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 stated 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.
The result is a decimal you convert to a percentage. For example, if the formula gives you 0.0487, that's 4.87% APY.
Key Takeaways
- APY accounts for compounding, so it's always equal to or higher than the stated interest rate.
- Daily compounding produces slightly higher APY than monthly or quarterly compounding with the same stated rate.
- You can calculate APY by hand using the formula (1 + r/n)^n − 1, or use a calculator to avoid arithmetic errors.
- Your bank is required to disclose APY on savings accounts, so you can compare accounts without doing the math yourself.
- The difference between APY and the stated rate grows larger as the stated rate increases.
Why APY matters more than the stated rate
Banks advertise both a stated interest rate and an APY. The stated rate is what the bank pays you on your balance. The APY is what you actually earn because of compounding—interest earning interest.
If you deposit $10,000 at a 4% stated rate compounded daily, you don't earn exactly $400 in a year. You earn slightly more because each day's interest gets added to your balance, and the next day's interest is calculated on that larger amount. That compounding effect is baked into the APY.
The higher the stated rate, the bigger the gap between the rate and the APY. At 0.01%, the difference is negligible. At 5%, it becomes meaningful. This is why comparing APY across accounts gives you a true picture of which account will earn you more money.
Working through a real calculation
Say your bank offers 4.5% interest compounded daily. You want to know the actual APY.
Convert 4.5% to a decimal: 0.045. Daily compounding means n = 365. Plug into the formula:
APY = (1 + 0.045/365)^365 − 1
First, divide: 0.045 ÷ 365 = 0.000123288
Add 1: 1.000123288
Raise to the 365th power: 1.046003 (approximately)
Subtract 1: 0.046003
Convert to percentage: 4.60% APY
So a 4.5% stated rate with daily compounding yields 4.60% APY. The difference is small but real—on $10,000, that's $10 more per year than the stated rate alone would suggest.
How compounding frequency changes the result
The same stated rate produces different APY depending on how often interest compounds. More frequent compounding means higher APY.
| Compounding Frequency | n Value | APY on 4.5% Stated Rate |
|---|---|---|
| Annually | 1 | 4.50% |
| Quarterly | 4 | 4.59% |
| Monthly | 12 | 4.60% |
| Daily | 365 | 4.60% |
At 4.5%, the gap between quarterly and daily compounding is only 0.01%. But at higher rates, the difference grows. This is why high-yield savings accounts almost always compound daily—it's a real advantage to the customer, and it's a selling point for the bank.
Using a calculator instead of doing it by hand
The exponent in the formula (raising a number to the 365th power) is tedious to calculate without a tool. Most people use a scientific calculator, a spreadsheet, or an online APY calculator.
In Excel or Google Sheets, the formula is: =(1+rate/periods)^periods-1
If your stated rate is in cell A1 and compounding periods is in cell B1, you'd type: =(1+A1/B1)^B1-1
Online APY calculators exist on many financial websites. You enter the stated rate and compounding frequency, and the tool does the math. This is the fastest route if you're comparing multiple accounts.
Where to find the APY your bank already calculated
You don't have to calculate APY yourself. Banks are required by federal law to disclose it on savings accounts, money market accounts, and certificates of deposit.
Look for APY on your account's disclosure document (sometimes called a "Truth in Savings" form), on the bank's website, or in your account statements. It's usually displayed prominently next to the stated interest rate so you can compare accounts side by side.
When you're shopping for a savings account, use the APY to compare, not the stated rate. Two banks might advertise different stated rates but offer the same APY if one compounds more frequently than the other.
What changes your APY over time
The APY your bank advertises today may not be the APY you earn next month. Banks change their stated interest rates based on Federal Reserve decisions and market conditions. When the Fed raises or lowers rates, banks typically adjust their savings account rates within days or weeks.
Your compounding frequency doesn't change—that's set by the bank's account terms. But the stated rate does, which means your APY changes too. A 4.60% APY today might become 4.35% APY next month if the Fed cuts rates and your bank follows.
This is why high-yield savings accounts are attractive during periods of higher interest rates. The APY is locked in only for the period the rate stays in effect, not for the life of the account.
Frequently Asked Questions
Is APY the same as interest rate?
No. The interest rate is what the bank pays on your balance. APY includes the effect of compounding, so it's always equal to or higher than the stated rate. Banks must disclose both so you know the true earnings.
Why is my APY lower than the stated rate I was quoted?
This shouldn't happen. APY should always be equal to or higher than the stated rate. If you see the opposite, contact your bank—it may be an error in how the rate was displayed or calculated.
Does APY change if I withdraw money from my savings account?
The APY itself doesn't change, but your earnings do. APY is the rate the bank pays. If you withdraw money, your balance is lower, so you earn less interest even though the APY stays the same.
Can I use the APY formula to predict how much I'll earn?
The formula calculates APY, not your total earnings. To find total earnings, multiply your balance by the APY and divide by 100. For example, $10,000 at 4.60% APY earns $460 in a year (before taxes).
What if my bank compounds continuously instead of daily?
Continuous compounding uses a different formula: APY = e^r − 1, where e is approximately 2.71828 and r is the stated rate as a decimal. This produces the highest possible APY for a given stated rate, but most banks compound daily, not continuously.