Financial Calculators

APR vs APY — what's the real yield?

Convert an Annual Percentage Rate to its Annual Percentage Yield given a compounding frequency.

APR vs APY Calculator

Table of contents

◦APR vs APY
◦Formula
◦How to use
◦Worked examples
◦FAQ

APR vs APY

APR (Annual Percentage Rate) is the stated rate before compounding. APY (Annual Percentage Yield) is what you actually earn (or pay) once compounding is folded in. They're equal only when compounding happens once a year.

This calculator converts an APR to its equivalent APY at any compounding frequency — useful for comparing savings accounts (advertised in APY) against bonds and loans (advertised in APR).

Formula

APY = (1 + APR/n)<sup>n</sup> − 1

Where:

  • APR is the stated annual rate (as a decimal — divide percent by 100)
  • n is the number of compounding periods per year (12 for monthly, 365 for daily, etc.)

How to use

  1. Enter the APR as a percent (e.g. 5 for 5%).
  2. Enter how many times per year interest compounds:

    3. - 1 = annual - 4 = quarterly - 12 = monthly - 365 = daily

The APY and the APR-to-APY spread appear instantly.

Worked examples

5% APR: | Compounding | APY | Spread | |---|---|---| | Annual (n=1) | 5.0000% | 0 | | Quarterly (n=4) | 5.0945% | +0.09 | | Monthly (n=12) | 5.1162% | +0.12 | | Daily (n=365) | 5.1267% | +0.13 |

The spread between APR and APY grows with both the rate and the compounding frequency. At 20% APR (typical credit card), the daily-compounded APY is 22.13% — a 2.13-point hit hiding in the fine print.

FAQ

Why do banks advertise savings in APY but loans in APR?

Because APY is bigger for the saver (it makes the rate look better) and APR is smaller for the borrower (it makes the rate look better). Both are accurate; they just disclose different aspects.

Is APY always higher than APR?

For positive rates with compounding more than once a year, yes. They're equal at annual compounding. APY can never be lower than APR.

What if compounding is "continuous"?

The mathematical limit as n → ∞ is APY = e<sup>APR</sup> − 1. For 5% APR, continuous APY is 5.1271%. The difference between daily (5.1267%) and continuous is rounding noise.

Does APY include fees?

No — it's a pure interest measure. Loan APR may include some fees (origination, etc.) depending on jurisdiction; APY never does. For total cost-of-funds, look at the disclosure documents.

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