APR vs APY: Why Banks Quote Them Differently
APR and APY measure the same interest rate from opposite sides of a mirror. The difference is compounding — and the reason banks pick one over the other on any given product is pure marketing. Once you know the conversion, you can cut through every fine-print ad on the internet in about ten seconds.
Last updated: May 4, 2026.
The one formula you need
APR (annual percentage rate) is the stated yearly rate. APY (annual percentage yield) is what you actually earn or pay once compounding is factored in. The bridge between them is:
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. That's it. Every APR-to-APY question on the internet reduces to plugging numbers into that one line.
Going the other direction is the same formula rearranged:
APR = n × ((1 + APY)1/n − 1)
A worked example: 6% APR, monthly compounding
Say a high-yield savings account advertises "6% APY" and a CD at the same bank lists "6% APR, compounded monthly." Are they the same? Let's work it out.
Divide the APR by the number of compounding periods:
0.06 / 12 = 0.005 (that's half a percent per month)
Add 1 and raise to the 12th power:
(1.005)12 = 1.06168
Subtract 1:
1.06168 − 1 = 0.06168
So a 6% APR with monthly compounding is a 6.17% APY. The savings account at 6% APY is actually the better deal by 0.17 percentage points, even though the sticker numbers look identical. On a $50,000 balance held for ten years, that difference is worth roughly $900 — not life-changing, but not nothing.
Why banks pick one over the other
Here's the tell: banks always quote whichever number makes them look better.
- Savings accounts, CDs, money market: APY. Compounding works in your favor here, so the bigger number is the honest one to advertise. The 2011 Truth in Savings Act actually requires APY on deposit products, so this one is also regulatory.
- Mortgages, auto loans, personal loans: APR. Compounding works against you, so the smaller number wins the ad. Regulation Z (the Truth in Lending Act) mandates APR disclosure on most consumer loans.
- Credit cards: APR — and this is where it gets sneaky.
Both numbers are mathematically honest. They just flatter the product being pitched. Once you see it, you can't unsee it: big APY on the billboard means they're selling, big APR means they're lending.
The credit-card trick
Credit cards state an APR. Almost all of them compound monthly (on the average daily balance, but the math is the same). That means the rate you actually pay on a revolving balance is always higher than the number on your statement.
Take a card with a 24% APR. The effective annual rate is:
(1 + 0.24/12)12 − 1 = (1.02)12 − 1
= 1.26824 − 1 = 0.26824
That's a 26.82% APY. Carrying a $5,000 balance for a year costs $1,341 in interest, not the $1,200 you'd estimate from the APR alone. The extra $141 is the compounding effect — the interest itself earning interest for the issuer while you sleep.
Go higher and it gets worse. A 29.99% APR card (common on subprime offers) actually charges a 34.49% APY. Nobody ever puts that number in the mailer.
What most people get wrong: 0% APR with deferred interest
This is the trap that catches smart people every holiday season. You walk into a furniture store or sign up for a medical-financing plan and see "0% APR for 12 months!" You think: free money, make the minimums, pay it off at month 11, no harm done.
Read the fine print. A huge number of these promos — especially on store cards, medical financing like CareCredit, and appliance retailers — use deferred interest, not true 0% APR. The difference is enormous.
With a real 0% APR offer, you pay no interest during the promo window, full stop. If a balance remains after, interest starts accruing from that date forward.
With deferred interest, interest is accumulating the entire time at the regular 25–30% APR — it's just waived if and only if you pay the full balance by the end date. Miss the deadline by a dollar, a day, a payment-processing delay, and that retroactive interest slams onto your account in one lump, calculated all the way back to the purchase date.
A real example: $3,000 of furniture on a "12 months no interest" card at 28.99% deferred. Pay $2,950 by the due date — still $50 outstanding — and you don't owe interest on the $50 going forward. You owe roughly $870 of backdated interest on the full $3,000, charged at the moment the promo expires. One day late. Call the card company and beg; sometimes they'll waive it once. Sometimes they won't.
Rule of thumb: if the offer says "no interest if paid in full by [date]," it's deferred interest. If it says "0% intro APR for X months," it's a true promo rate. The wording matters more than the percentage.
How to convert in your head
You won't always have a calculator. Two shortcuts that get you close:
- For APRs under about 10%: APY ≈ APR + (APR² / 2) when compounded monthly. A 6% APR: 6 + (0.36/2) = 6.18%. Actual is 6.17%. Close enough.
- For everything else: monthly compounding adds roughly APR/200 in percentage points for rates under 20%, and more as you climb. A 24% APR is about 2.8 points higher as APY; a 12% APR is about 0.7 points higher.
For anything involving real money, just run the exact formula on the financial calculator. The compounding key handles it in one keystroke.
When the two numbers are identical
APR equals APY in exactly one case: when interest compounds once per year (n = 1). Plug it in: (1 + r/1)1 − 1 = r. That's why some bonds and older savings vehicles that pay simple annual interest can quote either number without lying. Everything else — monthly, daily, continuously compounded — produces an APY higher than the APR.
Frequently asked questions
So which number should I compare when shopping?
Compare APY to APY, always. It's the apples-to-apples measure. If one bank quotes APR and the other quotes APY, convert the APR to APY using (1 + APR/n)^n − 1 and then compare. Don't let different advertising choices trick you into thinking two products have different rates when they don't.
Does daily compounding really beat monthly by much?
Not really. A 6% APR is 6.168% APY monthly and 6.183% APY daily. On a $10,000 balance over a year, that's $1.50 more with daily compounding. The difference between annual and monthly is what matters; past monthly, you're splitting hairs. Don't pick a savings account based on "daily compounding" marketing alone.
Why do mortgages list both APR and interest rate?
That's a different distinction. Mortgage APR includes fees (origination, points, certain closing costs) rolled into an annualized cost. The "interest rate" is just the note rate with no fees. APR on a mortgage is closer to the true cost of borrowing, which is why federal law requires it alongside the note rate.
Can I negotiate to have deferred interest removed if I miss the deadline?
Sometimes, if it's your first time and you were very close to paying it off. Call the issuer immediately, be polite, and ask for a courtesy waiver. Success rates are maybe 50/50 with major retailers, lower with medical-financing cards. The real lesson is to set a calendar alert two months before the promo ends and overpay by a small buffer to cover any weird processing timing.
Is there an APR/APY rule for continuous compounding?
Yes — as n goes to infinity, the formula becomes APY = eAPR − 1, where e ≈ 2.71828. A 6% APR continuously compounded is 6.184% APY, versus 6.168% monthly. The gain over daily compounding is microscopic, which is why almost no consumer product bothers with it. It shows up mostly in finance textbooks and some derivatives pricing.
Try it yourself
The easiest way to internalize this is to run your own numbers. Take whatever loan, card, or savings account you have in front of you right now, grab the APR off the statement, and convert it on the financial calculator. The gap between the number you were told and the number you're actually paying (or earning) is rarely small enough to ignore.
This article is for general education and is not financial advice. See our Terms.