APR to APY Calculator (Effective Annual Rate)
APR to APY calculator: convert a nominal annual rate into the effective annual yield for any compounding frequency, or back.
APY = (1 + rn)n − 1
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
APY (annual percentage yield) shows what you really earn or pay in a year once interest compounds: APY = (1 + r/n)ⁿ − 1, where r is the nominal rate (APR) and n the number of compounding periods per year.
Compare savings accounts and loans by their APY, since two offers with the same APR but different compounding are not equal.
Estimates for information only, not financial advice.
Formula
APY = (1 + rn)n − 1
| Symbol | Quantity | Units |
|---|---|---|
| r | Nominal annual rate (APR) | %, × |
| n | Compounding periods per year | — |
| APY | Effective annual rate (APY) | %, × |
Worked example
Given: r = 5 % · n = 12
APY = (1 + rn)n − 1
Result: APY = 5.11619 %
Frequently asked questions
What is the APY of 5 % compounded monthly?
(1 + 0.05/12)¹² − 1 = 5.116 %.