The formula for APY is straightforward: multiply your interest rate by the number of times interest compounds per year, then add 1, raise that to the power of the number of compounding periods, subtract 1, and multiply by 100 to get a percentage.
In practice, you do not need to do this math yourself—your bank publishes the APY, and you can find it on your account statements, the bank's website, or the disclosure documents they send you. But understanding how the number is built helps you compare accounts accurately and spot when a bank is advertising a rate that compounds less frequently than you might assume.
The reason APY matters more than the advertised interest rate is that compounding means you earn interest on your interest. A savings account that compounds daily will grow faster than one that compounds monthly, even if both advertise the same interest rate. APY captures that difference in a single number, so you can compare apples to apples.
Key Takeaways
- APY is always higher than the stated interest rate because it accounts for compounding—the number of times per year the bank adds earned interest back into your account.
- You can calculate APY using the formula (1 + rate ÷ compounding periods) raised to the power of compounding periods, minus 1, then multiplied by 100.
- Banks are required to disclose APY on savings accounts, so you will find it on statements, online portals, and account agreements without having to calculate it yourself.
- Two accounts with the same interest rate can have different APYs if one compounds daily and the other compounds monthly, so always compare the APY number, not the rate.
Why APY is different from the interest rate
The interest rate your bank advertises—often called the annual percentage rate or APR—is the percentage of your balance the bank will pay you over one year, before compounding. APY includes the effect of compounding, so it is always equal to or higher than the rate.
Here is a concrete example. Suppose you have $10,000 in a savings account with a 4% interest rate that compounds monthly. After one month, the bank adds $33.33 to your account (4% ÷ 12 months = 0.33% per month; 0.33% of $10,000 = $33.33). In month two, you earn interest not just on the original $10,000, but on $10,033.33. That extra $0.11 in month two is interest on your interest—compounding at work.
Over a full year, that monthly compounding adds up. The actual return on your $10,000 is closer to 4.07% than 4%. That 4.07% is the APY. The difference seems small with one account, but when you are comparing multiple savings options or moving larger sums, choosing the account with the higher APY can mean hundreds of dollars more per year.
The APY calculation step by step
If you want to verify a bank's published APY or calculate it yourself, the formula is:
APY = (1 + r ÷ n)^n − 1
Where r is the annual interest rate (as a decimal) and n is the number of times interest compounds per year. Multiply the result by 100 to express it as a percentage.
Using the $10,000 example with a 4% rate compounding monthly:
- Convert the rate to a decimal: 4% = 0.04
- Divide by the number of compounding periods: 0.04 ÷ 12 = 0.00333
- Add 1: 1 + 0.00333 = 1.00333
- Raise to the power of 12 (the number of months): 1.00333^12 = 1.04074
- Subtract 1: 1.04074 − 1 = 0.04074
- Multiply by 100: 0.04074 × 100 = 4.074%
The APY is 4.074%. That is the true annual return on your money, accounting for monthly compounding.
How compounding frequency affects your returns
The more often interest compounds, the higher your APY will be, even if the interest rate stays the same. Banks compound daily, monthly, quarterly, or annually, depending on the account type and the institution.
Here is how the same 4% rate looks under different compounding schedules:
| Compounding Frequency | Calculation | APY |
|---|---|---|
| Annually (1 time) | (1 + 0.04 ÷ 1)^1 − 1 | 4.00% |
| Quarterly (4 times) | (1 + 0.04 ÷ 4)^4 − 1 | 4.06% |
| Monthly (12 times) | (1 + 0.04 ÷ 12)^12 − 1 | 4.07% |
| Daily (365 times) | (1 + 0.04 ÷ 365)^365 − 1 | 4.08% |
The gap between annual and daily compounding is small at 4%, but it widens at higher rates. At 5%, annual compounding gives you 5.00% APY, while daily compounding gives you 5.13%—a difference of 0.13 percentage points. On $50,000, that is about $65 per year.
Most online savings accounts and high-yield savings accounts compound daily, which is why they often advertise higher APYs than traditional banks that compound monthly or quarterly.
Where to find the APY your bank publishes
You do not need to calculate APY yourself in most cases. Banks are required by federal law to disclose it clearly, and you can find it in several places:
- Account statements: Your monthly or quarterly statement lists the APY for that period.
- Online account portal: Log into your bank's website or app and look for account details or rates.
- Account agreement or disclosure document: When you open an account, the bank sends you a document (often called a Truth in Savings disclosure) that lists the APY, the interest rate, and how often it compounds.
- The bank's website: Current rates for new accounts are posted on the main savings page, though these may differ from the rate on your existing account.
If you cannot find the APY in any of these places, call your bank's customer service line and ask for the current APY on your specific account. They will give you the number in seconds.
Comparing APY across different banks
When you are shopping for a savings account, always compare the APY, not the interest rate. Two banks might advertise a 4% rate, but if one compounds daily and the other compounds annually, their APYs will differ.
Write down the APY for each account you are considering, along with any fees (monthly maintenance fees, minimum balance requirements, or withdrawal limits can eat into your returns). Then calculate how much you would earn in a year on your expected balance. If you plan to keep $25,000 in the account, multiply $25,000 by the APY as a decimal. At 4.07% APY, you would earn about $1,017.50 per year before taxes.
Remember that APY changes over time. Banks raise and lower rates based on the Federal Reserve's decisions and market conditions. The APY you see today may be different in three months, so check your account's current rate periodically if you are trying to maximize returns.
What happens to APY when rates change
The Federal Reserve does not set savings account rates directly, but its decisions influence them. When the Fed raises its benchmark rate, banks typically raise the APY on savings accounts within days or weeks. When the Fed cuts rates, banks usually lower APY more slowly, but they do eventually follow.
Your bank will notify you of APY changes, usually by email or a notice in your online account portal. The change takes effect on a date the bank specifies, and it applies to new interest earned going forward—it does not affect interest you have already received.
If your bank's APY drops significantly and you have other options, you can move your money to a bank offering a higher rate. There is no penalty for moving savings between banks (unlike some checking accounts or CDs with early withdrawal fees). Many people move their savings accounts annually to chase the highest available APY.
Frequently Asked Questions
Is APY the same as the interest rate?
No. The interest rate is the percentage the bank pays before compounding. APY includes the effect of compounding, so it is always equal to or higher than the rate. The difference grows as the interest rate rises and as compounding happens more frequently.
Can I calculate APY on a calculator or spreadsheet?
Yes. Use the formula (1 + r ÷ n)^n − 1, where r is the annual rate as a decimal and n is the number of compounding periods per year. Most spreadsheet programs and scientific calculators can handle the exponent (^) function. Many online APY calculators also do this math for you if you enter the rate and compounding frequency.
Does APY change if I withdraw money from my savings account?
The APY itself does not change, but your earnings will be lower because you have less money in the account. If you withdraw $5,000 midway through the year, you earn interest only on the remaining balance for the rest of the year. Some banks also calculate interest daily based on your balance, so a withdrawal when ready reduces the amount earning interest.
Why do some banks advertise a rate but not the APY?
Banks are required to disclose APY, so if you see only a rate, you have not found the full picture. Ask the bank for the APY, or calculate it yourself using the compounding frequency they provide. If they will not give you the APY, that is a red flag.
Does APY account for taxes on interest earned?
No. APY is the gross return before taxes. Interest you earn on a savings account is taxable income, so your actual after-tax return will be lower depending on your tax bracket. The bank will send you a 1099-INT form at the end of the year listing the interest you earned.