Some version of the above question pops up in reader emails perhaps once a month. I thought it might make sense to explain exactly how it works. Along the way, we’re going to get into the ideas of APR and APY and how they affect you.
Interest Accrued Annually
Most of the time, we deal with interest that accrues annually. This is the way most people seem to think about interest – it’s easy to understand and works in most situations.
Let’s stop for a moment and talk about what accrue means. When interest accrues, it means that the bank calculates how much interest you owe (or are owed) and applies that to your balance.
For example, let’s say you had a $100,000 debt with a 12% interest rate. If the interest is accrued annually, the calculation is really easy. You just multiply the amount – $100,000 – by the interest rate – 12% (which you’d type into a calculator as 0.12) – and that gives you $12,000 in new interest, giving you a new balance of $112,000.
Often, you’ll see on bill statements and advertisements that companies talk about both APR and APY as the percentage rates. APR is short for Annual Percentage Rate, while APY is short for Annual Percentage Yield. With interest that accrues annually, there is no difference between APR and APY. It only matters when interest accrues more frequently than that, as we’ll see below.
Interest Accrued Monthly
Some debts accrue monthly instead of annually. Here, things get a little trickier.
The first number here that’s important is the APR, which is the truly important number when it comes to debts (and interest). Every debt and every savings account you come across will have an APR that describes how much interest pays into that account over the course of a year. (As we’ll see, that number only tells you part of the story, but it’s still vital.)
If you’re accruing interest monthly, you have to divide that APR into 12 equal parts – one for each month. So, let’s keep looking at that $100,000 debt from the earlier example, the one with the 12% APR. If we divide that 12% into 12 equal parts, we get 1% per month.
So, in January, you do the first accrual. You take $100,000, multiply it by 1% (giving you $1,000), and add it back to the balance, giving you $101,000.
In February, you do it again. You take the new balance, $101,000, multiply it by 1% (giving you $1,010), and add it back to the balance, giving a new balance of $102,010.
In March, you do it again. You take the new balance of $102,010, multiply it by 1% (giving you $1,020.10), and add it back to the balance, giving a new balance of $103,030.10.
You get the idea. So, let’s skip ahead to December.
In December, you would take your balance of $111,566.83, multiply it by 1% (giving you $1,115.67), and add it back to the balance, giving a new balance of $112,682.50.
Here’s the thing to notice. You have the same starting balance – $100,000 – and the same APR – 12% – but if you accrue it annually, you have an ending balance of $112,000. If you accrue it monthly, you have an ending balance of $112,682.50.
The difference in how the money is accrued makes a difference of $682.50.
Here’s where APY becomes important. In this case, the APY is 12.6825%. If you take the original balance of $100,000 and multiply it by the APY, you’ll get $12,682.50. Add that back to the balance and you get $112,682.50 … the balance you get when you accrue monthly.
In other words, APY is the number that banks quote when more frequent accrual is taken into account. When they want to make the interest rate look bigger, they’ll use APY. This happens when you’re opening a savings account, for example. When banks want the interest rate to look smaller, they’ll use APR – when you’re taking out a loan, for example.
Interest Accrued Daily and Continuously
Some banks will accrue interest daily. Some even accrue it continuously. Rest assured, the more often a bank accrues interest on your debt, the worse it is for you (on the other hand, the more often a bank accrues interest on your savings account, the better it is for you).
So, let’s look again at the $100,000 loan at 12% APR.
If interest is being accrued daily… you better break out the spreadsheet. You’ll need to divide 12% by 365, giving you 0.032876712% calculated each day. Then, you have to do the calculation described above 365 times. I’ll save you the trouble – if interest is accrued daily, you’ll end up with a balance of $112,747.46. This debt would have an APY of 12.74746%, in other words.
What about constant accruing? It uses a mathematical formula that essentially breaks the time slices down even further until the time slices approach zero (here’s a if you want to dip your toes into the math). If you use that method, the balance is $112,749.69, or a 12.74969% APY.
Why This Matters
It’s all about your money. On large balances, the differences in how interest rates are accrued can easily mean hundreds or thousands of dollars a year.
If there’s one single message you should take home from this article, it’s this: if you’re borrowing money, look at the APY. That’s the actual interest rate you’ll be paying when the different “accrual” methods are taken into account. In situations where the APR is the same across banks (or very close), those accrual rates can make all the difference and can save you hundreds or thousands of dollars. The reverse is true with savings accounts – the APY will tell you how much you’ll actually earn in a year if you leave the balance alone.