The formula for APY starts with your interest rate and compounds it
APY (annual percentage yield) tells you what you actually earn in a year when interest compounds. The formula is: APY = (1 + r/n)^n − 1, where r is the annual interest rate and n is the number of times interest compounds per year.
Most savings accounts compound daily, which means n = 365. If your bank advertises a 4.50% APY, that number already includes the compounding effect — you do not have to calculate it yourself. But if you see only an interest rate (sometimes called APR on savings products), you can use the formula to find the true yield.
The reason this matters: a 4.50% rate compounded daily earns more than a 4.50% rate compounded monthly. The compounding frequency changes how much money actually lands in your account by the end of the year.
Key Takeaways
- Banks must disclose APY, not just the interest rate, so you can compare accounts fairly across different compounding schedules.
- Daily compounding (365 times per year) produces a higher APY than monthly or quarterly compounding at the same interest rate.
- To calculate APY yourself, use (1 + r/n)^n − 1, where r is the annual rate as a decimal and n is the compounding frequency.
- The difference between rate and APY grows larger as rates rise, so checking APY becomes more important in higher-rate environments.
Why banks show APY instead of just the interest rate
The Federal Reserve requires banks to disclose APY so customers can compare savings accounts on equal ground. Without this rule, a bank could advertise a high interest rate but compound it only once a year, while another bank compounds daily at a lower rate — and the second account would actually pay more.
APY is the standardized number. When you see 4.50% APY on a savings account, that is the actual annual return you will receive, accounting for how often the bank adds interest to your balance. You do not have to do any math; the bank has already done it.
The difference between rate and APY is small at low rates but becomes visible at higher ones. At 0.01% interest compounded daily, APY is nearly identical. At 5.00% compounded daily, the APY is slightly higher because you earn interest on the interest more often.
How to calculate APY step by step with an example
Suppose your bank offers a 4.80% interest rate compounded daily. To find the APY:
- Convert the rate to a decimal: 4.80% = 0.048
- Divide by the compounding frequency: 0.048 ÷ 365 = 0.0001315
- Add 1: 1 + 0.0001315 = 1.0001315
- Raise to the power of 365: (1.0001315)^365 = 1.04916
- Subtract 1 and convert back to a percentage: 1.04916 − 1 = 0.04916 = 4.916%
The APY is 4.916%, which is slightly higher than the 4.80% rate. That extra 0.116% comes from compounding — you earn interest on your interest 365 times during the year.
In practice, you will not need to do this calculation. Your bank's disclosure documents and website will show the APY. But running through the math shows why daily compounding matters and why two accounts with different compounding schedules can produce different returns even at the same advertised rate.
Compounding frequency and how it changes your earnings
The more often interest compounds, the higher your APY becomes at the same interest rate. Here is how a 5.00% rate looks under different compounding schedules:
| Compounding Frequency | Times Per Year | APY at 5.00% Rate |
|---|---|---|
| Annually | 1 | 5.00% |
| Quarterly | 4 | 5.09% |
| Monthly | 12 | 5.12% |
| Daily | 365 | 5.13% |
The difference grows as rates rise. At 1.00%, the gap between annual and daily compounding is only 0.01%. At 5.00%, it is 0.13%. This is why high-yield savings accounts — which offer rates above 4.00% — almost always compound daily. The banks know customers will notice the difference.
Most online banks and credit unions compound daily. Some brick-and-mortar banks still compound monthly or quarterly, which is one reason their APY may be lower even if the advertised rate looks similar.
What happens when interest rates change
Banks adjust APY when the Federal Reserve changes its benchmark rate or when they choose to raise or lower their own rates. When you see a savings account advertised as "variable rate," the APY can move up or down without notice.
Your bank will notify you of rate changes, usually by email or through your online account. The new rate takes effect on a date the bank specifies — sometimes immediately, sometimes at the start of the next statement cycle. Interest already earned at the old rate stays in your account; only new interest going forward uses the new APY.
If you lock in a rate, that APY is may provide for a set period. High-yield savings accounts typically do not offer rate locks, but some certificates of deposit (CDs) do. A CD might may provide 5.25% APY for 12 months, meaning your rate will not change even if the bank lowers rates for new customers.
How to use APY to compare savings accounts
When comparing two savings accounts, always compare APY to APY, not rate to rate. Look at the APY disclosure on each bank's website or in the account terms. The disclosure will state the APY, the interest rate, and the compounding frequency.
Check whether the APY is may provide or variable. A variable APY can drop at any time; a may provide APY (usually only on CDs) is locked for the term. If you are comparing a high-yield savings account at one bank to a money market account at another, the APY tells you which will actually earn more money over a year.
Also check the minimum balance required to earn the advertised APY. Some banks pay the full APY only if you maintain a certain balance — $1,000, $10,000, or more. If your balance falls below that threshold, the APY may drop significantly. This detail is usually in the fine print of the account terms.
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 factored in. APY is always equal to or higher than the interest rate. Banks must disclose both so you can see the full picture.
Do I need to calculate APY myself, or does the bank do it?
The bank does it. Federal law requires banks to show APY on all savings account disclosures. You can calculate it yourself to verify the number or to compare accounts, but you do not have to — the bank's APY figure is the official one.
What if my savings account compounds monthly instead of daily?
Monthly compounding produces a lower APY than daily compounding at the same interest rate. The difference is small at low rates but becomes noticeable above 4.00%. If you are choosing between two accounts with similar rates, pick the one that compounds daily.
Does APY change if I withdraw money during the year?
No. APY is an annual rate. If you withdraw money, you earn less total interest because your balance is lower, but the APY itself does not change. The bank still pays that rate on whatever balance you hold.
Can a bank change the APY after I open the account?
Yes, if the account has a variable rate. Most savings accounts are variable, meaning the bank can raise or lower the APY at any time. The bank will notify you of changes. CDs and some money market accounts may offer fixed rates that do not change for the term.