What is Annual Percentage Rate (APR)?

An APR is like a milepost…

A sign along the highway can give a general idea of how far away your destination is, but it can’t tell you exactly when you’ll get there. You’ll need more information — such as your traveling speed — to estimate your arrival time. Similarly, an APR can help you gauge how much a loan or credit product might cost. But you’ll need more information to estimate the true cost, such as how fast you intend to pay it off, whether additional costs are excluded, or the effect of compound interest.

Annual percentage rate gives you an idea of the cost to borrow money over a year. You can find APRs for credit cards, auto loans, personal loans, mortgages, and other sources of credit. APR is more accurate than interest rate alone because it often includes other fees and charges. However, APR doesn’t always include all fees, and it doesn’t take into account compound interest — Or what happens when you pay interest on interest you’ve accumulated. As the name suggests, APR is expressed as a percentage.

APRs can either be fixed or variable. A fixed rate stays the same for the life of the loan. A variable APR changes over time, primarily based on fluctuations in the prime rate, which is the interest rate that banks charge customers with the highest credit ratings. The prime rate, in turn, responds to changes in the federal funds rate, which is the interest rate at which banks lend to each other. The Federal Reserve, the nation’s central bank, can take actions that influence the federal funds rate in order to boost or restrain the economy. With a variable APR, what you owe can rise and fall with these changes.

A simple interest rate will tell you how much you will pay in interest alone when you borrow money. But if you want to know how much a loan or credit product will cost you in a year including loan fees, you can calculate the APR in five steps:

1. Add the total interest amount to loan fees.
2. Divide this figure by the amount of the loan (principal).
3. Divide by the total number of days in the term of the loan (n).
4. Multiply by 365 (for days in a year) to find the annual rate.
5. Multiply by 100 to convert the annual rate into a percentage.

The formula is:

APR = (((Fees + Interest)/Principal)/n) * 365) * 100

For example, say you are looking at a one-year personal loan of $10,000 with a 10% interest rate and a loan origination fee of 2%.

Interest = $10,000 x 0.1 = $1000 Fees = $10,000 x 0.02 = $200 Principal = $10,000 n = 1 x 365 = (365)

So your APR is: ((($1000 + $200 /$10,000)/365) x 365) x 100 = 12%

It’s important to keep in mind that APR only includes simple interest. It ignores compound interest, which is the interest charged on accumulated interest that is added to your balance. APR won’t give you an accurate sense of what you’ll owe if your lender compounds interest.

Annual percentage rate gives you an idea of what a loan or credit card debt will cost over a year, but it turns a blind eye to compound interest. The effective annual rate (EAR) is an alternative that takes compound interest into account.

To figure out EAR, all you need to know is the APR (i) and how often interest is compounded each year (n). Here’s the formula:

EAR = ((1 + i/n)^n) - 1

Let’s figure out the EAR of an 8% APR for a loan that compounds interest monthly (12 periods in a year):

EAR = ((1 + .08/12)^12) -1

Once you do the math, you end up with 0.08299950672. Turning that into a percentage and rounding, you get 8.3%. So while our APR is 8%, the EAR is actually 8.3%.

Compound interest is something we’d like to avoid when it comes to debt, since it means paying more overall. But compound interest is great when you can earn it through savings. Annual percentage yield (APY) is a way of measuring what we stand to earn on savings and deposit accounts in one year, including compound interest.

Mathematically, APY is calculated exactly the same way as EAR. Why two names for the same thing? Because banks don’t want to call the interest you’re paying them a “yield” — It’s not good public relations to advertise that they are gaining from your debt. So, banks call the earnings you make off them through compound interest APY, and they call what you pay them to borrow money (including compound interest) EAR.

Financial institutions often use APY, instead of APR, for savings accounts and money market accounts because they want to show the maximum returns you stand to earn. Not surprisingly, lenders and credit card companies prefer to advertise APR, since it understates what you may end up paying thanks to compound interest.

Credit card APRs are usually expressed as a range, such as 14% - 29%. The APR you get within this range depends on going rates, as well as your credit history and other factors in your background. Most credit card APRs are based on variable interest rates.

Credit card APRs don’t include fees that you might incur for balance transfers, cash advances, and late fees because it is too difficult to determine ahead of time if you will incur them. Because they exclude so many potential charges, credit card APRs act more like an annual interest rate.

Credit cards can also come with different types of APRs for different charges or events in a single account:

• Purchase APR: This applies to new purchases you make with your card.
• Cash Advance APR: This applies when you pull cash out from the credit line on your card.
• Late Penalty APR: Your APR can increase permanently or for a limited time if you don’t make a minimum payment by your due date.
• Introductory APR: Some cards offer a low or 0% APR for a limited time for balance transfers or new customers.

Again, credit card APRs do not take compound interest into account. If you carry a balance, credit cards add interest to your balance daily — or compound it — using a daily periodic rate. The next day, they charge interest on that interest.

You can calculate your daily periodic rate by dividing your APR by 365 (the number of days in a year). For example, the daily periodic rate for a 24% APR would be (24% / 365 = 0.00065753424.) You can also find your daily periodic rate in a box (called a Schumer box) on your credit disclosure documents.

In order to understand what the true cost of carrying a balance on your credit card is, you need to use the effective annual rate (EAR) formula described above, which accounts for compound interest. If you plug in an APR of 20% into the EAR formula, you’ll find that a credit card with an APR of 20% is actually going to cost you 22% if you carry a balance. How you use a credit card has the biggest effect on how much a credit card will cost.

Annual percentage rates for mortgages include the interest rate and can include some of the closing costs required to get a mortgage, such as loan origination fees, processing fees, underwriting fees, broker fees, and points (optional fees you pay up front to lower the interest rate). This is why a mortgage’s APR is generally higher than its interest rate. A mortgage can come with interest rates that are variable, fixed, or a combination of both.

You need more information than APR to understand what a home loan truly costs. Not all lenders include the same fees in their APR calculation. You may want to confirm which fees are included, the length of the mortgage term, the interest rate, and other important variables to get a more accurate picture.

The fees included in a mortgage APR can sometimes be negotiable. Depending on the lender and the loan product, you may have the flexibility of paying more fees up front to lower your APR, or roll the fees into the mortgage resulting in a higher APR. This is why it’s important to understand exactly which fees are included in a home loan APR and why it can be difficult to compare loan products by APR alone.