APY vs APR, the two rates that quietly run your money

APR and APY both describe an interest rate, and that is where the confusion starts. APR is the simple annual rate with the compounding stripped out. APY folds the compounding back in, so it shows what the rate actually does over a full year. For money you earn, like a savings account, you want a high APY. For money you owe, like a loan or a credit card, you want a low APR. Same idea, two names, and banks pick which one to show you based on whether the number flatters them.

What each letter actually means

APR stands for annual percentage rate. It is the plain yearly rate before any compounding. If a card lists 24% APR, that is the headline cost of carrying a balance for a year, quoted as if interest were charged once at the end. APR is the rate lenders are required to advertise on loans and cards, because it is the honest baseline cost of borrowing.

APY stands for annual percentage yield. It takes the same underlying rate and accounts for how often interest gets added to your balance. Every time interest posts, your balance grows a little, and the next round of interest is calculated on that slightly larger number. APY captures that snowball. Because of it, APY is always equal to or higher than the APR it came from. They match only when interest compounds exactly once a year.

Why the two numbers split apart

Compounding is the whole reason APY and APR differ. Take a 12% APR that compounds monthly. The bank does not wait until December to charge or pay the full 12%. It splits the year into twelve pieces and applies 1% each month, because 12% divided by 12 months is 1%.

The catch is that the second month's 1% is charged on a balance that already grew by the first month's 1%. Then the third month builds on the second, and so on. By the end of the year you have not paid 12%, you have paid a bit more, because interest kept stacking on interest. Run the twelve months out and the effective rate, the APY, lands at about 12.68%. You can reproduce any version of this in our compound interest calculator by changing how often it compounds.

The worked example: 12% APR becomes 12.68% APY

Start with $1,000 and a 12% APR that compounds monthly. Each month the balance gets multiplied by 1.01 (that is the 1% monthly slice). Here is the first quarter and the year-end result, so you can see the snowball build.

Notice the interest column climbs every month even though the rate never changes. Month one earns $10.00. Month two earns $10.10, because it is 1% of a bigger balance. By month twelve the same 1% is worth $11.16. After the full year your $1,000 has grown to $1,126.83, which is a gain of $126.83, or 12.68%. That 12.68% is the APY. The 12% you started with was the APR.

The arithmetic behind it is one line: take 1 plus the monthly rate, raise it to the number of compounding periods, and subtract 1. So (1 + 0.12/12)^12 - 1 = 0.1268, or 12.68%. Compound the same 12% APR daily instead of monthly and the APY creeps up to about 12.75%. More frequent compounding always pushes APY a little higher, which is why the gap between APR and APY widens as the rate climbs.

Earning vs owing: which way to root for

The direction you want each number to move depends on which side of the money you are on.

• Money you earn (savings, CDs, money market). You want a high APY. A high-yield savings account at 4.50% APY pays you more than a big-bank account at 0.01% APY on the exact same deposit. Since deposits are quoted in APY, you can compare two savings accounts directly. See our banking guide for where to keep cash that earns instead of sitting idle.
• Money you owe (cards, auto loans, mortgages). You want a low APR. A card at 22% APR costs you far less to carry than one at 29% APR. Loans are quoted in APR, so card to card and loan to loan you are comparing the same measure.

The danger zone is comparing across measures. A credit card advertised at 22% APR is actually charging you more like 24.6% APY once daily compounding is counted, which is the number that shows up in what you really pay. We break that down in how credit card interest is really calculated. Meanwhile a savings account at 22% APY would be paying you the full 22% after compounding. Same digits, different meaning, because one is the rate before the snowball and one is the rate after it.

How to compare without getting fooled

The rule is short: compare the same measure on both things you are weighing. APY against APY, or APR against APR. Never APY against APR. If one account gives you APR and the other gives you APY, convert one so they match before you decide.

On the savings side this is usually easy, because banks already quote deposits in APY. Line up the APYs and pick the bigger one. On the borrowing side, lenders quote APR, so line up the APRs and pick the smaller one. The place people slip is treating a card's APR as if it were the full cost, or treating a savings APY as if it were a simple rate. The conversion protects you. When in doubt, push both numbers into the same form and the better deal becomes obvious.

One more habit worth keeping: on a savings account, the difference between a 4.50% APY and a 0.40% APY on $10,000 is about $410 versus $40 in a year. That gap is free, and it costs you nothing but a transfer to claim it. Move the cash, then compare your debt the same careful way, and you have used both rates the way the bank uses them.

FAQ

Which is which, APR or APY?

APR is the annual percentage rate, the simple yearly rate before compounding. APY is the annual percentage yield, the same rate after compounding is counted. A quick memory hook: yield is what you actually get, so APY is the truer number, and it is the one banks show you on savings because it looks bigger. APR is the headline borrowing rate, and it is the one banks show you on loans and cards because it looks smaller.

Why are the two numbers different at all?

Because of compounding. Interest gets added to your balance more than once a year, and each round is calculated on the new, slightly larger balance. APR ignores that effect and APY includes it, so APY ends up higher whenever interest compounds more than once a year. A 12% APR compounding monthly becomes a 12.68% APY. If interest compounded only once a year, APR and APY would be identical.

Which one should I compare when I am shopping?

Compare the same measure across both options. For savings accounts, compare APY to APY and choose the higher one, since deposits are already quoted in APY. For loans and credit cards, compare APR to APR and choose the lower one, since debt is quoted in APR. The only mistake that matters is mixing them: never weigh an APY on one account against an APR on another without converting first.

Does more frequent compounding really change much?

At low rates, barely. At high rates, enough to notice. A 12% APR is 12.68% APY compounded monthly and about 12.75% APY compounded daily, a difference of less than a tenth of a percent. On a 1% savings rate the gap between monthly and daily compounding is a rounding error. The frequency matters most on high-rate debt, where daily compounding on a 25%+ APR quietly adds a few percentage points to what you actually pay over a year.