--- title: "APR to APY Converter, Any Compounding | Honest Interest" description: "Convert APR to APY and back for daily, monthly, continuous or any compounding, with a table across every frequency and the Reg DD formula explained." url: https://honestinterest.bond/ --- Calculator 01 · Rates # APR to APY converter The APR is the rate on the label. The APY is what a year of compounding does with it. Enter either one, pick how often interest is added, and see both side by side at every frequency. **Educational use only — not financial advice.** The rate is whatever you type in; nothing here is an offer, a quote or a forecast. ## What the two numbers mean An **APR** (annual percentage rate) is a yearly rate before compounding. Divide it by the number of compounding periods and you get the rate added each period: 5% APR compounded monthly is 0.4167% a month. The **APY** (annual percentage yield) is what that does over a whole year once each period's interest starts earning interest of its own. APY = (1 + APR ÷ n)n − 1 continuous: APY = eAPR − 1 back again: APR = n × ((1 + APY)1/n − 1) **Worked example:** 0.05 ÷ 12 = 0.0041667, and 1.004166712 = 1.05116, so 5% APR compounded monthly is an APY of 5.116%. On $10,000 that is $511.62 in a year rather than $500. US savings accounts quote an APY because the Truth in Savings rules (Regulation DD) require it, worked out as APY = 100 × [(1 + interest ÷ principal)365 ÷ days in term − 1]. Loans and credit cards quote an APR under the Truth in Lending rules (Regulation Z). The same arithmetic runs in reverse on debt: a 22% card APR charged daily grows an unpaid balance by about 24.6% a year. ## Sources - Consumer Financial Protection Bureau, Regulation DD (Truth in Savings), [Appendix A to Part 1030 — Annual Percentage Yield Calculation](https://www.consumerfinance.gov/rules-policy/regulations/1030/a/): the APY formula and the 365-day term for accounts without a maturity. - Consumer Financial Protection Bureau, [Regulation Z (Truth in Lending), 12 CFR Part 1026](https://www.consumerfinance.gov/rules-policy/regulations/1026/): how APRs are disclosed on loans and credit cards. - U.S. Securities and Exchange Commission, Investor.gov, [Compound interest calculator](https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator). ## More entries in the book Four more calculators for the interest you earn and the interest you pay. 1. [Simple vs compound interest Two balances side by side, year by year, with a growth chart and the gap interest on interest makes.](https://honestinterest.bond/simple-vs-compound-interest/) 2. [Credit card payoff calculator Months and total interest at a fixed payment, or the payment that clears the card by a set month, with a full schedule.](https://honestinterest.bond/credit-card-payoff-calculator/) 3. [Minimum payment trap What paying only the minimum costs, compared with a fixed payment, and the warning box your statement shows.](https://honestinterest.bond/minimum-payment-calculator/) 4. [Buy now, pay later true cost Pay-in-4 and monthly plans with fees and late fees, the yearly rate those fees equal, and a card for comparison.](https://honestinterest.bond/buy-now-pay-later-calculator/) ## Recommended Two free services for the online side of comparing money products. 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[Try WebTraceCheck](https://webtracecheck.com/) ## Questions **Which number should I compare between savings accounts?** The APY. It already includes compounding, so accounts that add interest on different schedules can be compared directly. Comparing two APRs only works when both compound on the same schedule. **Does daily compounding make a big difference?** Less than you might expect at savings rates: 5% APR is 5.116% compounded monthly and 5.127% daily. The gap grows with the rate. At 22% the step from monthly (24.36%) to daily (24.60%) is about a quarter of a point. **What does continuous compounding mean?** Interest added in infinitely small steps. It is the mathematical ceiling for a given APR: APY = e^APR − 1, so 5% continuous gives 5.127%, a hair above daily. You meet it more in finance textbooks than on account statements. **Can an APY be lower than its APR?** No. With compounding once a year the two are equal, and more frequent compounding can only push the APY above the APR. If you see a lower APY than APR, check that both figures describe the same account and the same compounding.