The formula for APY accounts for compounding: divide the interest rate by the number of compounding periods per year, add one, raise it to the power of the number of periods, then subtract one
APY (annual percentage yield) tells you what percentage of your account balance you'll earn in interest over one year, accounting for compounding. The basic formula is: APY = (1 + r/n)^n − 1, where r is the stated interest rate and n is the number of times interest compounds per year. For most savings accounts, interest compounds daily, which means the bank calculates and adds interest to your balance every day. You don't need to do this calculation yourself—your bank publishes the APY so you can compare accounts—but understanding how it works helps you see why daily compounding matters.
The reason APY exists is that compounding means you earn interest on your interest. If you deposit $1,000 at 4% APY with daily compounding, you don't simply earn $40 at the end of the year. Instead, the bank adds a tiny fraction of interest each day, and the next day's interest is calculated on the slightly larger balance. By year-end, you've earned a bit more than $40 because of those compounding gains. APY captures that total gain as a single percentage, making it easier to compare accounts.
Key Takeaways
- APY already includes the effect of compounding, so it's always equal to or higher than the stated interest rate.
- Banks must disclose APY on savings accounts, so you can find it in account disclosures or on the account details page of their website.
- Daily compounding produces more interest than monthly or quarterly compounding because interest accrues more frequently.
- To compare two savings accounts, look at the APY, not the interest rate—APY is the number that tells you what you'll actually earn.
Why APY is different from the interest rate
The interest rate (sometimes called the nominal rate) is what the bank pays you per year before compounding. The APY is what you actually earn after compounding is factored in. For example, a savings account might advertise a 4.00% interest rate, but if interest compounds daily, the APY might be 4.08%. That 0.08% difference comes entirely from compounding—the bank adds interest to your balance every day, and each day's interest earns interest of its own.
The more frequently interest compounds, the higher the APY relative to the interest rate. An account with monthly compounding will have a lower APY than one with daily compounding, even if both have the same stated interest rate. This is why daily compounding is better for you: you earn more. Most online savings accounts and high-yield savings accounts compound daily, which is why they often advertise both the interest rate and the APY side by side.
How to do the calculation yourself
If you want to verify the APY or calculate it for a hypothetical scenario, use this formula:
APY = (1 + r/n)^n − 1
Here's what each part means:
- r = the annual interest rate (as a decimal; so 4% becomes 0.04)
- n = the number of times interest compounds per year (365 for daily, 12 for monthly, 4 for quarterly)
- ^n = raise the result to the power of n
Let's work through an example. Suppose you have a savings account with a 4.00% interest rate and daily compounding (365 times per year):
APY = (1 + 0.04/365)^365 − 1 APY = (1 + 0.0001096)^365 − 1 APY = (1.0001096)^365 − 1 APY = 1.0408 − 1 APY = 0.0408, or 4.08%
That 4.08% is what you'll actually earn on your balance over the course of a year. If you deposit $10,000, you'll earn approximately $408 in interest (before taxes), not $400. The extra $8 comes from compounding—your interest earns interest as the year goes on.
Using an APY calculator instead
Most people don't calculate APY by hand. Banks publish the APY on their websites, and free online APY calculators can do the math for you in seconds. You can also use a spreadsheet: in Excel or Google Sheets, the formula is =POWER(1+rate/periods, periods)−1, where rate is the interest rate as a decimal and periods is the number of compounding periods per year.
When you're comparing savings accounts, the bank's website will show you the APY in the account details or in a disclosure document called the Truth in Savings Act disclosure. You don't need to calculate it yourself—just look for the APY number and use that to compare accounts. The account with the highest APY will earn you the most money, assuming you keep the same balance for the same length of time. This is the fastest way to shop for savings accounts: pull up three or four banks' websites, note their APYs, and pick the highest one that doesn't have fees or minimum balance requirements that would eat into your earnings.
How compounding frequency affects your earnings
The table below shows how the same 4.00% interest rate produces different APYs depending on how often interest compounds:
| Compounding Frequency | Times Per Year | APY | Interest on $10,000 |
|---|---|---|---|
| Annual | 1 | 4.00% | $400 |
| Quarterly | 4 | 4.06% | $406 |
| Monthly | 12 | 4.07% | $407 |
| Daily | 365 | 4.08% | $408 |
The difference between annual and daily compounding is small on a $10,000 balance—only $8 per year—but it grows as your balance grows. On a $100,000 balance, daily compounding earns you $80 more per year than annual compounding. Over five years, that's $400 in extra interest from compounding alone. Most online savings accounts and money market accounts compound daily, which is why they tend to offer higher APYs than traditional banks.
What happens to APY when rates change
Banks can change the interest rate on savings accounts at any time, which means the APY changes too. When the Federal Reserve raises or lowers its benchmark rate, banks often adjust their savings account rates within days or weeks. Your bank will notify you of rate changes, usually by email or through your online account portal. The new APY takes effect on the date the bank specifies, and interest accrues at the new rate from that point forward.
If you're shopping for a savings account, remember that the APY you see today may not be the same six months from now. Some banks offer promotional rates that are higher for a limited time, then drop to a lower rate. Read the account disclosure carefully to see whether the rate is variable (can change) or fixed (locked in for a period). Most savings accounts have variable rates, which means they move with market conditions.
APY vs. APR: which one matters for savings
APY is for savings accounts, money market accounts, and certificates of deposit (CDs)—products where the bank pays you. APR (annual percentage rate) is for loans and credit cards—products where you pay the bank. APR does not account for compounding in the same way APY does; instead, it represents the cost of borrowing. When you're evaluating a savings account, ignore APR entirely and focus on APY. When you're evaluating a loan or credit card, look at APR. They measure different things and are not directly comparable.
This distinction matters because mixing them up can lead you to choose the wrong account or loan. A savings account advertising 4% APY is better than one advertising 3.5% APY, but a loan at 5% APR is not necessarily better or worse than one at 4% APY—they're measuring opposite sides of the transaction. Always match the metric to the product type.
Frequently Asked Questions
Does my bank automatically calculate APY for me?
Yes. Your bank calculates and compounds interest according to the terms of your account. You don't have to do anything. The bank publishes the APY so you can compare it to other accounts, but the compounding happens automatically behind the scenes.
If I withdraw money mid-year, do I lose interest?
No. Interest accrues daily, so you earn interest on your balance for each day the money is in the account. If you withdraw $5,000 on day 200 of the year, you've earned interest on the full balance for 200 days and a smaller balance for the remaining 165 days. You don't forfeit the interest you've already earned.
Can APY go negative?
In the United States, savings account APY does not go negative. Even in a low-rate environment, banks pay at least 0.01% APY or higher. However, if you keep money in a non-interest-bearing checking account, you earn 0% APY, which is effectively negative when you account for inflation.
Is a higher APY always better?
For savings accounts, yes—a higher APY means you earn more interest on the same balance. However, make sure the account doesn't have hidden fees, minimum balance requirements, or other restrictions that could offset the higher rate. Compare the full terms, not just the APY.
How often does interest post to my account?
Interest compounds daily at most banks, but it may post (appear as a deposit) monthly or quarterly. Compounding and posting are different: compounding is when the bank calculates interest on your balance, and posting is when that interest shows up as a transaction. Daily compounding with monthly posting is common and is better than monthly compounding, because you earn interest on your interest more frequently.