Method Deck / finance
APR to APY (effective annual rate)
Converts a nominal annual percentage rate compounded periodically into the effective annual percentage yield.
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Inputs
- nominal_annual_rate_percent (number, %, required) min 0 : Nominal annual rate (APR)
- compounds_per_year (integer, required) one of: 1, 2, 4, 12, 52, 365 : Number of compounding periods per year
Outputs
- effective_annual_rate_percent (%): Effective annual rate (APY)
Steps
- Convert the nominal rate to a decimal: r = nominal_annual_rate_percent / 100.
- Periodic rate i = r / compounds_per_year.
- APY as a decimal = (1 + i) ^ compounds_per_year - 1.
- effective_annual_rate_percent = APY * 100, rounded to 4 decimals for display as a percent with 2 shown.
Constants
None.
Sources
- Principles of Corporate Finance (McGraw-Hill, 2026-09-30T19:31:29Z) - APY = (1 + APR/n)^n - 1
Worked example and test vectors
| Name | Inputs | Answer |
|---|
| worked example | {"nominal_annual_rate_percent":12,"compounds_per_year":12} | 12.68% |
| test vector: quarterly compounding | {"nominal_annual_rate_percent":6,"compounds_per_year":4} | 6.14% |
Published card
- Address:
035b0d84792e2c80de55d6a3f7c5cbee
- Made at:
2026-09-30T22:39:30.722Z
- Method sha256:
f3b0995a9d6d3d74550a8a7f13f03b4cbbef7ba31a2b6b9111a9aec73f94bee6