Learn About APR, APY, and EAR Interest Rates

When most people shop for financial products, they tend to focus too much on the listed interest rate. It is easy to dismiss the fine print under the immense amount of legal wording, which usually includes the terms APR (annual percentage rate) and APY (annual percentage yield)—or to use a synonym for the latter, EAR (effective annual rate)—as just arcane trios of letters.

However, there’s plenty of difference between the similar but not identical APR and APY. Each expression sounds straightforward enough, but misidentifying one as the other can cost you plenty.

Annual percentage rate (APR) is a measure that attempts to calculate what percentage of the principal you’ll pay per period (in this case a year), taking every charge from monthly payments over the course of the loan, upfront fees, etc. into account.

As it turns out, the Alpha Mortgage—interest only—loan in the example above carries the lower APR. With the Beta Mortgage—interest with an upfront charge—loan, you’re essentially paying $3,000 for the privilege of borrowing $100,000, and thus effectively borrowing only $97,000. However, you’re still making interest payments that the lender is basing on a $100,000 loan, not a $97,000 one. A lower denominator has the same effect as a higher numerator. The APR on the Alpha Mortgage loan is 5.00%, but the APR on the Beta Mortgage loan is 5.02%.

To calculate the APR for a loan that incorporates costs beyond those of the principal borrowed, first determine how much the periodic payments are.

For the Beta Mortgage loan, each monthly payment is:

The $100,000 is the gross principal borrowed, .0475 the interest rate, 12 is the number of periods in a year, and 360 is the number of periods over the course of the loan. After calculating, you’ll find that the monthly payment is $521.65.

Then, divide the monthly payment into the net amount you’re borrowing,

The APR is the unknown quantity that solves this equation:

You can’t figure this out through any amount of algebraic manipulation. You'll need either a fondness for trial-and-error and an awful lot of patience or a computer. [In Microsoft Excel, the formula is ‘RATE (nper, pmt, pv, fv, type, guess).' Use 360; -521.65 (rounded); and for the first three values, respectively]. Multiply by 12 to get the annual rate. The resulting rate is 5.02%.

Of course, in addition to the above-mentioned method of calculating an APR, you can compare the APRs of mortgages using a tool like a mortgage calculator. It is important to understand the fundamentals of calculating the APR, but using a mortgage calculator can save you time and simplify things. 

APY differs from APR in that the latter takes only simple interest into account. APY incorporates the additional complication of compound interest: interest charged on the simple interest, which again distorts the numbers and increases a borrower’s obligations – or a saver's gains – beyond the standard simple interest rate.

Note that APY and EAR are identical. They represent the same quantity but are quoted by one name or the other depending on the circumstance. The expressions are two sides of the same coin, in much the same way that an accounts payable for one business is an accounts receivable for another. A credit card issuer, for example, would use the term EAR (effective annual rate) rather than APY, because it’s not good public relations to talk in terms of the “yield” that the cardholders’ payments are generating for the issuer.

Compound interest – interest on interest – is a subject that should warrant its own article, and does, but suffice it to say that knowing that compound interest differs from simple interest isn’t enough. When calculating APY/EAR, the compounding period is everything. Interest that compounds semi-annually is far different from interest that compounds daily, as it does on most credit cards.

To determine the APR and APY on accounts with compounding interest, start with the interest rate per compounding period – in this case, that means per day. Target 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.

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 (disregarding for a moment that the issuer probably won’t let you make daily payments on your card, let alone have them post immediately, and also disregarding that pennies don’t carry out to two additional decimal places).

To calculate the APY, instead of multiplying 0.06273% by the number of compounding periods in a year, add 1 (which represents the principal) and take that number to the power of the number of compounding periods in a year. Subtract 1 from the result to get it as a percentage.

$\begin{aligned} &.0006273\times365=\textbf{22.9\%APR}\\ &\left(1.0006273^{365}\right)-1=\textbf{25.72072\%APY}\\ \end{aligned}$​.0006273×365=22.9%APR(1.0006273365)−1=25.72072%APY​

That’s pretty much it. The difference between APR and APY can be illustrated more forcefully in a couple of equations than in any amount of prose. The higher the interest rate, and to a lesser extent the fewer the compounding periods, the greater the difference between APR and APY.

Understand that of the two, APY is the more universally applicable measure, the one that states how much you’ll be paying in interest charges (or receiving, in the case of deposit accounts) regardless of compounding frequency. That’s why the Truth in Savings Act of 1991 mandates that APY be disclosed with every deposit account offered by financial services firms.

Given that an APR and a different APY can be used to represent the same interest rate, it stands to reason that lenders and borrowers will pick the more flattering number to state their case. A bank might 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, rather than the borrower, and thus tries to convince its borrowers that it’s charging a rate as close to zero as possible.

So what can a borrower overwhelmed with data do? As always, caveat emptor. Look for a listed APY before paying attention to APR. If no APY is listed, calculate it from the listed periodic interest rate via the method shown here. And if you’re concerned about how much your credit card issuer is charging you in interest, one foolproof way around that is to pay your balance in full every month. That’s a nominal rate, an APR and an APY of zero.