The formula for APY is straightforward: multiply your interest rate by the number of times interest compounds per year, then add 1 and raise it to that power, then subtract 1
The exact calculation depends on how often your bank compounds interest — daily, monthly, or quarterly. Most savings accounts compound daily, which means your bank calculates and adds interest to your balance every single day. The more frequently interest compounds, the more you earn, because you start earning interest on your interest.
Here is the formula banks use:
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. For a savings account with a 4.5% annual rate that compounds daily, you would plug in 0.045 for r and 365 for n.
The result tells you the actual percentage you will earn over a year, accounting for compounding. This is why APY is always slightly higher than the stated annual percentage rate (APR) — the difference is small but real.
Key Takeaways
- APY accounts for how often interest compounds, while APR does not, so APY is always equal to or higher than APR on a savings account.
- Most savings accounts compound interest daily, which means you earn interest on your interest 365 times per year.
- You can calculate APY by hand using the formula (1 + r/n)^n − 1, or you can use your bank's APY disclosure, which is required by law.
- The difference between APY and APR grows larger as interest rates rise, so comparing APY between accounts matters more when rates are high.
Why your bank shows you APY instead of just the interest rate
Banks are required by federal law to disclose APY on savings accounts, money market accounts, and certificates of deposit. This requirement exists because APY is the only honest way to compare what you will actually earn across different banks and account types.
If a bank only told you the interest rate, you could not compare it fairly to another bank's account that compounds more often. A 4.5% rate compounded daily earns more than a 4.5% rate compounded monthly, even though the stated rate is identical. APY removes that confusion by showing you the real annual return.
Your bank must display APY prominently in account disclosures, on the website, and in any marketing materials. If you see an interest rate quoted without APY, that is a red flag — it means the bank is hiding the compounding frequency.
How to calculate APY by hand for different compounding schedules
The compounding frequency changes the calculation slightly. Here are the most common scenarios:
| Compounding Frequency | Value of n | Example: 4.5% rate |
|---|---|---|
| Daily | 365 | (1 + 0.045/365)^365 − 1 = 4.60% |
| Monthly | 12 | (1 + 0.045/12)^12 − 1 = 4.59% |
| Quarterly | 4 | (1 + 0.045/4)^4 − 1 = 4.57% |
| Semi-annually | 2 | (1 + 0.045/2)^2 − 1 = 4.55% |
| Annually | 1 | (1 + 0.045/1)^1 − 1 = 4.50% |
Notice that daily compounding yields the highest APY, and the difference shrinks as compounding happens less often. At 4.5%, daily versus annual compounding is only a 0.10% difference — but at higher rates, the gap widens.
To do the calculation, divide the interest rate by n, add 1, raise the result to the power of n, then subtract 1. A scientific calculator or spreadsheet makes this much faster than doing it by hand.
Why APY matters more when interest rates are high
When savings rates were near zero, the difference between APY and the stated rate was negligible — a few hundredths of a percent. Now that rates have risen, the compounding effect is more visible.
At a 5.0% rate compounded daily, APY is 5.13%. At a 5.5% rate compounded daily, APY is 5.65%. The gap between the stated rate and the actual return grows as rates climb. This means comparing APY between accounts becomes more important — a 0.25% difference in APY can add up to real money over a year.
If you are shopping for a high-yield savings account, always compare the APY figures, not the interest rates. Two banks might advertise similar rates, but one might compound more frequently and deliver a slightly higher APY.
What happens if your bank changes the interest rate
Banks change savings rates frequently — sometimes weekly. When the rate changes, the APY changes with it. Your bank must notify you of any rate decrease before it takes effect, but they can raise rates without advance notice.
The APY you see today is not locked in. It applies only to the current rate and only for as long as that rate remains in effect. If you want to lock in a specific return, you would need to move money to a certificate of deposit (CD), which guarantees a fixed rate for a set term.
Your bank will show you the current APY on your account statement or online dashboard. If you want to know what you will earn over the next year, multiply your current balance by the current APY and divide by 100. That gives you a rough estimate, assuming the rate does not change.
How to use an online APY calculator if you do not want to do the math
Most online banks and financial websites offer free APY calculators. You enter the interest rate and the compounding frequency, and the calculator does the formula for you. This is faster and less error-prone than calculating by hand.
You can also use a spreadsheet. In Excel or Google Sheets, the formula is =POWER(1+rate/n,n)−1, where you replace "rate" with the decimal interest rate and "n" with the compounding frequency. This is useful if you want to compare multiple accounts at once.
However, you do not need a calculator to shop for accounts. Your bank is required to show you the APY in all disclosures and marketing materials. If you are comparing two savings accounts, just look at the APY figures side by side — the higher APY is the better deal, assuming the account has no fees.
The difference between APY and APR on a savings account
APR (annual percentage rate) is the interest rate without compounding factored in. APY (annual percentage yield) includes compounding. On a savings account, APY will always be equal to or higher than APR.
The difference is small on savings accounts because the interest rates are low. On a credit card or loan, the difference can be much larger because the rates are higher. But the concept is the same: APY shows you the real return or cost, while APR shows you only the stated rate.
When you see a bank advertising a rate, they must also show the APY. If they show only the APR, that is a violation of federal disclosure rules. Always look for the APY figure when comparing accounts.
Frequently Asked Questions
Does APY change if I add more money to my savings account?
No. APY is a percentage, not a dollar amount. It stays the same regardless of your balance. However, the total dollars you earn will be higher if your balance is higher. If you have $10,000 earning 4.60% APY, you earn about $460 per year. If you have $20,000 at the same APY, you earn about $920 per year.
Can I calculate APY if interest compounds continuously?
Yes, but it requires a different formula: APY = e^r − 1, where e is approximately 2.71828 and r is the interest rate as a decimal. Very few savings accounts use continuous compounding — most use daily, monthly, or quarterly. Your bank will tell you the compounding frequency in the account disclosure.
Is the APY I see today may provide for the whole year?
No. The APY shown is the current rate and applies only while that rate is in effect. Banks can change savings rates at any time. If you want a may provide return for a full year, you need a CD with a fixed term. Regular savings accounts have variable rates that can go up or down.
What if my bank compounds interest more than 365 times per year?
Some banks use continuous compounding, which theoretically compounds infinite times per year. The APY will be slightly higher than daily compounding, but the difference is usually less than 0.01%. For practical purposes, daily compounding and continuous compounding produce nearly identical results at savings account interest rates.
How do I know if my bank is calculating APY correctly?
Use the formula (1 + r/n)^n − 1 with your bank's stated interest rate and compounding frequency. If your calculation matches the APY your bank shows, they are doing it right. If there is a significant difference, contact your bank to ask how they calculated it — there may be fees or other factors affecting the actual return.