The Basic Formula for APY
APY (Annual Percentage Yield) tells you how much interest you'll earn in a year, including the effect of compounding. 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. If your bank compounds daily, n = 365. If it compounds monthly, n = 12. If it compounds quarterly, n = 4.
Most savings accounts compound daily, which means the bank calculates interest on your balance every day and adds it back in. That daily interest then earns interest itself the next day—that's compounding, and it's why APY is always higher than the stated rate.
A Real Example You Can Follow
Say you have $10,000 in a savings account with an annual interest rate of 4.50%, compounded daily. Here's how to calculate the APY:
First, convert the rate to a decimal: 4.50% = 0.045. Then plug it into the formula:
APY = (1 + 0.045/365)^365 – 1 APY = (1 + 0.000123288)^365 – 1 APY = (1.000123288)^365 – 1 APY = 1.04602 – 1 APY = 0.04602, or 4.602%
That 0.102% difference between the stated rate (4.50%) and the APY (4.602%) is what compounding adds. On $10,000, that difference means you earn about $10 more per year than you would if interest were simple (not compounded).
Key Takeaways
- APY includes the effect of compounding, so it's always equal to or higher than the stated annual interest rate.
- Most savings accounts compound daily, meaning interest is calculated and added to your balance 365 times per year.
- You can calculate APY yourself using the formula (1 + r/n)^n – 1, where r is the annual rate as a decimal and n is the number of compounding periods.
- The difference between the stated rate and APY grows larger as the rate increases and as the compounding frequency increases.
- Your bank is required to disclose the APY on savings accounts, so you can compare accounts without doing the math yourself.
Why Your Bank Already Shows You the APY
You don't actually have to calculate APY yourself. Federal law requires banks to display the APY prominently on savings account disclosures and marketing materials. When you're comparing savings accounts online or in a branch, the number you see labeled "APY" is already the compounded figure.
The reason banks show APY instead of just the interest rate is to make comparison fair. Two accounts might have different compounding schedules—one daily, one monthly—and the APY accounts for that difference. By law, banks must calculate APY the same way, so you can trust that a 4.60% APY at one bank is directly comparable to a 4.60% APY at another.
If you see only an interest rate and no APY listed, that's a red flag. Ask the bank or credit union to provide the APY before you open the account.
How Compounding Frequency Changes the Result
The more often interest compounds, the higher your APY will be—even if the stated rate stays the same. Here's why: when interest is added to your balance more frequently, that interest starts earning interest sooner.
Using the same 4.50% rate, here's what APY looks like under different compounding schedules:
| Compounding Frequency | Formula Input (n) | Resulting APY |
|---|---|---|
| Annually | 1 | 4.500% |
| Quarterly | 4 | 4.586% |
| Monthly | 12 | 4.597% |
| Daily | 365 | 4.602% |
The jump from annual to quarterly is noticeable. The jump from monthly to daily is smaller because you're already compounding very frequently. Most savings accounts use daily compounding, so you'll rarely see anything lower than that.
What Happens When You Withdraw Money Mid-Year
APY assumes your money stays in the account for the full year. If you withdraw part of your balance, the interest you earn will be lower because you're earning on a smaller amount for part of the year.
For example, if you have $10,000 earning 4.602% APY and you withdraw $5,000 after six months, you won't earn half the annual interest. You'll earn interest on $10,000 for six months, then interest on $5,000 for the remaining six months. The bank calculates this daily, so the exact amount depends on which day you withdraw.
This is why APY is useful for planning: if you know you won't touch the money for a year, you can predict roughly how much interest you'll earn. But if you're making regular deposits or withdrawals, the actual interest will differ from the APY calculation.
How Interest Rates and APY Change Over Time
Banks change their interest rates regularly, sometimes weekly. When a rate changes, the APY changes with it. If your bank drops the rate from 4.50% to 4.25%, the APY drops too—and so does the interest you earn on new deposits.
Interest already earned and added to your balance stays in the account. The rate change only affects interest going forward. So if you earned $460 in interest during the first year at 4.602% APY, and the rate drops to 4.25% APY in year two, you'll earn less in year two—but you keep the $460 from year one.
When you're shopping for a savings account, look at the current APY, but also check whether the bank has a history of competitive rates. Some banks offer high rates to new customers and then drop them after a few months. Reading recent reviews or calling the bank to ask about their rate history can help you avoid that trap.
Frequently Asked Questions
Is APY the same as the interest rate?
No. The interest rate is what the bank pays; APY is what you actually earn after compounding is included. APY is always equal to or higher than the stated rate. If a bank shows only an interest rate without an APY, ask them to provide the APY so you can compare fairly with other banks.
Do I need to calculate APY myself, or will my bank tell me?
Your bank is required to show you the APY. You'll see it on account disclosures, online banking platforms, and marketing materials. You only need to calculate it yourself if you want to verify the bank's math or understand how compounding works.
What's the difference between APY and APR?
APY includes compounding and is used for savings accounts and money market accounts. APR (Annual Percentage Rate) does not include compounding and is used for loans and credit cards. For savings, always compare APY to APY. For borrowing, always compare APR to APR.
If I withdraw money early, do I lose the interest I earned?
No. Interest you've already earned stays in your account. Withdrawals only affect future interest because you're earning on a smaller balance going forward. Some accounts have penalties for early withdrawal, but those are separate from how interest is calculated.
Can APY go down after I open the account?
Yes. Banks can change interest rates at any time, and most do when the Federal Reserve changes its rates. Your existing balance keeps earning at the new rate, but you don't lose interest already credited to your account. If rates drop significantly, you can move your money to a different bank offering a higher APY.