# Interest Rates: APR vs. APY

When comparing interest rates that a bank offers on a mortgage, home equity line of credit, car loan, credit card, certificate of deposit, or savings account, it’s important to know exactly what rate you are looking at.

Even a 0.5% difference in interest rate could cost you hundreds or thousands of dollars when compounded over years.

This post will serve as a quick primer on interest rate terminology and calculations.

## What is Annual Percentage Rate (APR)

Annual percentage rate, or APR, is the interest rate, without compounding.

It is often referred to as the nominal APR, or nominal interest rate.

Mortgage and other loan products will quote you an APR. It is essentially the yearly interest rate you pay if compounding is done only on an annual basis, and no other fees are factored in.

## What is Annual Percentage Yield (APY)?

Annual percentage yield, or APY, is the effective interest rate, with compounding factored in. For that reason, it is also referred to as the *effective* APR, or EAR.

Banking institutions have deposit products that compound over various periods – daily, weekly, monthly, annually, etc. They are required to express interest rates in the form of APY, or EAR, so that you can compare rates between institutions.

It is essentially the real rate you are are effectively receiving or paying, when compounding is factored in.

## How to Calculate APR and APY

**APR** = Periodic rate x number of periods in a year

For example, a credit card with a 1% monthly interest rate would have a 12% APR (1% x 12 = 12%)

**APY** = (1 + nominal APR/n)^n – 1

- n = the number of compounding periods per year.
- nominal APR is expressed in decimal format (i.e. 12% = 0.12)

For example, a credit card with a 12% APR, compounded monthly, would have an EAR equal to 12.68%. The equation would be (1 + .12/12)^12 – 1 = .1268 = 12.68%

If the credit line compounded daily, the EAR equation would be (1 + .12/365)^365 – 1 = .1274 = 12.74%

## Why APY is Important

In any borrowing or investment scenario that involves compounding and/or fees, you want to know what the EAR (APY) is.

In a mortgage or loan scenario, you’ll want to know what the EAR is after closing or other fees are factored in.

In a credit card scenario, companies will often quote you a nominal APR (annual percentage rate). However, since your balance compounds monthly, you do not end up paying the nominal APR. Due to the compounding, your EAR will be higher.

Knowing EAR allows you to compare apples to apples and make precise calculations.

## APR vs. APY Discussion:

Do you ever feel like you were misled by a bank or credit card company when only being presented with APR vs. APY?

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This is a great math lesson, and a good resource for people who want to try these calculations out themselves later on. I have always noticed banks reporting their products one way or the other, and it is important to know the difference. Even if it is a tenth off one way or the other, that could result in more or less money than you were planning on!

Hasn’t everyone been mislead by clearly promoting APR vs. APY? Looking at the math, maybe it’s for a good reason? I can see it being somewhat difficult to understand APY.

Agreed that this is a very important concept and at the core of financial literacy. Great job explaining quickly and clearly. I would add that while it is beneficial to understand the math behind an APY calculation, a simple financial calculator app downloadable for free is also a quick way to determine your APY. So those intimidated by the math have no excuses.

Good article. You did a good job of explaining it. Most people don’t know the concept and how it impacts their calculations when forecasting savings/gains. Question around apy is the most common query that we get from our users.

For people who use excel to do financial math shouldn’t just divide apy by 12 to get monthly interest if the calculations require compounding. It will be a double count. Instead, convert the apy to apr before using (monthly) compounding formula to get better forecast of your interest/investment gains. Almost all retirement/goal calculators on the web don’t differentiate between apy and apr and just ask for gains.

-R

Not enough people even know there is such a thing as an EAR. This is a great breakdown and explanation of how it works. I know that when I turned 18 I would have loved to have been aware of this – and I definitely feel like I was conned in the process!

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