Banking
Annual percentage yield
Divide the nominal rate by the compounding frequency, add one, raise to that frequency, and subtract one. The result is the true one-year return.
The Formula
APY = (1 + r/n)^n - 1
Divide the nominal rate by the compounding frequency, add one, raise to that frequency, and subtract one. The result is the true one-year return.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| r | Nominal annual rate as a decimal | decimal | The quoted APR. Divide percentages by 100: 5% becomes 0.05. |
| n | Compounding periods per year | periods per year | 1 annually, 2 semiannually, 4 quarterly, 12 monthly, 365 daily. Check the account agreement for the actual convention. |
| APY | Effective annual yield | decimal | Multiply by 100 for the quoted percentage. This is the figure deposit disclosures must publish. |
What Each Symbol Means
rdecimal
Nominal annual rate as a decimal
The quoted APR. Divide percentages by 100: 5% becomes 0.05.
nperiods per year
Compounding periods per year
1 annually, 2 semiannually, 4 quarterly, 12 monthly, 365 daily. Check the account agreement for the actual convention.
APYdecimal
Effective annual yield
Multiply by 100 for the quoted percentage. This is the figure deposit disclosures must publish.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate apy page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate APY, filed under Finance. Every number the guide produces comes from substituting into this one line.