To calculate APY, take the nominal interest rate as a decimal, divide it by the number of compounding periods in a year, add one, raise the result to the power of that same number of periods, and subtract one. Written out, the formula for how to calculate APY is (1 + r/n)n – 1, where r is the nominal rate and n is the compounding frequency. Both numbers appear on your account disclosures, which banks are required to provide under the Truth in Savings Act and Regulation DD.1eCFR. 12 CFR Part 1030 – Truth in Savings (Regulation DD)
The Two Inputs
You need the nominal interest rate and the compounding frequency. Nothing else.
The nominal rate is the base annual rate your bank quotes before compounding is applied. Convert it from a percentage to a decimal before using it in the formula. A rate of 5.50% becomes 0.055. Forget this step and the answer will be off by a factor of 100.
The compounding frequency is how often the bank calculates interest and adds it to your balance. Common values are 365 for daily, 12 for monthly, 4 for quarterly, and 1 for annual compounding. Your account agreement and periodic statements list both figures.
Working Through a Monthly Example
Say your savings account pays a 5% nominal rate compounded monthly. The steps:
- Convert the rate: 5% ÷ 100 = 0.05
- Divide by the number of periods: 0.05 ÷ 12 = 0.004167
- Add one: 1 + 0.004167 = 1.004167
- Raise to the twelfth power: 1.00416712 = 1.05116
- Subtract one: 1.05116 – 1 = 0.05116
The APY is 5.116%. On a $10,000 deposit held for a full year, that yields about $511.60 in interest instead of the flat $500 you would get from simple interest. The extra $11.60 is the interest earned on interest already credited during the year.
The math itself is straightforward once you see the logic. Dividing r by n gives the rate applied in a single cycle. Adding one preserves your principal so you’re tracking total value. Raising to the n-th power runs that periodic rate through every cycle in the year. Subtracting one at the end strips the principal back out, leaving only the yield expressed as a decimal.
How Compounding Frequency Changes the Answer
More frequent compounding produces a higher APY, but the extra earnings shrink quickly. Here is the same 5% nominal rate calculated at four different frequencies:
- Annually (n = 1): (1 + 0.05/1)1 – 1 = 5.000% APY
- Quarterly (n = 4): (1 + 0.05/4)4 – 1 = 5.095% APY
- Monthly (n = 12): (1 + 0.05/12)12 – 1 = 5.116% APY
- Daily (n = 365): (1 + 0.05/365)365 – 1 = 5.127% APY
Moving from annual to quarterly adds close to a tenth of a percentage point. Moving from quarterly to daily adds only about three hundredths. On a $50,000 balance, the daily-versus-monthly gap works out to roughly $5.50 over a year. Two accounts advertising the same nominal rate will produce slightly different APYs if their compounding schedules differ, but the gap is usually small enough that other account features matter more.
Continuous Compounding
Some instruments assume interest compounds at every instant rather than at fixed intervals. That case uses a different formula built around the constant e (about 2.71828):
APY = er – 1
At a 5% nominal rate, e0.05 = 1.05127, so the APY is 5.127%. On a scientific calculator, use the ex key with 0.05 as the exponent. In a spreadsheet, the function is EXP(0.05).
Continuous compounding represents the mathematical ceiling for any given nominal rate. Daily compounding already sits so close to that ceiling that the two match to three decimal places at 5%. Continuous compounding shows up mostly in bond pricing and financial theory; for a deposit account, the daily figure will do.
Checking Your Bank’s APY Against Dollars Earned
If you know the actual dollar interest your account earned and the principal, you can back into the APY using the regulatory formula from Regulation DD:
APY = 100 × [(1 + Interest/Principal)(365/Days in term) – 1]2Legal Information Institute. 12 CFR Appendix A to Part 1030 – Annual Percentage Yield Calculation
The appendix gives a worked benchmark: $61.68 earned on $1,000 in a NOW account over 365 days produces an APY of 6.17%. Plug your own numbers into that formula and compare the result to what the bank shows on your statement. Both formulas, forward from the rate and backward from the dollars, produce the same figure when the bank has calculated correctly. The APY calculation assumes a 365-day year.3Consumer Financial Protection Bureau. Appendix A to Part 1030 – Annual Percentage Yield Calculation
What APY Does Not Tell You
APY is a clean number, and that cleanliness leaves things out. Three of them matter before you decide the advertised rate is what you’ll actually pocket.
Fees. Regulation DD defines “interest” in a way that excludes fee effects, so the APY on a bank’s advertisement ignores monthly maintenance charges, wire fees, and other account costs.1eCFR. 12 CFR Part 1030 – Truth in Savings (Regulation DD) An account paying 4.50% APY on a $1,000 balance earns about $45 in a year; a $12 monthly maintenance fee drains $144 over the same period, leaving you $99 in the hole. On a $25,000 balance, that same fee barely registers. Subtract expected annual fees from expected interest before comparing accounts.
Tiered rates. Many savings and money market accounts change the rate at balance thresholds, and the APY for each tier is different. Banks must disclose the APY and minimum balance for every tier. Some banks apply the higher rate to your whole balance once you cross the threshold; others apply each tier’s rate only to the dollars within that tier, the way tax brackets work. The disclosure will say which method applies. Use the APY for your actual balance, not the top-tier number in the headline.
Taxes. Interest is taxable as ordinary income at the federal level, with 2026 marginal rates ranging from 10% to 37% depending on total income.4Internal Revenue Service. IRS Releases Tax Inflation Adjustments for Tax Year 2026, Including Amendments From the One, Big, Beautiful Bill Most states tax it too. A $500 interest payment at a 22% federal rate leaves about $390 in your pocket. Banks report interest of $10 or more on Form 1099-INT, and smaller amounts are still reportable on your return.5Internal Revenue Service. Publication 1099 General Instructions for Certain Information Returns – 2026 The APY inside a tax-advantaged account like an IRA produces a better after-tax result than the same APY in a regular savings account.
One boundary worth flagging: APY and APR are not the same measure. APY governs deposit accounts and includes compounding. APR governs loans and, on most consumer credit products, does not.6Consumer Financial Protection Bureau. What Is the Difference Between a Loan Interest Rate and the APR If you’re comparing what you earn on savings against what you pay on debt, convert both to the same measure first, because the formulas above only describe what you earn.