alt-text

Get the Marcus App

Easy mobile access

APR vs. APY: Isn’t It All Just Interest?

Share this article

What we’ll cover:

  • Savings accounts generally include APY, which represents the interest rate plus the power that compounding could have on your savings over the course of a year
  • When you borrow money, you’ll typically see the APR, which represents the cost of borrowing money
  • When you take out a loan, the APR summarizes the interest, upfront costs and fees you’ll pay over the course of the year
  • When you borrow using credit, the APR is the interest rate you are charged on purchases not paid in full by the statement balance due date
  • Learn how to calculate both APY and APR in this article 

If you’ve worked with a bank to borrow money, to save more, or to do a little of both, you’ve probably tangled with interest in some form or fashion. But the experience if you’re borrowing or saving is a little different.

When you drop money into a savings account, money market account or certificate of deposit, you may see the account APY in various places, or, at the very least, on the promotional information for these accounts.

But, when you’re borrowing money, interest is calculated a little differently and loan and credit statements include APRs instead of APYs.

If it’s all interest, shouldn’t the measurements be the same? You’d think so, but APY applies when you’re saving money (think savings accounts, CDs, money market accounts) and APR pops up when you’re borrowing money. We dive into the details here, that is, if you’re interested in learning more.

Interest: Why it exists 

When you open a savings account, you expect banks to offer a little something in return for leaving your money with them. Banks do this because they then turn around and use that money (your money) to, amongst other things, offer loans at a rate that’s higher than what they’re offering savings customers. 

When you take out a loan (including credit cards), things work in reverse. Instead of banks courting your deposits by offering interest so they can turn around and lend it, now borrowers are the ones seeking some financial support. And that financial support comes with a price – interest – in addition to the money that’s being borrowed. It’s a key way lenders earn money by loaning money.

Saving: What’s behind the Annual Percentage Yield (APY)

Savings accounts generally tout an annual percentage yield (APY) instead of an interest rate. If you see the APY and interest rate side by side, you’ll notice the APY is usually slightly higher. This is because APY represents the interest rate in addition to the impact compounding can have on your savings over the course of a year. Compounding adds interest you’ve earned to the balance, and the interest rate applies to the bigger balance.  

Keep in mind that the APY is a general guideline because if you’ve got an account with a variable interest rate you could earn more interest if the rate rises during the year, and a little less if it drops.

How to calculate APY

This is the basic formula for APY: APY =(1+r/N)^N-1

= Interest rate: The percentage that your bank has stated your account will earn.

N = Number of compounding periods per year or the number of days in the term of the account. You can usually put 365 since there are 365 days in a year (though some banks consider a year 360), unless the terms indicate another stated maturity, such as 6 months or 18 months. If you’re using 365, the formula becomes a lot simpler:

APY = 100 (Interest/Principal)

For example, if you know that you will earn a 2.23% interest rate and your account compounds interest daily, like at Marcus, you can get the following:

  • APY=(1+.0223/365)^365-1=2.25%

Lending: What’s behind the Annual Percentage Rate (APR)

If you’re borrowing money from someone other than your parents or best friend, you can expect to pay interest on top of the money you’re borrowing. To ballpark what that loan will cost once you’ve finished paying it off, you’ll want to look at the Annual Percentage Rate (APR).  

But what goes into that calculation depends on how you’re borrowing the money, because APRs are calculated differently for loans and credit cards.

When you take out a loan

The APR summarizes the interest, upfront costs and fees you’ll pay over the course of the year. This summary is expressed as a percentage of the amount borrowed.

Comparing APRs could help you compare loans because they provide a shared baseline – they represent the rate and any upfront fees you’ll pay. You’ll also want to read a loan’s fine print to make your decision, but looking at the APR is generally considered a good filter when you’re assessing your options.

How to calculate APR for a loan

This is a two-part calculation that includes determining your monthly payment and then the APR.

For example, let’s say you get a $50,000 personal loan with a fixed 10% interest rate for five years. This loan also has a $300 origination fee.

1. To calculate your monthly payment using Excel:

  • The Excel formula is = PMT (interest rate/number of months, loan term in months, loan amount including fees, final value)

 

2. How to calculate APR (RATE): Once you have the monthly payment, you can calculate APR.

  • The Excel formula is = RATE (loan term in months, monthly payment amount, loan amount minus fees, final value)*12

For this formula you’ll need to subtract any fees from the loan amount. You’ll also have to multiply the rate by 12 to get the actual annual percentage rate. 

Here is what the monthly payment would be in our example:

  • =RATE (60,-1062.35,49700,0)*12
  • The result is 10.26%

When you borrow using credit

The APR is the interest rate you are charged on purchases not paid in full by the statement balance due date. If you pay your balance in full and on time, chances are you won’t pay any interest.

But there is a bit more to it than that (had to be too simple, right?). One thing to know about credit card APRs is that a single card could offer different APRs, depending on what you’re using the card for. For example, you could end up with a card that applies one APR to cash advances, another for purchases, and another if you’ve triggered a penalty. Rates can be variable, so the rate you have one month may not be the rate you have the next month.

How to calculate APR for a credit card

This calculation includes four steps – finding the Daily Periodic Rate, finding your daily average balance, identifying your billing period and calculating.

1. Find the Periodic Rate, which is the compounding frequency

The simplest way to find this is to scan your credit card statement look for the table also known as the “Schumer Box”, which summarizes the cost of a credit card. In this case, you’re looking for how the card computes your balance or the “finance calculation method.” Many credit cards charge interest using the average daily balance; this means they charge interest daily (the daily periodic rate). If there’s no grace period – also in the Schumer Box – this means interest starts building immediately. Grace periods are common. They are the amount of time between the billing cycle and the payment due date. You won’t pay interest if you pay in full on time, and have a grace period. 

2. Divide the APR by the periodic rate

Since the APR (also in the Schumer Box) is an annual figure, you’ll want to divide it by the finance method. If it’s daily, you’ll divide the APR by 365. If it’s monthly, by 12.

3. Calculate your average daily balance

This is a little more involved because you need a record of how much credit you’ve used at the end of each day of a billing period. (Apps that track your purchase history can be a big help here). For a month with 30 days, this means adding the balance at the end of each of these days and dividing them by the number of days in the billing cycle.

4. Complete the calculation

Multiply the average daily balance (step 3) by the periodic rate (step 2). Then multiply this result by the number of days in the billing cycle.

1. Find the Periodic Rate, which is the compounding frequency

The simplest way to find this is to scan your credit card statement look for the table also known as the “Schumer Box”, which summarizes the cost of a credit card. In this case, you’re looking for how the card computes your balance or the “finance calculation method.” Many credit cards charge interest using the average daily balance; this means they charge interest daily (the daily periodic rate). If there’s no grace period – also in the Schumer Box – this means interest starts building immediately. Grace periods are common. They are the amount of time between the billing cycle and the payment due date. You won’t pay interest if you pay in full on time, and have a grace period. 

2. Divide the APR by the periodic rate

Since the APR (also in the Schumer Box) is an annual figure, you’ll want to divide it by the finance method. If it’s daily, you’ll divide the APR by 365. If it’s monthly, by 12.

3. Calculate your average daily balance

This is a little more involved because you need a record of how much credit you’ve used at the end of each day of a billing period. (Apps that track your purchase history can be a big help here). For a month with 30 days, this means adding the balance at the end of each of these days and dividing them by the number of days in the billing cycle.

4. Complete the calculation

Multiply the average daily balance (step 3) by the periodic rate (step 2). Then multiply this result by the number of days in the billing cycle.

For example, you make one $5,000 charge on the first day of your 30-day billing cycle. Your APR is 25% on a card that calculates interest using the average daily balance.

  • The daily periodic rate is 25% APR/365 periodic rate = 0.06849%
  • Average daily balance is $5,000
  • Days in the billing period is 30

$5,000 x 0.06849% x 30 = $102.74 in interest you’d pay on that month’s bill if you carried the balance

Saving for a better future? See how you can start growing your money today with a Marcus Online Savings Account.

This article is for informational purposes only and is not a substitute for individualized professional advice. Articles on this site were commissioned and approved by Marcus by Goldman Sachs®, but may not reflect the institutional opinions of The Goldman Sachs Group, Inc., Goldman Sachs Bank USA or any of their affiliates, subsidiaries or divisions.