The basic formula for APY
APY (annual percentage yield) tells you what percentage of your balance you'll earn in interest over one year, including the effect of compounding. To calculate it yourself, use this formula:
APY = (1 + r/n)^n − 1
In this formula, r is the interest rate your bank quotes (called the APR, or annual percentage rate), and n is the number of times per year your interest compounds. Most savings accounts compound daily, which means n = 365. Some compound monthly (n = 12) or quarterly (n = 4).
The reason you need this formula is that compounding means you earn interest on your interest. Each time the bank adds interest to your account, the next interest calculation is based on a slightly larger balance. Over a year, that adds up to more than the simple rate alone would suggest.
Key Takeaways
- APY accounts for compounding, so it is always equal to or higher than the APR your bank advertises.
- Most savings accounts compound daily (365 times per year), which means you divide the APR by 365 before using the formula.
- You can calculate APY by hand using the formula (1 + r/n)^n − 1, or use your bank's online calculator or a spreadsheet.
- The difference between APY and APR grows larger as the interest rate rises and as compounding happens more often.
- Your bank is required to disclose the APY on savings accounts, so you can compare accounts without calculating it yourself.
Working through a real example
Suppose your bank offers a savings account with an APR of 4.50%, compounded daily. To find the APY:
First, divide the APR by the number of compounding periods: 4.50% ÷ 365 = 0.0123% per day (or 0.000123 as a decimal).
Next, add 1 to that daily rate: 1 + 0.000123 = 1.000123.
Then raise that number to the power of 365 (the number of days in a year): 1.000123^365 = 1.04603.
Finally, subtract 1 and convert to a percentage: 1.04603 − 1 = 0.04603, or 4.603% APY.
In this example, the APY (4.603%) is higher than the APR (4.50%) because of daily compounding. The difference is about 0.10 percentage points—small in this case, but it compounds over time and across larger balances.
Why your bank already calculates this for you
Federal law requires banks to disclose the APY on all savings accounts, money market accounts, and certificates of deposit. You will find it on the account's product page, in the account agreement, and on statements. The bank must show APY so that you can compare accounts fairly across different institutions.
Because APY is always disclosed, you rarely need to calculate it yourself. The real value of understanding the formula is knowing why one account's APY differs from another's, and recognizing that a higher APR does not always mean a higher APY if the compounding frequency is different.
How compounding frequency changes the result
The more often interest compounds, the higher your APY will be—even if the APR stays the same. Here is how the same 4.50% APR looks under different compounding schedules:
| Compounding Frequency | Times Per Year (n) | Resulting APY |
|---|---|---|
| Annually | 1 | 4.500% |
| Quarterly | 4 | 4.586% |
| Monthly | 12 | 4.597% |
| Daily | 365 | 4.603% |
The difference widens as the APR rises. At 5.00% APR, daily compounding yields 5.127% APY, a gap of 0.127 percentage points. At 2.00% APR, the gap shrinks to 0.020 percentage points. This is why high-yield savings accounts, which often have rates above 4%, benefit more from daily compounding than traditional savings accounts with lower rates.
Using a spreadsheet or calculator to avoid the math
If you do not want to calculate by hand, you can use a spreadsheet. In Excel or Google Sheets, enter the formula =POWER(1 + (APR/365), 365) − 1 and replace APR with your rate as a decimal. For a 4.50% rate, you would type =POWER(1 + (0.045/365), 365) − 1 and the spreadsheet will return 0.04603, or 4.603% APY.
Many banks also provide APY calculators on their websites. You enter the APR and compounding frequency, and the tool returns the APY instantly. Some savings account comparison sites include APY calculators as well, so you can test different rates without opening a spreadsheet.
What APY means for your actual earnings
APY is an annual rate, but interest accrues and compounds throughout the year. If you deposit $10,000 in an account with 4.603% APY and leave it untouched for one year, you will earn approximately $460.30 in interest (before taxes). That $460.30 is the result of daily compounding over 365 days.
If you withdraw money partway through the year, your earnings will be proportionally lower. If you deposit additional money, that new deposit begins earning interest from the day it is added. The APY rate itself does not change, but the total dollars you earn depend on your balance and how long the money stays in the account.
Some banks also change their APY periodically in response to Federal Reserve rate changes. When rates rise, your APY may increase; when rates fall, it may decrease. Always check your account statements or log into your online banking to see your current APY, because it is not fixed for the life of the account.
Frequently Asked Questions
Is APY the same as interest rate?
No. The interest rate your bank quotes is usually the APR (annual percentage rate). APY includes the effect of compounding, so it is always equal to or higher than the APR. Banks must show you both numbers so you can understand the true return on your money.
Why is my APY lower than the APR?
It should not be. APY is always equal to or higher than APR because compounding adds to your earnings. If you see an APY that is lower, check that you are reading the correct account type—some accounts have different rates for different balance tiers.
Does APY change if I withdraw money?
The APY rate itself does not change, but your total interest earnings will be lower if you withdraw money, because you are earning interest on a smaller balance for part of the year. The rate your bank pays remains the same; only your earnings shrink.
Can I use the APY formula for other accounts?
Yes. The same formula works for money market accounts, certificates of deposit, and any account where interest compounds. The only variable that changes is the compounding frequency—check your account agreement to see how often interest is added.
What happens to APY when interest rates rise?
Your bank may raise the APY on your savings account when the Federal Reserve raises rates. The timing and amount of the increase depend on your bank's policy. Some banks raise rates quickly; others lag behind. Check your statements regularly or log into your account to see if your rate has changed.