The basic formula for APY

APY (Annual Percentage Yield) tells you how much money you'll actually earn in a year, including the effect of compounding — when the bank pays interest on your interest. To calculate it yourself, you need three pieces of information: the interest rate the bank offers (called the APR or annual percentage rate), how often the bank compounds that interest (daily, monthly, quarterly, or yearly), and the formula itself.

The formula is: APY = (1 + r/n)^n − 1, where r is the APR as a decimal and n is the number of times interest compounds per year. If your bank offers 4.5% APR compounded daily, you'd convert 4.5% to 0.045, divide by 365, add 1, raise it to the 365th power, then subtract 1. The result is your APY.

In practice, you almost never need to do this math yourself. Your bank is required to show you the APY on every savings account before you open it, and it updates that number whenever the rate changes. The point of learning the formula is understanding why APY is always slightly higher than APR — and why daily compounding beats monthly compounding.

Key Takeaways

  • APY includes the effect of compounding, so it is always equal to or higher than the APR your bank advertises.
  • Banks must show you the APY before you open an account, so you can compare savings accounts fairly without calculating it yourself.
  • Daily compounding produces a slightly higher APY than monthly or quarterly compounding, because interest gets added to your balance more often.
  • The difference between APR and APY grows larger as the interest rate rises, so it matters more when rates are high.

Why APY matters more than APR

When you compare two savings accounts, the APR can look the same but the APY can differ. This happens because of how often each bank compounds your interest. A bank offering 4.5% APR compounded daily will give you slightly more money than a bank offering 4.5% APR compounded monthly — even though the APR is identical.

Here's why: when interest compounds daily, the bank adds a tiny amount of interest to your account every single day. The next day, you earn interest on that interest too. When interest compounds monthly, you wait 30 days before that first interest payment hits your account, so you miss out on those daily compounding cycles. Over a year, those missed cycles add up.

The difference is small when interest rates are low (maybe a few cents on a $1,000 balance), but it grows noticeably when rates are high. This is why reading the APY — not the APR — is the only fair way to compare savings accounts.

What the numbers actually look like

Let's use a real example. Suppose you have $10,000 in a savings account earning 4.5% APR compounded daily. Using the formula above, the APY works out to about 4.60%. That means in one year, you'll earn roughly $460 in interest (4.60% of $10,000), not $450.

If the same bank offered 4.5% APR but compounded monthly instead, the APY would be about 4.59% — one-hundredth of a percent lower. On $10,000, that's a difference of about $1 per year. On $100,000, it's about $10 per year. The difference sounds small, but it compounds year after year, and it's why daily compounding is always better than less frequent compounding.

You can verify these numbers by checking your bank's account disclosures or by using an online APY calculator (many banks provide these on their websites). The goal is not to become a mathematician — it's to understand that APY is the real number that matters when you're deciding where to keep your money.

How to find the APY your bank shows you

Your bank displays the APY in the account details section of its website, usually near the interest rate or in a document called the "Truth in Savings Disclosure" or "Account Terms and Conditions." If you're shopping for a new account, the APY appears in the product comparison table or in the account details before you open it.

Some banks update their APY daily because they change their interest rates frequently. Others update it less often. If you're comparing accounts and the rates seem to change between one day and the next, that's normal — the bank has adjusted its APR, and the APY has shifted along with it. Always check the APY on the day you're making your decision, not a week earlier.

If you can't find the APY on the website, call the bank's customer service line or visit a branch. They are required by law to provide it, and it should take less than a minute to get the answer.

When to calculate APY yourself

You might want to calculate APY yourself if you're comparing accounts from banks that don't clearly display it, or if you're trying to understand how a specific compounding schedule affects your money. It's also useful if you're learning about how interest works in general.

For everyday banking decisions, though, you don't need to calculate anything. The bank has already done the math and shown you the APY. Your job is to read it, compare it across accounts, and choose the one that pays the most. If you do want to verify the bank's number or understand the math more deeply, an online calculator takes the work out of it — just plug in the APR and compounding frequency, and it shows you the APY when ready.

The difference between APY and actual earnings

APY tells you the percentage you'll earn, but it doesn't account for one important thing: your balance might change during the year. If you deposit $10,000 on January 1st and leave it untouched for 12 months, you'll earn almost exactly what the APY predicts. But if you withdraw $5,000 in June, you'll earn less, because you had a smaller balance for the second half of the year.

Banks calculate interest based on your daily balance, so every deposit and withdrawal changes how much you earn. The APY is a useful standard for comparing accounts, but your actual interest earnings depend on how much money you keep in the account and for how long.

Frequently Asked Questions

Is APY the same as interest rate?

No. The interest rate (APR) is what the bank pays you. APY is that rate plus the effect of compounding — interest earned on your interest. APY is always equal to or higher than APR, and it's the number you should use to compare accounts.

Why do banks show APY instead of just APR?

Federal law requires banks to show APY because it's the only fair way to compare accounts. Two banks might offer different APRs and different compounding schedules, making direct comparison impossible without APY. By showing APY, the law ensures you can see the true earning power of each account.

Does my bank recalculate APY every day?

No. APY is recalculated only when the bank changes its interest rate. However, the APY displayed on the website reflects the current rate and compounding schedule, so if you check it on different days and the number has changed, the bank has adjusted its APR.

Can I earn more than the APY shows?

No. APY is the maximum you can earn in a year if you keep your money in the account the entire time and don't make any deposits or withdrawals. If you withdraw money during the year, you'll earn less because your balance was lower for part of the year.

What if my bank compounds interest more than once a day?

Some banks compound interest multiple times per day, but the difference in APY is negligible — usually less than a hundredth of a percent. Daily compounding is already so frequent that more frequent compounding adds almost nothing. Focus on comparing APY across banks rather than worrying about compounding frequency.