Quick answer
APY = (1 + APR ÷ n)^n − 1, where n is the compounding periods per year. A 5% nominal rate compounded monthly has an APY of 5.1162%.
Enter the nominal rate and compounding frequency. The calculator returns the APY.
Related tools: Simple Interest Calculator: Interest earned or owed without compounding. Compound Interest Calculator: Future value with compound interest and regular contributions. Interest Per Day Calculator: Daily interest on a balance at an annual rate.
How to use the APY Calculator
- Enter nominal annual rate (APR) (%) (between 0 and 100).
- Choose compounding: Monthly, Annually, Semi-annually, Quarterly, Daily and Weekly.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Nominal annual rate (APR) | A number, in % | ≥ 0, ≤ 100 |
| Compounding | Choose one: Monthly; Annually; Semi-annually; Quarterly; Daily; Weekly | Starts at Monthly |
Formula and method
Formula
APY = (1 + APR ÷ n)^n − 1
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Effective annual rate for n compounding periods per year.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Nominal annual rate (APR) = 5; Compounding = Monthly.
| Result | Value |
|---|---|
| APY | 5.1162 % |
Example 2
Inputs: Nominal annual rate (APR) = 5; Compounding = Annually.
| Result | Value |
|---|---|
| APY | 5 % |
Example 3
Inputs: Nominal annual rate (APR) = 0; Compounding = Monthly.
| Result | Value |
|---|---|
| APY | 0 % |
The first line is the headline result (aPY). IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Why APY exceeds APR
Interest earned in each period earns interest itself. With monthly compounding, the monthly rate is 0.4167% and (1.004167)^12 = 1.051162. Daily compounding at 5% gives 5.1267%; annual compounding gives 5%.
Using APY
Banks quote APY on savings accounts so rates compare fairly, while loans quote APR. For savings, compare APYs; for borrowing, compare APRs.
How the result changes with nominal annual rate
Holding every other input at the first worked example, this table changes only nominal annual rate. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Nominal annual rate | APY |
|---|---|
| 2.5 | 2.5288 % |
| 5 | 5.1162 % |
| 10 | 10.4713 % |
| 20 | 21.9391 % |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Nominal annual rate (APR): entering "-1" shows "Nominal annual rate (APR) must be at least 0." beside that field and no result.
Choosing between the APY Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Simple Interest Calculator](/finance/simple-interest-calculator/) | principal, annual rate and time | Interest |
| [Compound Interest Calculator](/finance/compound-interest-calculator/) | initial amount, annual interest rate and years | Future value |
| [Interest Per Day Calculator](/finance/interest-per-day/) | balance, annual rate and day-count basis | Interest per day |
| [Continuous Compounding Calculator](/finance/continuous-compound/) | principal, annual rate and years | Future value |
| [Real Interest Rate Calculator](/finance/real-interest-rate-calculator/) | nominal interest rate and inflation rate | Real interest rate |
Background: interest, saving and investing
A nominal rate (APR) does not include the effect of compounding; the annual percentage yield (APY) does: APY = (1 + r/n)^n − 1. A 5% nominal rate compounded annually is 5.000%, semi-annually about 5.063%, quarterly about 5.095% and monthly about 5.116%, so more frequent compounding helps, but with diminishing returns.
The rate you enter in a projection is an assumption, not a promise: real returns vary and can be negative. Fees and taxes are not modelled unless the page says so.
Assumptions and limitations
- Annual compounding gives APY = APR
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for nominal annual rate (APR) to confirm this.
Frequently asked questions
What is the APY of 4% compounded quarterly?
4% compounded quarterly gives APY = (1 + 0.04 ÷ 4)⁴ − 1 ≈ 4.06%.
Does APY include fees?
No. APY reflects compounding only; account fees reduce what you actually earn.
Which is larger, APY or APR?
APY, whenever compounding is more often than annual.
What does the APY Calculator calculate?
Convert a nominal rate (APR) into the effective annual yield (APY). It returns APY.
What formula does the APY Calculator use?
APY = (1 + APR ÷ n)^n − 1. Effective annual rate for n compounding periods per year.
What do I need to enter in the aPY Calculator?
You enter Nominal annual rate (APR) (%) and Compounding.
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. Annual compounding gives APY = APR.
What does the “Compounding” option change?
It sets how the aPY is worked out. The choices are Monthly, Annually, Semi-annually, Quarterly, Daily and Weekly.
What is an example of a aPY result?
With nominal annual rate (APR) 5 and compounding Monthly, the aPY is 5.1162 %.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: Annual compounding gives APY = APR.
Related calculators
- Simple Interest Calculator — Interest earned or owed without compounding.
- Compound Interest Calculator — Future value with compound interest and regular contributions.
- Interest Per Day Calculator — Daily interest on a balance at an annual rate.
- Continuous Compounding Calculator — Growth with continuously compounded interest.
- Real Interest Rate Calculator — Inflation-adjusted interest rate using the exact Fisher relation.
- Auto Loan Calculator — Monthly car payment after down payment and trade-in.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.