Albert Einstein reportedly referred to compound interest as the greatest force on earth. Whether you agree or not (and far be it from us to dispute one of the best brains in scientific history), 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 applied to investment products and loans (including credit card debt), but they are not created equal, and they significantly affect how much you earn or must pay when they're applied to your account balances.

### What Is Compounding?

At its most basic, compounding refers to earning interest on previous interest, which is added to the principal sum of a deposit or loan. Most loans and investments use 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 vs. 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 will help you spot which interest rate you are really getting.

### Defining APR and APY

APR is the annual rate of interest that is paid on an investment, without taking into account the compounding of interest within that year. Alternatively, APY 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.

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. APY is calculated by adding 1+ the periodic rate as a decimal and multiplying it by itself a number of times equal to the number of periods that the rate is applied, then subtracting 1.

Or, in formula form:

For example, a credit card company might charge 1% interest each month; therefore, the APR would equal 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.

### 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 means that compounding interest is factored in.

When looking for a mortgage, for example, 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.

This is because banks will often quote you the annual percentage rate (APR) 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 (every six months), quarterly (every three months) or monthly (12 times per year). 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:

As you can see, even though a bank may have quoted you a rate of 5%, 7% or 9%, depending on the frequency of compounding (this may differ depending on the bank, state, country, etc.), you could 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 will 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 wants 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 are seeking 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. They want to quote the highest possible rate they can to entice you – hey, they're trying to run a business. 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 that your savings could accrue.

It should be noted that different countries have different rules and regulations in place to combat some of the unscrupulous activity surrounding quoting rates that has arisen in the past.

### 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, banks and 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.