APY calculator
Convert a nominal rate into an effective annual yield.
- Formula and assumptions shown
- Table and CSV export
- Runs in your browser
How it works
APY expresses the one-year result after compounding. Enter a nominal annual rate and the number of compounding periods to see the effective annual percentage yield.
APY = (1 + nominal rate ÷ periods per year)^(periods per year) − 1.
This is a rate-conversion model. It does not compare live accounts, account minimums, promotional terms, or changing rates, and it should not be confused with APR for borrowing.
Assumptions
- The nominal annual rate is constant for one year and is divided evenly across the selected periods.
- There are no deposits, withdrawals, taxes, or account fees.
- This is a mathematical conversion using equal periods; it does not apply the actual-day conventions used in a provider's regulated APY disclosure.
- The result is rounded only for display.
Worked example
$1,000 at 5% compounded monthly
The model gives (1 + 0.05 ÷ 12)^12 − 1 = 5.116%, or about $51.16 of interest on $1,000 after one year.
Step by step
- Divide the nominal rate by the compounding periods. 5% ÷ 12 = 0.4167% per month (0.0041667 as a decimal).
- Compound for one year. (1 + 0.0041667)^12 = 1.051162. This is what each dollar grows to after twelve monthly credits.
- Subtract 1 to get the yield. 1.051162 − 1 = 0.051162, or an APY of 5.1162%, displayed as 5.12%.
- Apply it to the deposit. $1,000 × 0.051162 = $51.16 of interest after one year, compared with $50.00 if the 5% were credited once at year end. Compounding adds $1.16.
How to read your result
Effective annual yield is the APY: the percentage a deposit grows in one year once compounding is included. Nominal annual rate repeats the rate you entered, and Interest after one year applies the APY to your deposit. The bar chart and table put the nominal rate and the APY side by side on the same scale.
APY is the figure to use when comparing savings accounts or CDs that compound on different schedules, because it puts them on a one-year basis. If an account advertises an APY, that number already includes compounding and should not be run through this conversion again.
The conversion assumes the rate stays fixed for the year and that nothing is added or withdrawn. It uses equal periods, while banks’ regulated APY disclosures follow Regulation DD’s formula based on the actual days in the term, so a bank’s figure can differ in the last decimal place.
What changes the result most
- Compounding frequency
- At a 5% nominal rate, the APY is 5.00% with annual compounding, 5.0625% semiannually, 5.0945% quarterly, 5.1162% monthly, and 5.1267% daily. The step from monthly to daily adds about $0.11 a year per $1,000.
- Rate level
- The gap between nominal rate and APY widens as the rate rises. With monthly compounding, 2% becomes a 2.0184% APY, while 10% becomes 10.4713%.
Questions
Is APY the same as APR?
No. APY describes the effect of compounding on a deposit or investment rate. APR is a borrowing-cost measure that can include fees.
Why does more frequent compounding increase APY?
Interest is added to the balance more often, allowing later periods to earn on the accumulated interest.
Is this a provider's official APY disclosure?
No. The estimate divides a nominal annual rate across equal periods. Financial institutions may use actual days in the term and other disclosure rules.
What does APY mean?
APY stands for annual percentage yield. It is the percentage return on a deposit over one year including the effect of compounding. Under the Truth in Savings rules (Regulation DD, linked below), banks and credit unions quote APY on deposit accounts so rates can be compared on the same basis.
What is the difference between APY and the interest rate?
The interest rate is the nominal annual rate before compounding. APY includes compounding, so it is equal to or higher than the interest rate. A 5% rate compounded monthly is a 5.12% APY; with annual compounding the two are the same.
What does 4% APY mean?
A deposit would grow by 4% over one year if the rate stayed the same and no money moved in or out: $10,000 would earn $400. The nominal rate that produces a 4% APY with monthly compounding is about 3.93%.
How often do savings accounts compound interest?
It depends on the account; daily and monthly compounding are both used. Truth in Savings rules require account disclosures to state how often interest is compounded and credited. Because APY already reflects the frequency, two accounts with the same APY pay the same over a year regardless of schedule.
More in Savings & investing
Sources
These references explain the concepts behind the calculation. They do not endorse this site. Estimates leave out any cost or condition you did not enter.