APR vs APY: The Most Important Percentage Distinction in Finance

Definitions

• APR (Annual Percentage Rate) — the simple annual rate, ignoring compounding within the year.
• APY (Annual Percentage Yield) — the effective annual rate, including the effect of compounding.

APY is always equal to or greater than APR, with the gap increasing as compounding frequency increases.

The formula

APY = (1 + APR/n)ⁿ − 1

Where n is the number of compounding periods per year.

Worked example

A savings account advertised at 5% APR compounded monthly (n = 12):

APY = (1 + 0.05/12)¹² − 1
    = (1.00417)¹² − 1
    = 1.05116 − 1
    = 5.116%

You earn 5.116%, not 5%.

Why this matters for credit cards

Credit card “APR” is required by law in the US, but interest typically compounds daily. A credit card with 20% APR has an effective APY of:

APY = (1 + 0.20/365)³⁶⁵ − 1
    ≈ 22.13%

The card costs you 22.13% per year, not 20%. Many consumers underestimate credit card costs because of this.

Quick conversion table at 5% APR

Compounding	APY
Annual (n=1)	5.000%
Semi-annual (n=2)	5.063%
Quarterly (n=4)	5.095%
Monthly (n=12)	5.116%
Daily (n=365)	5.127%
Continuous (e^0.05)	5.127%

The takeaway

When shopping for savings products, prefer APY. When evaluating loan costs, the true rate is the APY — even though lenders typically advertise APR (which is lower).