Understanding Interest Rates

# Annual Percentage Yield (APY)

## Overview, Calculations, and Comparison to APR

Annual percentage yield (APY) is a helpful tool for evaluating how much you earn on your money. Compared to a simple interest rate quote, APY is a more accurate reflection of your true potential earnings.

APY is a number that tells you how much you earn with compound interest over the course of one year. It accounts for the interest you earn on your original deposit, as well as interest you earn on top of other interest earnings.

A higher APY is best when you’re comparing bank accounts for your savings. When paying interest on loans, a lower rate is better.

When you deposit funds into a savings account, money market, or certificate of deposit (CD), you earn interest. APY can show you exactly how much interest you’ll earn. With that information, you can decide which bank is best, and whether or not you want to lock up your money in CDs for a higher rate.

## What Makes APY Unique?

APY is useful because it takes compounding into account—a simple “interest rate” does not. Compounding happens when you earn interest on the interest that you previously received, which means you’re earning more than the quoted interest rate.

Example: You deposit \$1,000 in a savings account that pays a 5 % annual interest rate. At the end of the year, you have \$1,050 (assuming your bank pays interest only once per year). However, your bank might calculate and pay interest monthly. In that case, you end the year with \$1,051.16, and you would have earned an APY of more than 5 percent. The difference may seem small, but over many years (or with bigger deposits), the difference is substantial.

Single Payment Per Year: If your bank calculates and pays interest only once at the end of the year, the bank would add \$50 to your account.

Monthly Compounding: When your bank calculates and pays interest monthly, you receive small additions every month. In the table below, notice how the earnings increase slightly every month.

APY accounts for those more frequent interest calculations, so it’s more accurate than an interest “rate.” Fortunately, you almost always see the APY quoted from banks—so you don’t have to do any calculations yourself. But you can calculate APY yourself, and we’ll cover that below.

## APR vs. APY

Annual percentage rate (APR) is similar to APY, but it does not take compounding into account.

APY is more accurate than APR in some situations because it tells you how much a loan costs as interest costs compound. But when you borrow money, you typically only see the APR. In reality, you might pay APY—which is almost always higher with certain types of loans.

Credit card loans are an excellent example of the importance of understanding APR vs. APY.

If you carry a balance, you pay an APY that is higher than the quoted APR. Why? Card issuers typically add interest charges to your balance each month. In the following month, you’ll have to pay interest on top of that interest. It is similar to earning interest on top of interest you earn in a savings account.

The difference might not be significant, but there is a difference. The larger your loan and the longer you borrow, the bigger that difference becomes.

With a fixed-rate mortgage, APR is more accurate because you usually don’t add interest charges and increase your loan balance. What’s more, APR accounts for closing costs, which add to your total borrowing cost. However, some fixed-rate loans actually grow (if you don’t pay interest costs as they accrue). For more information, learn about different types of APR.

## Calculating APY

Calculating an investment’s APY can be challenging. But spreadsheets like Excel or Google Sheets make it easier. Use this spreadsheet (which already has the examples above filled in), or follow the process below.

• Enter the interest rate in cell A1 (interest rates need to go in decimal format).
• Enter the compounding frequency in cell B1 (use 12 for monthly, one for annually, etc.).
• Paste the following formula into any other cell: =POWER((1+(A1/B1)),B1)-1

For example, if the stated annual rate is 5%, type “.05” in cell A1. Then, for monthly compounding, enter “12” in cell B1. Note that for daily compounding you might use 365 or 360 depending on your bank or lender.

In the example above, you’ll find that the APY is 5.116%. In other words, a 5% interest rate with monthly compounding results in an APY of 5.116%. Try changing the compounding frequency, and you’ll see how the APY changes. For example, you might show quarterly compounding (four times per year) or the unfortunate one payment per year—which just results in a 5 % APY.

## The APY Formula

If you like doing math the old-fashioned way, here’s how to calculate APY:

APY = (1 + r/n )n – 1 where r is the stated annual interest rate and n is the number of compounding periods per year.﻿﻿

Finance people might recognize this as the Effective Annual Rate (EAR) calculation.

APY = 100 [(1 + Interest/Principal)^365/Days in term) – 1] where Interest is the amount of interest received and Principal is the initial deposit or account balance.﻿﻿ The carat ("^") means "raised to the power of."

Continuing our example, you receive \$51.16 of interest over the year, and your account balance was \$1,000. What was the APY?

1. APY = 100 [(1 + 51.16/1000)^365/365) – 1]
2. APY = 5.116%

APY is higher with more frequent compounding periods. If you're saving money in a bank account, find out how often the money compounds. Daily or quarterly is usually better than annual compounding—but check the APY for each option just to be sure.

You can also pump up your own “personal APY.” Look at all of your assets as part of the larger picture.

In other words, don’t think of one CD investment as separate from your checking account—they all work together toward your goals, and they should be positioned accordingly. Think of yourself as the Chief Financial Officer of You, Inc.

To maximize your personal APY, find ways to make sure that your money is compounding as frequently as possible. If two CDs pay the same interest rate, pick the one that pays out interest most often (and therefore has the highest APY). You can automatically reinvest your interest earnings—the more frequently, the better—and you'll start earning more interest on those interest payments.

### Article Sources

1. University of Wisconsin. "Cheat Sheet 2," Accessed Sept. 24, 2019.

2. Federal Deposit Insurance Corporation. "FDIC Law, Regulations, Related Acts," Accessed Sept. 24, 2019.