The formula and what each number means
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 interest rate the bank quotes you (called the APR, or Annual Percentage Rate), and n is how many times per year the bank compounds your interest. Most savings accounts compound daily, which means n = 365. Some compound monthly (n = 12) or quarterly (n = 4). The bank must disclose both the rate and the compounding frequency in your account agreement or on the rate sheet.
The reason APY matters: if a bank compounds daily instead of monthly, you earn slightly more, even at the same quoted rate. Compounding means the bank pays interest on your interest. The more often it happens, the more you earn.
Key Takeaways
- APY includes the effect of compounding, while the quoted rate (APR) does not, so APY is always equal to or higher than the rate the bank advertises.
- Most savings accounts compound daily (365 times per year), which is better for you than monthly or quarterly compounding at the same rate.
- You can calculate APY yourself using the formula (1 + r/n)^n – 1, where r is the quoted rate and n is the number of compounding periods per year.
- Banks are required to show you the APY, not just the rate, so you can compare accounts fairly across different institutions.
- The difference between APY and the quoted rate grows larger as rates rise, so at higher rates, compounding frequency matters more.
Working through a real example
Suppose you have a savings account with a quoted rate of 4.50% that compounds daily. Plug the numbers into the formula:
APY = (1 + 0.045/365)^365 – 1
First, divide the rate by 365: 0.045 ÷ 365 = 0.000123288. Add 1: 1.000123288. Raise it to the 365th power: 1.04602. Subtract 1: 0.04602, or 4.602%.
So a 4.50% rate compounded daily gives you an APY of 4.602%. The difference is small in dollar terms—on $10,000, you'd earn about $1.20 more per year than if the rate were simple interest—but the math is what banks use, and it's what you should compare when shopping for accounts.
Why banks show you APY instead of just the rate
Federal law requires banks to disclose APY so you can compare accounts on equal footing. If banks only showed the quoted rate, a 4.50% account compounded monthly would look identical to a 4.50% account compounded daily, even though the daily one pays more. APY removes that confusion.
When you look at a savings account online or in a bank branch, the number you see advertised is almost always the APY, not the rate. That's the number to use when comparing one account to another. If a bank shows only the rate, ask for the APY before you open the account.
How compounding frequency changes the result
The same 4.50% rate produces different APYs depending on how often interest compounds:
| Compounding Frequency | n (periods per year) | APY |
|---|---|---|
| Quarterly | 4 | 4.586% |
| Monthly | 12 | 4.597% |
| Daily | 365 | 4.602% |
The differences look tiny, but they add up over time and at higher balances. On $100,000 over five years, daily compounding at 4.50% earns you roughly $120 more than quarterly compounding at the same rate. Most online savings accounts and high-yield savings accounts compound daily, which is why they're competitive even when their rates are only slightly higher than traditional banks.
When to use APY instead of the quoted rate
Always use APY when you're deciding between two savings accounts. It's the only number that accounts for how often interest is added to your balance. If you're calculating how much money you'll have at the end of a year, use the APY, not the quoted rate.
The quoted rate (APR) is useful only if you want to understand the raw interest rate before compounding, or if you're comparing accounts that compound at different frequencies and you want to see the effect of that difference. For most people, the APY is the only number that matters.
What happens if the rate changes
Most savings accounts have variable rates, meaning the bank can change the APY at any time. When rates rise or fall in the broader economy, your account's APY may change too. The bank must notify you before the change takes effect, usually by email or through your online account portal.
If your APY drops and you're unhappy with it, you can move your money to a different bank. There's no penalty for closing a savings account. If rates are falling across the industry, you may not find a better option, but if your bank's rate drops faster than competitors', switching makes sense.
Using an online calculator vs. doing it by hand
You can calculate APY by hand using the formula, but most people use an online calculator or a spreadsheet. Many banks provide calculators on their websites. You can also use a spreadsheet: in Excel or Google Sheets, the formula is =(1+rate/compounding_periods)^compounding_periods-1.
The advantage of doing it yourself is that you can see exactly how compounding frequency affects the result. If you're comparing two accounts with the same rate but different compounding schedules, a calculator makes the difference obvious. But for everyday use, just look at the APY the bank shows you—it's already calculated and legally required to be accurate.
Frequently Asked Questions
Is APY the same as interest rate?
No. The interest rate (APR) is what the bank quotes; APY is the rate after compounding is factored in. APY is always equal to or higher than the rate. Banks must show you both, but APY is the number to use when comparing accounts.
Why do some accounts have higher APY than others if the rate is the same?
Compounding frequency is the reason. An account that compounds daily will have a higher APY than one that compounds monthly, even at the same quoted rate. Daily compounding is more common at online banks; traditional banks often compound less frequently.
Does APY change if I withdraw money?
The APY itself doesn't change—it's set by the bank. But the interest you earn does change, because you're earning it on a smaller balance. If you withdraw $5,000 from a $10,000 account, you'll earn interest only on the remaining $5,000.
Can I calculate APY if the rate changes during the year?
The standard APY formula assumes the rate stays constant for the full year. If your rate changes mid-year, the actual interest you earn will differ from what the APY predicts. Your bank will calculate your actual interest based on the rates in effect during each period.
What's the difference between APY and APR?
APR is the quoted rate without compounding. APY includes compounding. For savings accounts, APY is higher and is the number banks advertise. For loans, APR is what's advertised, and it's the number you should use to compare loans.