If a bank quotes you 5% on a savings account and a lender quotes you 5% on a loan, are you getting the same 5%? Almost certainly not. One is an APR, the other an APY, and the difference between them is real money that compounds for you or against you every single year. APR vs APY is the most quietly expensive confusion in personal finance — and the fix is one formula you can run on the back of a napkin.
What APR and APY Actually Mean
APR (Annual Percentage Rate) is the nominal, stated rate — the headline number, the one in the shop window. Its defining property is that it ignores compounding within the year. It treats the year as if interest were paid exactly once, at the end.
APY (Annual Percentage Yield), also called the Effective Annual Rate (EAR), is the rate you actually experience once intra-year compounding is folded in. It answers the only question that matters: if I put $1 in today, how much extra do I have in exactly one year?
They are connected by a single formula:
APY = (1 + APR ÷ n)n − 1
where n is the number of compounding periods per year: 12 for monthly, 365 for daily, 4 for quarterly, 2 for semiannual. If n = 1 (interest paid once a year), APY equals APR and the two are identical. The gap only opens once money compounds more than once a year — and it's that gap banks exploit in opposite directions.
The Formula That Separates Them
The math is the same compound interest you already know, compressed into a single year:
APY = (1 + r/n)n − 1
At 5% compounded monthly (n = 12): APY = (1 + 0.05/12)12 − 1 = 5.116%. The account billed as "5%" actually pays 5.116%.
If compounding is continuous, the formula collapses to APY = er − 1. At 5%, that's 5.127%. For practical purposes daily compounding is already within a hair of continuous — the extra frequency beyond daily buys you almost nothing.
How Big Is the Gap, Really?
Here's the gap between the stated APR and the true APY, at monthly compounding, across common rates:
| Stated APR | APY (monthly) | Gap |
|---|---|---|
| 1% | 1.005% | 0.005 pts |
| 5% | 5.116% | 0.116 pts |
| 10% | 10.471% | 0.471 pts |
| 15% | 16.075% | 1.075 pts |
| 20% | 21.939% | 1.939 pts |
| 24% | 26.824% | 2.824 pts |
Notice the pattern: double the rate and the gap doesn't double — it roughly quadruples. The APR–APY gap grows with the square of the rate. At 5% it's a rounding error; at 20% it's nearly two full percentage points of real money.
The gap also depends on how often the bank compounds. At a fixed 5% APR:
| Compounding | Periods / yr | APY |
|---|---|---|
| Annually | 1 | 5.000% |
| Semiannually | 2 | 5.062% |
| Quarterly | 4 | 5.095% |
| Monthly | 12 | 5.116% |
| Daily | 365 | 5.127% |
| Continuously | ∞ | 5.127% |
The jump from annual to monthly is where most of the money is; daily versus monthly buys a fraction of a basis point. So when banks fight over "daily compounding," they're fighting over almost nothing — the rate itself matters far more than the frequency.
Why Banks Advertise the Opposite Number
The same math shows up in two directions, and banks point it whichever way benefits them:
- On deposits, they quote APY — the higher number. A "5.00% APY" account compounded monthly is really a ~4.89% APR underneath. The APY is the honest number; the marketing just makes sure it's the biggest honest number available.
- On loans, they quote APR — the lower number. A "24% APR" credit card compounded daily is actually charging ~27.1% in effective terms. The APR is a legal disclosure, but it systematically understates the cost of anything that compounds.
Same rate, opposite marketing. That asymmetry is why APR vs APY is a genuine financial-literacy test: if you can convert one to the other in your head, the ads stop working on you.
Five Ways to Use This in Real Life
1. Compare savings accounts on equal footing
Account A offers 4.90% APY compounded monthly; account B offers 4.95% APR compounded quarterly. Which pays more? Convert B to APY: (1 + 0.0495/4)4 − 1 = 5.04%. B wins — and by more than the headline suggests. Never compare an APR against an APY without converting first.
2. See the true cost of credit card debt
A 24% APR card compounds daily, so the effective annual cost is about 27.1%. That's the number to hold in your head when deciding whether to carry a balance. It turns "24%" — which feels survivable — into "over a quarter of the balance, every year," which doesn't. Run the real cost through our Loan Calculator to see it in dollars.
3. Read loan offers with the right lens
Mortgages and car loans compound monthly, and in the US their quoted APR legally bundles in most lender fees — which makes APR a decent apples-to-apples comparison for loans. But for any investment or deposit, you want the APY; the APR will always undersell it.
4. Spot the "0% APR" trap
"0% APR for 12 months" sounds free, but many store cards use deferred interest: if the balance isn't paid in full by the cutoff, you owe retroactive interest on the entire original amount at a rate that's often 25%+. The 0% was a bet, not a gift — and the terms buried in the fine print decide who wins.
5. Convert any quote to one common number
Whenever two rates are thrown at you — one monthly, one annual, one APR, one APY — put them on the same footing before deciding. The conversion is one line of math, and it's the difference between comparing numbers and comparing realities.
When APR vs APY Still Isn't the Whole Story
Three caveats before you start correcting people at dinner parties:
- Loan APR isn't a pure interest rate. In the US, mortgage and auto APR includes closing costs and origination fees, so "APR" there is a regulatory term, not just the nominal rate. The formula above assumes no fees.
- Variable rates make APY a snapshot, not a promise. An APY computed today assumes the rate stays put for the year. With a floating rate, it won't.
- APY captures compounding, not fees, taxes, or inflation. A 5% APY account with a monthly maintenance fee may still lose to a 4.9% APY account with none.
Try It Yourself
Take any advertised rate. If it's an APR, convert it with (1 + r/n)n − 1; if it's an APY, that's already the real number — compare everything against it. For a single year that's the whole story. For multi-year growth, remember APY is a one-year number — the right tool there is CAGR. Now plug your rate into our Compound Interest Calculator and watch the gap compound into actual dollars over a decade. That moment, when a fraction of a percent turns into a visible sum, is when the difference stops being an acronym and becomes a decision.