The first time I tried to compare two credit card offers I got confused for a different reason than I expected. One card advertised “19.99% APR.” The other advertised “APY equivalent of 22.13%.” They were describing the same effective interest rate. The terms aren't synonyms, and which one a financial product chooses to display is a deliberate marketing decision: lenders quote APR (the smaller number), savings institutions quote APY (the bigger number), and the difference is real money either way.
This guide explains what APR and APY actually mean, when each is appropriate to quote, and the formula to convert between them. Most importantly, it shows why the difference matters in real-world decisions — credit cards, mortgages, savings accounts, and bond yields.
The definitions, in plain language
APR (Annual Percentage Rate): the simple annual interest rate without considering how often interest compounds. If a credit card has a 24% APR and you carry a balance, the APR is the headline number, but the actual cost depends on how often the issuer compounds (usually daily).
APY (Annual Percentage Yield):the actual annual return after accounting for compounding. APY is the “what does this turn into after one year” number. If you put $10,000 in an account with 5% APY, after one year you have $10,500 regardless of how the bank chose to compound.
The difference between the two is compounding. APR tells you the rate per period × the number of periods. APY tells you the actual ending balance after those compoundings happen. APY ≥ APR always; the gap grows as compounding frequency rises.
The conversion formula
For a given APR (r) and number of compounding periods per year (n):
APY = (1 + r/n)^n − 1
Some worked examples:
- 5% APR, compounded annually (n=1): APY = 5.00%. (No difference — only one compounding event per year.)
- 5% APR, compounded monthly (n=12): APY = 5.116%.
- 5% APR, compounded daily (n=365): APY = 5.127%.
- 5% APR, compounded continuously:APY = e^0.05 − 1 = 5.127%. (At daily compounding you're already very close to the continuous limit.)
For most consumer products you'll see, daily compounding is the norm, and APY is roughly APR × 1.025 for typical rates. The gap widens at higher rates: a 24% APR credit card with daily compounding has an APY of 27.1% — meaningfully higher than the headline.
Why credit cards advertise APR
Credit card issuers have been required by Truth in Lending Act regulations since 1968 to quote APR rather than APY. The regulatory choice was about standardization — APR is comparable across products without further math — but the practical effect is that APR makes the rate look smaller than what you actually pay.
On a card carrying a $5,000 balance:
- 22.99% APR sounds like roughly $1,150/year of interest.
- The actual cost, with daily compounding, is about $1,294/year.
- The extra $144/year is the compounding gap.
For very small balances paid off quickly, the gap is trivial. For revolving balances over years, the compounding gap is the difference between the advertised cost and the real cost.
Why savings accounts advertise APY
The flip side: when a high-yield savings account (HYSA) wants to advertise a yield, they show APY because it's the bigger number. The TILA equivalent for deposit accounts is the Truth in Savings Act, which requires APY for disclosure.
A 5% APY at one bank versus “5% interest” at another bank is not a fair comparison. The first is the actual yield. The second could be a 5% APR compounded monthly, which is only 5.12% APY — slightly worse. When comparing savings accounts, always compare APY to APY.
Mortgages: APR is more useful than the rate alone
For mortgages, the headline “rate” (e.g., 6.75%) is the contract interest rate. But mortgages also have origination fees, points, mortgage insurance, and other closing costs. The “APR” on a mortgage is a modified rate that accounts for some of those costs spread over the loan's life. It's your best apples-to-apples comparison number when comparing two lenders' offers.
Example: Lender A offers 6.50% rate, $5,000 origination, 0.5 points. Lender B offers 6.75% rate, $0 origination, 0 points. Same loan amount, same term. Lender A's headline rate is lower, but their APR (which spreads the $5,000 + points over the loan life) might be 6.65% — still better than B's 6.78% APR but by less than the rate-alone comparison suggested. The APR difference is what to compare. (Even better: compute the breakeven horizon for paying points using our mortgage calculator.)
Why the gap matters more at higher rates
The compounding gap (APY − APR) scales nonlinearly with the rate. At low rates, the gap is small. At high rates, it's large:
- 3% APR daily compounded → 3.05% APY (gap: 5 bps)
- 5% APR daily compounded → 5.13% APY (gap: 13 bps)
- 10% APR daily compounded → 10.52% APY (gap: 52 bps)
- 20% APR daily compounded → 22.13% APY (gap: 213 bps)
- 24% APR daily compounded → 27.10% APY (gap: 310 bps)
For low-rate products (mortgages, low-rate auto loans, savings accounts), the gap is small enough that APR and APY tell roughly the same story. For high-rate products (credit cards, payday loans, some buy-now-pay-later products), the gap is large enough that the headline rate substantially understates the cost of carrying a balance.
The compounding frequencies you'll encounter
- Continuous — a mathematical ideal; some bonds are priced against this. APY = e^r − 1.
- Daily — credit cards, most HYSAs, money market funds. Very close to continuous in practice.
- Monthly — many mortgages, some savings accounts. Slightly lower APY than daily for the same nominal rate.
- Quarterly — some bonds, some CDs.
- Semi-annually — most US Treasury notes/bonds.
- Annually — some longer-term CDs, some structured products. APY = APR exactly.
Real-world comparisons that matter
Credit card debt
A 24% APR credit card with daily compounding has an APY of 27.10%. Carrying $10,000 for a year costs $2,710 in interest, not the $2,400 the headline rate suggests. The extra $310 is the compounding effect — small in any single month but real over a year.
Savings accounts vs CDs
HYSA quoted at 4.50% APY versus a 12-month CD quoted at 4.55% APR (compounded monthly): the CD's APY works out to ~4.65%. The CD wins by 15 bps in yield in exchange for losing liquidity. For an emergency fund, the liquidity of the HYSA usually matters more than the 15 bps. For known-future cash (e.g., money you'll need in exactly 12 months for a wedding), the CD's extra yield is free money.
Bonds
Bond yields are often quoted as “yield to maturity” (YTM), which is essentially an APR with a specific compounding convention (usually semi-annual for US Treasuries). Bond Equivalent Yield (BEY) and Effective Annual Yield (EAY) are different conventions; the latter is essentially APY. When comparing a bond to a savings account, convert both to the same convention before comparing.
The math you can do in your head
For most consumer-rate questions, daily compounding adds about r²/2 to the APR to get APY (roughly, for r between 0% and 30%). So:
- 10% APR → ~10% + 0.50% = ~10.50% APY (actual: 10.52%)
- 20% APR → ~20% + 2% = ~22% APY (actual: 22.13%)
- 5% APR → ~5% + 0.125% = ~5.13% APY (actual: 5.13%)
This rule-of-thumb gets you within 10–20 basis points and is good enough for quick mental comparisons. For exact comparisons, run the formula or use our calculator.
Common mistakes
- Comparing APR to APY directly. APR is always smaller, so this comparison always favors the lender quoting APR. Convert one to match the other.
- Ignoring compounding frequency. Two products with the same nominal rate compound at different frequencies have different effective yields.
- Treating mortgage APR as the rate. Mortgage APR includes fees and is higher than the contract rate. The contract rate determines your monthly payment; the APR determines your apples-to-apples cost comparison across lenders.
- Confusing nominal rate with the “periodic rate.”Periodic rate is APR ÷ n. A 12% APR card has a 1% monthly periodic rate, not 12%. The 12% is the annualized number.
- Forgetting that introductory rates expire. A 0% APR promotional card becomes a 24% APR card after 12 or 18 months. Plan for the real rate, not the teaser.
Tools that help
- Compound interest calculator — shows how different compounding frequencies change end balances
- Loan calculator— see total interest cost over a loan's life at any rate
- Mortgage calculator — total interest over 30 years at the contract rate
- Investment calculator — what regular contributions plus compound growth produce over time
Final thought
APR and APY are the same idea expressed in two different ways. The choice of which one a product advertises is almost always the one that makes the rate look more favorable to the issuer. Knowing the formula and how to convert between them is one of the simplest, most-used pieces of financial literacy. Once you internalize it, you stop being surprised by the difference between the headline rate and the bottom-line cost.