The formula for APY and what it tells you

APY (annual percentage yield) is the total interest you earn in one year, expressed as a percentage of your account balance. Banks publish an APY so you can compare accounts fairly—it accounts for compounding, which means interest earned on top of interest. The formula is:

APY = (1 + r/n)^n − 1, where r is the annual interest rate and n is the number of times interest compounds per year.

Most savings accounts compound daily (n = 365), though some compound monthly (n = 12). The more often interest compounds, the higher your APY will be compared to the stated rate. You do not need to calculate this yourself—banks are required to disclose the APY on every savings account—but understanding the math helps you see why one account's 4.50% APY beats another's 4.45% even if the difference looks small.

Key Takeaways

  • Banks must display APY on savings accounts, so you can compare accounts without doing math yourself.
  • APY includes the effect of compounding, while the interest rate alone does not, which is why APY is always equal to or higher than the stated rate.
  • Daily compounding (365 times per year) produces slightly higher APY than monthly compounding (12 times per year) on the same interest rate.
  • To estimate your earnings, multiply your account balance by the APY and divide by 100—this gives you the dollars you will earn in one year if the rate stays the same.

Why APY matters more than the interest rate alone

The interest rate and APY are not the same thing. A bank might advertise a 4.50% interest rate, but the APY could be 4.51% or higher because of compounding. Each time interest is added to your account, that interest itself starts earning interest. Over a year, this effect adds up.

When you compare two savings accounts, always look at the APY, not the rate. A high-yield savings account with a 4.50% APY will earn you more money than a traditional savings account with a 4.50% rate, because the rate alone does not account for how often interest compounds. The bank's website and account disclosures will show both numbers, but APY is the one that matters for your actual earnings.

How to estimate your annual earnings

Once you know the APY, calculating how much you will earn is simple. Multiply your account balance by the APY (as a decimal), then divide by 100. For example, if you have $10,000 in an account with a 4.50% APY:

$10,000 × 4.50 ÷ 100 = $450 per year

This assumes the rate stays the same for the full year and you do not add or withdraw money. In reality, rates change, and most people deposit or withdraw throughout the year. Banks calculate interest daily, so your actual earnings will be slightly different—but this formula gives you a useful estimate for comparing accounts or planning how much you will earn.

What happens when rates change

Banks can raise or lower the APY on savings accounts at any time. High-yield savings accounts have changed rates frequently over the past few years as the Federal Reserve adjusted its benchmark rate. When a bank lowers your APY, the change usually takes effect immediately on new interest earned, though some banks give notice first.

You will not lose money you have already earned, but your future earnings will be lower if the APY drops. If you are comparing accounts, check the current APY on the bank's website or app—the rate you see in an advertisement may be outdated. Some banks lock in a rate for a set period (like a certificate of deposit), but regular savings accounts have variable rates that can change without warning.

Compounding frequency and how it affects your total

Interest compounds when the bank adds earned interest to your account, and then that interest starts earning interest too. The more often compounding happens, the more you earn. Most savings accounts compound daily, which means interest is calculated and added 365 times per year. A few accounts compound monthly (12 times) or quarterly (4 times).

The difference between daily and monthly compounding is small on most balances. On $10,000 at 4.50% APY, daily compounding might earn you about $450 per year, while monthly compounding might earn $449.50—a difference of 50 cents. But on larger balances or higher rates, the gap widens. When you compare accounts, the APY already reflects the compounding frequency, so you do not have to adjust for it yourself.

How banks calculate APY (the full math)

Banks use the formula APY = (1 + r/n)^n − 1 to convert the interest rate into an annual yield. Here is a concrete example: suppose a bank offers a 4.50% interest rate compounded daily.

r = 0.045 (the 4.50% rate as a decimal), n = 365 (daily compounding). Plug in: (1 + 0.045/365)^365 − 1 = (1.000123288)^365 − 1 = 0.04596 = 4.596%. So the APY is 4.596%, slightly higher than the 4.50% rate. This is the number the bank will display on the account, and it is what you should use to compare accounts or estimate your earnings.

You do not need to do this calculation yourself—the bank is required by law to show you the APY—but understanding it helps you see why daily compounding beats monthly compounding and why the APY is always at least as high as the stated rate.

Frequently Asked Questions

Is APY the same as interest rate?

No. The interest rate is what the bank pays on your balance, while APY includes the effect of compounding. APY is always equal to or higher than the interest rate. Use APY when comparing accounts, because it shows your actual earnings.

Do I have to calculate APY myself?

No. Banks are required to disclose the APY on every savings account. You will see it on the account page, in advertisements, and in the account terms. You can use the APY to estimate your earnings, but you do not have to calculate it from the interest rate.

What if I withdraw money during the year?

Banks calculate interest daily on your current balance, so your actual earnings will be lower if you withdraw money. The APY assumes your balance stays the same for the full year. If you withdraw $2,000 halfway through the year, you will earn less than the APY estimate because you earned interest on a smaller balance for part of the year.

Does APY change, and how often?

Yes. Banks can change the APY on savings accounts at any time, usually in response to changes in the Federal Reserve's benchmark rate. High-yield savings accounts have changed rates frequently in recent years. Check your bank's website or app to see the current APY, because rates advertised online may be outdated.

Why do different banks offer different APYs?

Banks set their own rates based on their costs and competition. High-yield savings accounts at online banks often offer higher APYs than traditional banks because they have lower overhead. Credit unions may also offer competitive rates. The APY you see depends on the bank and the account type, so comparing accounts before you open one can save you money over time.