you carry that balance for the year, your effective interest rate becomes 12.68% as a result of compounding each month.

## What Is Compounding?

At its most basic level, compounding refers to earning or paying interest on previous interest, which is added to the principal sum of a deposit or loan. Most loans and investments use a compound interest rate to calculate interest. All investors want to maximize compounding on their investments, and at the same time minimize it on their loans. Compound interest differs from simple interest in that the latter is the result of multiplying the daily interest rate by the number of days between payments.

Compounding is especially important in our APR versus APY discussion because many financial institutions have a sneaky way of quoting interest rates that use compounding principles to their advantage. Being financially literate in this area can help you spot which interest rate you really get.

## The Borrower's Perspective

As a borrower, you are always searching for the lowest possible rate. When looking at the difference between APR and APY, you need to be worried about how a loan might be disguised as having a lower rate. Another term for APY is earned annual interest (EAR), which factors in compounding interest.

For instance, when you're shopping around for a mortgage, you are likely to choose a lender that offers the lowest rate. Although the quoted rates appear low, you could end up paying more for a loan than you originally anticipated.

Different countries have different rules and regulations in place to combat some of the unscrupulous activity surrounding quoting rates that have arisen in the past.

This is because banks often quote you the annual percentage rate on the loan. But, as we've already said, this figure does not take into account any intra-year compounding of the loan either semi-annually, quarterly, or monthly. The APR is simply the periodic rate of interest multiplied by the number of periods in the year. This may be a little confusing at first, so let's look at an example to solidify the concept.

What You Are Actually Paying | |||
---|---|---|---|

Bank Quote APR | Semi-annual | Quarterly | Monthly |

5% | 5.06% | 5.09% | 5.11% |

7% | 7.12% | 7.19% | 7.23% |

9% | 9.20% | 9.30% | 9.38% |

Even though a bank may quote you a rate of 5%, 7%, or 9%, depending on the frequency of compounding, you may actually pay a much higher rate. If a bank quotes an APR of 9%, the figure isn't taking into account the effects of compounding. However, if you were to consider the effects of monthly compounding, as APY does, you will pay 0.38% more on your loan each year*—*a significant amount when you are amortizing your loan over a 25- or 30-year period.

This example should illustrate the importance of asking your potential lender what rate they are quoting when seeking a loan. It is also important when comparing borrowing prospects to compare apples to apples—comparing the same types of figures—so that you can make the most informed decision.

## The Lender's Perspective

Now, as you may have already guessed, it is not hard to see how standing on the other side of the lending tree can affect your results in an equally significant fashion, and how banks and other institutions often entice individuals by quoting APY. Just as those who are seeking loans want to pay the lowest possible rate of interest, those who are lending money (which is what you're technically doing by depositing funds in a bank) or investing funds want to receive the highest rate of interest.

Let's suppose that you are shopping around for a bank to open a savings account. Obviously, you want one that offers the best rate of return on your hard-earned dollars. It is in the bank's best interest to quote you the APY, which includes compounding and therefore will be a sexier number, as opposed to the APR, which doesn't include compounding.

Just make sure you take a hard look at how often that compounding occurs, and then compare that to other banks' APY quotes with compounding at an equivalent rate. It can significantly affect the amount of interest your savings could accrue.

## The Bottom Line

Both APR and APY are important concepts to understand for managing your personal finances. The more frequently the interest compounds, the greater the difference between APR and APY. Whether you are shopping for a loan, signing up for a credit card, or seeking the highest rate of return on a savings account, be mindful of the different rates quoted.

Depending on whether you a borrower or a lender, financial institutions have different motives for quoting different rates. Always make sure you understand which rates they are quoting and then look at comparable rates from other institutions. The difference in the numbers may well surprise you*—*and the lowest advertised rate for a loan can actually turn out to be the most expensive.