APY vs APR — What Your Bank Statement Actually Means

APY and APR look almost identical, which is exactly the problem. Banks deliberately use whichever number sounds better in their marketing. For savings accounts they advertise APY (higher). For credit cards they advertise APR (sounds lower than the actual cost). Here is what each one really means.

The One-Sentence Difference

APR is the rate before compounding. APY is the rate after compounding. APY is what you actually earn (or pay).

Quick Conversion Table

APR	Compounding	APY
4.00%	Annual	4.000%
4.00%	Quarterly	4.060%
4.00%	Monthly	4.074%
4.00%	Daily	4.081%
5.00%	Annual	5.000%
5.00%	Monthly	5.116%
5.00%	Daily	5.127%
18.00%	Daily (credit card)	19.716%
24.00%	Daily	27.115%

The gap widens at higher rates and with more frequent compounding. At credit-card rates (18-24% APR), the actual APY is 2-3 percentage points higher than advertised. That is real money over a year of carrying a balance.

The Formula

APY = (1 + APR/n)^n - 1

Where n is the number of compounding periods per year. For daily compounding, n = 365. For monthly, n = 12. For quarterly, n = 4. For annual, n = 1.

Example. A bank advertises a savings account with 5% APR compounded daily.

APY = (1 + 0.05/365)^365 - 1

APY = (1.000137)^365 - 1

APY = 1.05127 - 1

APY = 0.05127 = 5.127%

So 5% APR daily compounded actually earns 5.127% APY — about 0.13% extra per year.

Why Banks Use APY for Savings

Higher number sounds better. A bank with 5.0% APR will market it as "5.13% APY" to make the account look more competitive. The math is honest — the customer really does earn 5.13% — but the framing is chosen to be the largest possible number.

Why Lenders Use APR for Loans

Lower number sounds better when it is a cost to you. A credit card with a 22% APR has an effective APY closer to 24-25% when you compound daily and carry a balance for a full year. Lenders prefer the lower-sounding APR for marketing.

Mortgages are a special case. Mortgage APR includes some upfront fees (origination, points) that pure interest does not, which is why mortgage APRs can be slightly higher than the stated note rate. This makes mortgage APR a more honest comparison number than the note rate.

Comparing Savings Accounts — Always Use APY

If one bank says "5.00% APR daily compounded" and another says "5.05% APY," which is better? Convert both to APY:

• Bank A: 5.00% APR daily = 5.127% APY
• Bank B: 5.05% APY (already converted)

Bank A wins by 0.077%. On a $10,000 balance held for one year, that is $7.70 of extra interest. Real, but tiny — and certainly not worth switching banks for.

When the APY/APR Gap Matters Most

1. Credit card debt. A 24% APR card actually charges ~27% APY when you compound daily. Carrying a $5,000 balance for a year costs $1,200 in stated APR but $1,355 in actual APY interest.
2. Long-term investing. A 0.1% APY difference compounds into thousands of dollars over 30 years on a large balance.
3. CDs and high-yield savings. The whole point of these accounts is the rate, so even small differences matter for shopping.

When the Gap Does Not Matter

1. Short-term holdings. $5,000 in a savings account for 3 months barely earns enough interest for the APR/APY difference to register in dollars.
2. Compound frequency higher than monthly. Going from monthly to daily adds about 0.05% — pennies on most balances.
3. When the rate itself is tiny. The difference between 0.5% APR and 0.51% APY is irrelevant to your financial life.

Practical Takeaway

When comparing savings accounts, always look at APY. When evaluating credit card debt or loans, mentally add 1-2 percentage points to the stated APR to get the real annual cost. And when reading bank marketing, ask yourself which number they chose to highlight and why.

The compound interest calculator uses APR-style inputs (you enter the annual rate and the compounding frequency separately), which lets you see how the two relate as you change frequency.