APY and APR both describe a yearly interest rate, and they are not the same number. APY (annual percentage yield) includes compounding - interest earning interest. APR (annual percentage rate) does not. Feed the same underlying rate into both and the APY always comes out a little higher, because it counts the snowball effect and the APR ignores it.
The split is easy to remember because the two numbers live on opposite sides of your money. Savings accounts advertise APY, the number that flatters what you earn. Loans and credit cards advertise APR, the number that understates what you pay. Neither is a lie - each is a legally defined disclosure - but if you do not know which one you are looking at, you will mis-compare offers on both sides.
Here are the definitions, the exact math that turns 4.00% into 4.074%, and why a “22% APR” credit card actually costs closer to 25%.
The two definitions
APR is the flat version of a rate. Take the periodic rate a product actually charges or pays and scale it to a year with plain multiplication: a rate of 1% a month is a 12% APR (1% x 12). No compounding is counted.
APY is the compounded version. It answers the real-world question: if the money sat for one full year, with interest added on schedule and then earning its own interest, what would the total yearly growth be? That 1%-a-month rate compounds to an APY of about 12.68%, not 12% - the extra 0.68 points is interest on interest.
The reason both exist is regulation, and it is worth knowing. The Truth in Savings Act requires banks to disclose deposit rates as APY, so savers can compare accounts on one honest, all-in number no matter how often each bank compounds. The Truth in Lending Act requires lenders to disclose borrowing costs as APR. Different laws, different sides of the ledger, two different yearly numbers.
Which number you will see where
| Product | Number quoted | What to do with it |
|---|---|---|
| Savings account / HYSA | APY | Compare APY to APY - it already includes compounding |
| CD (certificate of deposit) | APY | Same - APY makes different compounding schedules comparable |
| Credit card | APR | Real cost is higher if you carry a balance (math below) |
| Mortgage | APR (plus the note rate) | Mortgage APR also folds in certain fees and points, so it sits above the note rate |
| Auto / personal loan | APR | Compare APR to APR across lenders |
One asymmetry worth noticing: for savings you are handed the number that already includes compounding, but for credit cards you are handed the one that does not - and the compounding on a card works against you.
The math: how 4.00% becomes 4.074% APY
The conversion formula is:
APY = (1 + r / n)^n - 1
where r is the nominal annual rate (the APR-style flat rate) and n is how many times a year it compounds. Take a savings account paying a 4.00% nominal rate, compounded monthly - so r = 0.04 and n = 12 - and work it through step by step. (Each running product below is shown rounded to seven decimal places; keep full precision on your calculator and you will land on the same final number.)
- Monthly rate: 0.04 / 12 = 0.0033333… (one third of one percent each month; the threes repeat).
- Two months: multiply 1.0033333… by itself: 1.0066778.
- Four months: square that: 1.0134002.
- Eight months: square again: 1.0269799.
- Twelve months: multiply the eight-month factor by the four-month factor: 1.0269799 x 1.0134002 = 1.0407416.
- Subtract 1: 1.0407416 - 1 = 0.0407416, which is an APY of about 4.074%.
In dollars: $10,000 at a flat 4.00% would earn $400 in a year. Compounded monthly, it earns $10,000 x 0.0407416 = about $407.42 - an extra $7.42 that is purely interest earned by earlier interest. Small in year one, but this is the same force that makes long-term growth curve upward; the compound interest guide shows what it does over decades, and the compound interest calculator will run your own numbers with any compounding schedule.
The practical payoff of APY is comparison. Suppose Bank A pays 4.00% compounded monthly and Bank B pays 4.05% compounded once a year. B’s headline number looks higher - but A’s APY is 4.074% while B’s is exactly 4.050%. A wins, and you could only see it because APY put both accounts on the same footing. That is the entire job of the number.
Why card APR costs more than it says
Credit cards state an APR, but they do not charge you once a year - most charge daily. Your card’s daily periodic rate is its APR divided by 365, and every day you carry a balance, that day’s interest joins the balance and starts accruing its own.
Average credit card rates in 2026 sit above 20% APR, per the Federal Reserve’s G.19 consumer credit data. Run a typical 22% APR card through the math:
- Daily periodic rate: 0.22 / 365 = 0.0006027…, or about 0.0603% per day.
- On a $5,000 balance, that is 5,000 x 0.22 / 365 = about $3.01 in interest per day - roughly $91.67 over a statement month, which matches the quick monthly approximation (5,000 x 0.22 / 12).
- Compound that daily rate for a full year - multiply 1.0006027… by itself 365 times - and you get about 1.246: an effective annual rate of about 24.6%.
So the sticker rate understates a carried balance’s true yearly cost by around 2.6 percentage points. The card is not misquoting anything - APR is simply the flat number, and daily compounding does the rest. It is also why balances feel like they grow faster than the APR suggests, and why paying them down fast matters: the credit card payoff guide works through the escape plan. (If you pay your statement balance in full by the due date, the grace period means you pay no interest at all - the daily math only bites a carried balance.)
What this means for your savings
As of July 2026, top high-yield savings accounts pay roughly 4.0% to 4.2% APY per Bankrate’s tracking, with a few promotional offers above that - while big-bank savings accounts still pay a fraction of a percent. Because those top rates are quoted as APY, you can compare them directly: the compounding is already inside the number, so a 4.15% APY beats a 4.10% APY regardless of who compounds daily and who compounds monthly.
Two habits keep you on the right side of both acronyms. When saving, compare APY and only APY - our HYSA guide covers what else to check. When borrowing, remember the APR is the floor, not the ceiling: carried balances compound. And when you are saving toward something specific, the savings goal calculator turns an APY and a deadline into the exact monthly amount you need.
Common mistakes to avoid
Because the two acronyms look alike and both mean “yearly interest,” a few errors show up again and again.
Comparing an APR directly to an APY. They aren’t mirror images. A 6% APR loan and a 6% APY savings account share a headline but not their machinery: the loan’s rate leaves out compounding, so its true annual cost with monthly compounding is about 6.17%, while the savings account’s 6% APY already bakes compounding in and earns exactly 6%. Line them up as if 6 equals 6 and you quietly understate what the loan costs. To weigh a borrowing rate against an earning rate fairly, convert both to the same basis first - turn the APR into its APY (the formula above) before you compare.
Assuming a bare “interest rate” is the APY. If a savings offer quotes a plain rate, or an “APR,” without the letter Y, it may be the nominal figure before compounding. Ask for the APY - a US bank is required to disclose it, and it’s the only number that puts every account on equal footing no matter how often each one compounds.
Thinking a small APY gap isn’t worth chasing. On $500, the difference between 4.00% and 4.20% APY is about a dollar a year - trivial. But APY differences compound, so on a larger balance held for years the gap widens with the balance and the time. Since the number is already the all-in APY, the higher one wins by exactly as much as it looks, with no hidden compounding waiting to reshuffle the order.
FAQ
Is APY always higher than APR?
For the same nominal rate, APY is higher whenever compounding happens more than once a year, and equal only if interest compounds exactly once a year. The gap grows with the rate and the frequency: 4% compounded monthly adds about 0.07 points, while 22% compounded daily adds about 2.6.
Can I convert an APR to an APY myself?
Yes: APY = (1 + APR / n)^n - 1, where n is the number of compounding periods per year. Example: 6% APR compounded monthly is (1 + 0.06 / 12)^12 - 1 = (1.005)^12 - 1 = about 6.17%. The compound interest calculator does this for any rate and schedule.
Why do banks advertise APY but lenders advertise APR?
Because different laws govern each disclosure - the Truth in Savings Act for deposits, the Truth in Lending Act for credit. It is convenient for marketing that each side’s required number is the flattering one, but the disclosures themselves are standardized precisely so you can compare within each category.
Does a mortgage APR include compounding?
A mortgage APR’s main job is different: it folds certain upfront costs - origination fees, points - into the yearly rate so you can compare total loan cost across lenders. That is why a mortgage APR runs higher than the note rate. For cards and savings, the APR-vs-APY gap is about compounding; for mortgages, the APR-vs-rate gap is mostly about fees.
Sources
- Consumer Financial Protection Bureau - what APR means and how deposit rates are disclosed (consumerfinance.gov)
- Federal Reserve - Consumer Credit (G.19) and commercial bank interest rates, for average credit card APR (federalreserve.gov)
- Bankrate - Best high-yield savings accounts of July 2026 (bankrate.com/banking/savings/best-high-yield-interests-savings-accounts/)
- Rates cited are as of July 2026 and change frequently; verify current APYs before acting.
- Last reviewed July 5, 2026. This guide is general education, not personalized financial advice.
