APY vs APR Converter Guide: Formula & Worked Example
Short answer
Convert a nominal APR into the true annual yield, and back. In the fixed example below, apy is 5.1162%. Your answer depends on the inputs and assumptions you choose.
Formula
APY = (1 + APR/n)ⁿ − 1
Use the relationship above with consistent units. The inputs are rate, rate entered is, compounding. Use the input scale shown beside each field and keep time periods and units consistent. Only round the final result for display.
Worked example
- Rate
- 5
- Rate entered is
- apr
- Compounding
- 12
- APY: 5.1162%
- APR: 5%
Understanding the result
Convert a nominal APR into the true annual yield, and back. Start with the base example, then replace each value with the figure that matches your situation.
Rate
The example uses 5 % for rate. This is an illustration, not a recommended value. Keep the unit and time period shown by the field.
Rate entered is
The example uses APR (nominal) for rate entered is. This is an illustration, not a recommended value. Keep the unit and time period shown by the field.
Compounding
The example uses Monthly for compounding. This is an illustration, not a recommended value. Keep the unit and time period shown by the field.
What the comparison means
The comparison changes only rate, keeping every other example input fixed. This isolates that input's effect on the primary result. It does not predict future outcomes.
Rates, fees, eligibility, local tax rules and provider rounding can change the final amount. Reference tax and exchange-rate data may be outdated; verify the official source before deciding.
Comparison
| Scenario | Input | Result |
|---|---|---|
| Lower input | Rate: 4 % | APY: 4.0742% |
| Base example | Rate: 5 % | APY: 5.1162% |
| Higher input | Rate: 6 % | APY: 6.1678% |
Common mistakes
- Using the wrong units for rate.
- Comparing results while changing more than one input at a time.
- Rates, fees, eligibility, local tax rules and provider rounding can change the final amount. Reference tax and exchange-rate data may be outdated; verify the official source before deciding.
Checklist
- Confirm rate is expressed in %.
- Confirm rate entered is.
- Confirm compounding.
- Check the result against your source or provider.
Calculators Percentage Editorial Team
Calculator guides from the Calculators Percentage team. These introductory examples are educational, not professional advice.
Last reviewed:
Rates, fees, eligibility, local tax rules and provider rounding can change the final amount. Reference tax and exchange-rate data may be outdated; verify the official source before deciding.