APY ↔ APR Calculator

Convert between APR (nominal annual rate) and APY (effective annual yield) at any compounding frequency — both directions.

Inputs

Result

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How to use this calculator

  • Pick direction — APR → APY (most common) or APY → APR (rare; back-solve nominal from effective).
  • Enter the rate in percent (5.0 for 5%, not 0.05).
  • Choose the compounding frequency from the dropdown. For US savings accounts, "Daily" is the legal-compounding standard; for credit cards, "Monthly".
  • Read the converted rate plus the spread in basis points.

About this calculator

APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are NOT the same. APR is the nominal annual rate quoted on most credit products; APY is the effective annual rate after compounding. The conversion is APY = (1 + APR/n)^n − 1 where n is the number of compounding periods per year. For continuous compounding, APY = e^APR − 1. The two differ more as n grows — at 1×/yr they're identical; at daily compounding (n=365) the APY exceeds APR by about 0.13% on a 5% APR. US Regulation DD (Truth in Savings) mandates banks disclose APY for deposit accounts; Regulation Z (Truth in Lending) mandates APR for credit. Knowing both lets you compare a savings account quoting APY against a CD quoting APR-with-monthly-compounding without doing the math in your head.

Frequently asked

Why does my savings account say APY but my credit card says APR?+
US regulation. Reg DD (Truth in Savings) requires banks to quote APY on deposits — so you can compare savings rates apples-to-apples regardless of compounding. Reg Z (Truth in Lending) requires APR on credit — also for comparability. Both regulations chose the opposite default for the same reason: the customer-friendlier number.
What is continuous compounding?+
The mathematical limit as the number of compounding periods → ∞. APY_continuous = e^APR − 1. Almost no real product uses it; it's a theoretical upper bound. Daily compounding is within ~1 basis point of continuous for normal rates.
Does this match my bank's APY disclosure?+
For a deposit account quoting APR + daily compounding, yes — Reg DD prescribes exactly this formula (12 CFR 1030 Appendix A). For credit cards, the disclosed APR is usually the periodic rate × periods/year, so compounding daily APR ≈ EAR/APY ≈ stated APR + small spread.
Why does APY > APR?+
Because interest earned in earlier periods itself earns interest in later periods. The faster you compound, the more "interest-on-interest" builds up over a year. At annual compounding the effect vanishes (APY = APR).
When do APR and APY differ a lot?+
High rates + frequent compounding. A 20% APR credit card with monthly compounding has an APY of (1+0.2/12)^12 − 1 = 21.94% — about 1.94 percentage points higher than the headline. At 1% APR daily compounding, the spread is ~5 basis points (1.005%).
Source?+
12 CFR 1030 (Reg DD — Truth in Savings) Appendix A defines the APY-from-APR formula used by US banks. CFA Institute Curriculum Vol 1 (Quantitative Methods) — Effective Annual Rate. SEC Investor.gov compound-interest reference.

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