To calculate APY compounded daily, use the formula APY = (1 + r/365)^365 − 1, where r is the nominal annual interest rate written as a decimal. A savings account advertising a 4.00% interest rate actually yields about 4.08% once daily compounding is factored in. That gap between the stated rate and the effective return is exactly what APY measures, and the arithmetic takes about a minute on any calculator or spreadsheet.
The Formula and What Each Piece Does
Written out with its variables:
APY = (1 + r / n) ^ n − 1
- r is the nominal (stated) annual interest rate, expressed as a decimal. A 4.00% rate becomes 0.04.
- n is the number of compounding periods per year. For daily compounding, n = 365.
The logic runs like this. Dividing the annual rate by 365 gives you the slice of interest earned each day. Adding 1 turns that daily rate into a growth factor. Raising that factor to the 365th power simulates a full year in which each day’s interest earns its own interest the next day. Subtracting 1 strips away the original principal, leaving pure yield as a decimal that you multiply by 100 to get a percentage.
This matches the official calculation in Appendix A of Regulation DD, which requires banks to express APY as an annualized rate based on a 365-day year.1Consumer Financial Protection Bureau. Appendix A to Part 1030 — Annual Percentage Yield Calculation In a leap year, banks may use 366 days, though the standard calculation assumes 365.2eCFR. 12 CFR Part 1030 — Truth in Savings (Regulation DD)
A Worked Example at 4.00%
Say your savings account pays a 4.00% nominal interest rate, compounded daily. Here is the math broken into steps you can follow on a scientific calculator or spreadsheet.
Step 1. Convert the rate to a decimal. Divide the percentage by 100: 4.00 ÷ 100 = 0.04.
Step 2. Find the daily rate. Divide by 365: 0.04 ÷ 365 = 0.00010959.
Step 3. Add 1. This creates the daily growth factor: 1 + 0.00010959 = 1.00010959.
Step 4. Raise to the 365th power. In a spreadsheet, type =1.00010959^365. The result is approximately 1.04081.
Step 5. Subtract 1. 1.04081 − 1 = 0.04081.
Step 6. Convert back to a percentage. 0.04081 × 100 = 4.08%.
The APY on a 4.00% nominal rate with daily compounding is 4.08%. That 0.08 percentage point difference is the extra return generated by interest compounding on itself every day. On a $10,000 deposit left untouched for a year, you would earn about $408 rather than the $400 that simple interest would produce. The gap grows wider at higher rates and larger balances.
What You Need Before You Start
The only input the formula requires is the nominal interest rate, sometimes called the stated rate. This is the annual rate before compounding gets applied. The Truth in Savings Act requires banks to disclose it clearly, and Regulation DD requires the terminology to stay consistent across all documents you receive.2eCFR. 12 CFR Part 1030 — Truth in Savings (Regulation DD) Look for it in the account agreement, the rate sheet on the bank’s website, or the disclosure you received when you opened the account.
Most banks already display the APY alongside the nominal rate, so in practice you are often verifying their math rather than discovering the APY from scratch. If the bank only shows APY without the underlying interest rate, that APY is the number you would compare across institutions anyway. The formula is most useful when you have the nominal rate and want to see what daily compounding does to it.
One detail worth knowing: the 365-day convention applies to consumer deposit accounts. Some wholesale lending and money-market contexts use a 360-day “banker’s year” for short-term interest, which changes the math slightly. For standard savings accounts, checking accounts, and CDs, use 365.
Turning APY Into Dollars Earned
Once you have the APY, finding your dollar return is straightforward: multiply your balance by the APY in decimal form. A $25,000 balance earning 4.08% APY produces about $1,020 in interest over a full year, assuming no deposits or withdrawals change the balance.
That calculation assumes the money sits untouched for twelve months. Real life is messier. Federal rules require banks to accrue interest through the day before a withdrawal, so pulling money out mid-month does not erase the interest earned up to that point.2eCFR. 12 CFR Part 1030 — Truth in Savings (Regulation DD) The bank can, however, delay crediting the accrued interest until the next scheduled payment date. If you close the account before that date, some banks reserve the right to forfeit accrued but unpaid interest, provided they disclosed the policy at opening.
APY vs. the Stated Interest Rate
Banks must show the APY whenever they advertise a rate of return, and they can show the nominal interest rate alongside it, but the interest rate can never appear more prominently than the APY.3eCFR. 12 CFR 1030.8 — Advertising This rule exists because the APY is the number that tells you what you will actually earn. The nominal rate understates your return by ignoring compounding.
How wide the gap gets depends on compounding frequency. Annual compounding produces zero difference; the APY and the nominal rate are identical. Monthly compounding creates a small gap. Daily compounding widens it slightly further, and continuous compounding (a theoretical extreme where interest compounds every instant) pushes it to its mathematical maximum. For typical savings rates in the 3 to 5% range, the gap between daily and continuous compounding is negligible, which is why daily compounding is the practical ceiling for consumer accounts.
APY is not the same as APR. APR — annual percentage rate — applies to loans and credit cards and represents cost rather than earnings. APR includes certain fees along with the interest rate, while APY is purely about interest and compounding frequency. APY tells you how much you earn; APR tells you how much you pay.
Fees the Formula Does Not See
The APY formula does not account for fees. A savings account earning 4.08% APY sounds solid until a $5 monthly maintenance fee eats into the return. On a $2,000 balance, that is $60 a year in fees against roughly $82 in interest, cutting your effective return by nearly three-quarters. Regulation DD requires any advertisement mentioning APY to also state that fees could reduce earnings.3eCFR. 12 CFR 1030.8 — Advertising
Monthly fees at major banks range from nothing to around $7.50 on standard savings accounts, and most can be waived by maintaining a minimum balance or meeting other conditions. Online banks frequently charge no monthly fee at all. When comparing two accounts with similar APYs, the one with fees will always deliver less actual money to your pocket unless you qualify for the waiver.
Checking the APY Earned on Your Statement
Banks that send periodic statements must include a figure called the “annual percentage yield earned” for the statement period.2eCFR. 12 CFR Part 1030 — Truth in Savings (Regulation DD) This number often looks different from the advertised APY, and that is not a mistake. The advertised APY assumes your entire deposit stays put for 365 days with no transactions. The APY earned on your statement reflects what actually happened during that specific period, annualized to a yearly rate.
Regulation DD considers the APY accurate if it falls within 0.05 percentage points of the result from the official formula.2eCFR. 12 CFR Part 1030 — Truth in Savings (Regulation DD) If the figure on your statement differs from the advertised APY by more than that tolerance, and you have not made deposits or withdrawals that would explain the gap, it is worth a call to the bank.