APR vs. APY: what compounding actually costs you

A 5% APR and a 5% APY are not the same 5%. APR is the stated nominal rate; APY is what you actually earn or pay once compounding is applied over a year. The difference is small at low rates and short compounding gaps, but it's never zero once a rate compounds more than once a year.

The formula

APY = ((1 + APR ÷ 100 ÷ n)ⁿ − 1) × 100, where n is the number of compounding periods per year. Divide the rate down to one period, add 1, raise it to the number of periods, subtract 1, then convert back to a percentage.

A real example: a savings account

Take a savings account paying 5% APR, compounded monthly (n = 12).

1. Rate per period: 5 ÷ 100 ÷ 12 = 0.0041667.
2. Add 1: 1.0041667.
3. Raise to the 12th power: 1.004166712 ≈ 1.051162.
4. Subtract 1 and convert to a percent: 0.051162 × 100 ≈ 5.116%.

So a stated 5% APR actually pays out about 5.116% APY once monthly compounding is applied — roughly 0.116 percentage points more than the sticker rate, entirely from interest earning interest within the year.

A real example: a credit card

Now the direction that costs you money. Take a credit card with a 24% APR, also compounded monthly.

1. Rate per period: 24 ÷ 100 ÷ 12 = 0.02.
2. Add 1: 1.02.
3. Raise to the 12th power: 1.0212 ≈ 1.268242.
4. Subtract 1 and convert to a percent: 0.268242 × 100 ≈ 26.824%.

A stated 24% APR actually costs about 26.82% APY if a balance carries for a full year — nearly 2.82 percentage points above the number printed on the card.

How much compounding frequency alone matters

Hold the 5% APR fixed and change only n, the number of compounds per year:

• Annual (n = 1): APY = 5.000% — no compounding within the year, so APY equals APR exactly.
• Quarterly (n = 4): APY ≈ 5.095%.
• Monthly (n = 12): APY ≈ 5.116%.
• Daily (n = 365): APY ≈ 5.127%.

Most of the gap opens the moment a rate starts compounding at all — going from annual to quarterly adds 0.095 points, but going from monthly all the way to daily only adds another 0.011 points. Chasing "daily compounding" marketing language matters far less than knowing whether a rate compounds more than once a year in the first place.

Which direction you want

On money you're earning — savings, CDs — a higher APY relative to APR is good news; it means compounding is working in your favor. On money you owe — credit cards, some loans — the same math works against you, and the APY is the more honest number for what carrying a balance actually costs. Lenders are required to disclose APR; APY on debt is worth calculating yourself before assuming the printed rate is the full story.

What this doesn't capture

This is the pure compounding math on a rate that stays fixed all year. It doesn't include fees, promotional-rate expirations, or a balance that changes mid-year through new charges or payments — all of which move the real cost or yield further from either number.

Run your own numbers

The free APR ↔ APY calculator converts any rate and compounding frequency instantly — entirely on your device.