APR / APY Converter
Convert between APR (nominal annual rate) and APY (effective annual yield) for any compounding frequency: daily, monthly, quarterly, continuous.
APR / APY Converter
Convert between the two ways financial products quote rates. APR is the nominal annual rate (federally required by TILA); APY is the effective yield once compounding is included (federally required by TISA for deposit accounts). Same number, different compounding — the tool computes exactly what compounding frequency does to the gap.
APY at every compounding frequency (for the same APR)
| Frequency | n / year | APY |
|---|
How to Use the APR/APY Converter
Identify which rate you have
US loan products quote APR (Truth in Lending Act requirement). US deposit accounts quote APY (Truth in Savings Act requirement). Same underlying rate, different presentations.
Pick the compounding frequency
Daily for most US savings accounts and credit cards. Monthly for most US mortgages and personal loans. Quarterly for some CDs. Continuous (e^x) is the mathematical limit — rarely used in practice but useful as a theoretical reference.
Read the output
APY → APR direction is more common for savings shoppers comparing across accounts. APR → APY direction is more common for borrowers wanting to know the true cost of credit when interest compounds. The Δ shows the gap that compounding creates.
Use the frequency table to compare accounts
The table shows what the APY would be at every standard frequency for the same APR. Two savings accounts with the same APR can have different APYs — the one with daily compounding pays slightly more than monthly.
APR vs APY — The Two Numbers Behind Every Interest Rate
Nominal vs Effective — A Federally-Required Distinction
In US consumer finance, two federal disclosure regimes govern interest-rate quotes. The Truth in Lending Act (TILA, 1968) requires loan products to disclose APR (Annual Percentage Rate) — the nominal annual rate, plus most lender fees folded back in, expressed as a single comparable number. The Truth in Savings Act (TISA, 1991) requires deposit accounts (savings, checking, CDs, money market) to disclose APY (Annual Percentage Yield) — the effective annual yield once compounding is factored in. The two acts together force a transparent presentation, but they use different conventions: APR ignores compounding within the year; APY assumes compounding produces interest-on-interest.
The math: APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. At 5% APR with monthly compounding (n = 12), APY = 5.116%. With daily compounding (n = 365), APY = 5.127%. With continuous compounding (n → ∞), APY = e^0.05 − 1 = 5.127%. The gap between APR and APY widens as APR rises and as compounding frequency rises. At 20% APR with daily compounding, APY = 22.13% — a 2.13 percentage point premium that meaningfully changes the total cost of credit.
Which Number Should You Compare?
For deposit accounts (savings, CDs, money market): Compare APY. That's the effective yield you'll actually earn, which already factors in the bank's stated compounding frequency. Two accounts with the same APR but different compounding produce different APYs — the bank with daily compounding pays more than the bank with quarterly. The Truth in Savings Act requires banks to disclose APY prominently precisely so consumers can compare like-for-like.
For loans (mortgage, auto, personal): Compare APR. That's the federally-standardised cost-of-credit number that includes lender origination fees, points, and prepaid interest. Note that mortgage APR uses an annoying convention: APR doesn't include the compounding effect (so the true effective rate is slightly higher), but it does include lender fees amortised over the loan life. For shopping mortgages, APR is the right comparison; for understanding the actual cost over the long term, APY-style effective rate analysis is more accurate. Use our Loan Comparison Calculator for both views.
"At 20% APR with daily compounding, the APY is 22.13% — a 2.13 percentage point premium that adds USD 213 to a USD 10,000 balance every year. Compounding frequency matters more on high-rate products."
Continuous Compounding and the e^x Limit
As compounding frequency increases (annual → semi-annual → quarterly → monthly → daily → hourly → secondly), the APY approaches a mathematical ceiling: e^APR − 1, where e is Euler's constant (≈ 2.71828). This is "continuous compounding" and represents the theoretical limit of how much compounding can multiply a nominal rate. At 5% APR, the continuous APY is 5.127%, compared to 5.127% at daily compounding — the gap between daily and continuous is mathematically negligible.
Continuous compounding is rarely used in retail finance — daily is effectively the practical maximum. But it shows up in academic finance, derivatives pricing (Black-Scholes uses e^rt for continuous discount factors), and some specialised institutional products. For retail comparison shopping, daily compounding is the cap, and the APY-vs-APR gap is at its maximum at daily — which is why US savings accounts compete on daily compounding to advertise the highest APY against any given APR.
10 Facts About APR / APY
The Truth in Lending Act (1968) mandates APR disclosure on every US loan product. The Truth in Savings Act (1991) mandates APY for deposit accounts.
APY formula: (1 + APR/n)^n − 1, where n = number of compounding periods per year.
At 5% APR with daily compounding, APY = 5.127%. With monthly compounding, APY = 5.116%. The gap rises with APR.
Continuous compounding is the mathematical limit: APY = e^APR − 1. At 5% APR, APY = 5.127% (same as daily, rounded).
US credit cards compound daily — at 22.99% APR, the actual APY paid by carrying a balance is 25.83%.
US savings accounts typically compound daily and are required by TISA to advertise APY prominently.
US mortgages use monthly compounding — and APR by convention ignores intra-year compounding, slightly understating the effective cost.
EU consumer-credit law uses APRC (Annual Percentage Rate of Charge) which is the European equivalent of US APR — including most fees.
The Federal Reserve Regulation Z implements TILA, prescribing the exact APR calculation for every US consumer credit product.
At 20%+ APR, the APR-vs-APY gap exceeds 2 percentage points with daily compounding — making compounding frequency a real variable on high-rate products.
Frequently Asked Questions
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APR (Annual Percentage Rate) is the nominal annual rate — what's stated on the contract. APY (Annual Percentage Yield) is the effective rate once compounding within the year is factored in. APY is always equal to or greater than APR. The two are required by different US federal regimes: TILA for loans (APR), TISA for deposits (APY). The formula relating them: APY = (1 + APR/n)^n − 1, where n is the compounding periods per year.
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Always APY. The Truth in Savings Act requires US banks to disclose APY on every savings, checking, CD, and money market account precisely so consumers can compare like-for-like. APY already factors in the bank's stated compounding frequency, so two accounts with the same APY produce the same effective yield regardless of how often they compound. If you see APR on a deposit account, the bank is non-compliant or you're looking at a non-US product — ask for the APY.
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APR — but with a footnote. TILA requires APR to include most upfront lender fees (origination, points, discount fees) amortised over the loan life. That makes APR the better comparison metric than the note rate when shopping mortgages, auto loans, and personal loans. The footnote: APR by US convention ignores compounding within the year, so the actual effective rate (APY-style) is slightly higher than the disclosed APR. For credit cards specifically, the disclosed APR is your nominal rate, and the effective APY (which is what you actually pay if you carry a balance) is 1-3 percentage points higher due to daily compounding.
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Because interest accrued in earlier periods can itself earn interest in later periods — that's compounding. More frequent compounding means earlier interest gets more time to earn more interest. At 5% APR, monthly compounding produces 5.116% APY; daily compounding produces 5.127% APY. The gap is small at 5% but widens dramatically at high rates — at 25% APR with daily compounding, APY hits 28.39%. Compounding frequency is the lever that turns nominal rates into effective rates.
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Continuous compounding is the mathematical limit as compounding frequency approaches infinity. The formula simplifies to APY = e^APR − 1, where e is Euler's constant (≈ 2.71828). It produces the highest possible APY for any given APR. Continuous compounding is rarely used in retail finance (daily is the practical max), but shows up in derivatives pricing (Black-Scholes uses e^rt for continuous discount factors) and academic finance. For retail comparison shopping, daily compounding is effectively the cap.
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For US loan products under TILA, APR includes most upfront lender fees (origination, discount points, prepaid interest, mortgage insurance) amortised across the loan life. It excludes third-party fees the borrower could shop separately (title insurance, settlement, appraisal in some loan types). For US credit cards, APR is purely the interest rate — no fee amortisation. For US deposit accounts, APR (if quoted) and APY both exclude account-maintenance fees. Always read the disclosure tables — Section B and C of a mortgage Loan Estimate, for example, show fees that are not in APR.
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APRC (Annual Percentage Rate of Charge) under the EU Consumer Credit Directive (2008/48/EC) and the EU Mortgage Credit Directive (2014/17/EU). APRC includes most fees the borrower must pay to obtain the loan, amortised across the loan life, expressed as a single annual percentage. It's conceptually identical to US APR but the calculation can include slightly different fee categories. EU APRC and US APR are not strictly comparable across products, but both serve the same disclosure purpose: a single comparable cost-of-credit number.
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Daily compounding. US credit cards compound interest daily — at a 22.99% APR, the actual APY paid is 25.83%. So if you carry a USD 1,000 balance for a full year, you pay USD 258 in interest, not USD 230 (the naive APR-times-balance number). This is one of the highest-impact APR-to-APY conversions in personal finance, because card APRs are typically high (22-28%) where the compounding gap matters most. Use our Credit Card Minimum Payment Trap Calculator to see the full impact over time.
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Mostly aligned. Singapore's MAS requires Effective Interest Rate (EIR) disclosure on consumer credit products, which is conceptually identical to US APR with fee amortisation. Malaysia's BNM requires similar disclosure of Effective Lending Rate (ELR). Indonesia and Philippines have less developed disclosure regimes; some bank products there quote "flat rate" interest (computed on the original principal, not reducing balance) which can be misleading — a 6% flat-rate auto loan has an effective APR around 11-12%. If you're comparing offers across ASEAN and US markets, always confirm whether the rate is on reducing-balance (standard) or flat-rate (deceptive) basis before plugging into this tool.
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Convert both to USD-equivalent APY for like-for-like comparison. US high-yield savings accounts pay 4-5% APY in 2026 (compounded daily); Singapore equivalents pay around 3-4% APY (UOB One, OCBC 360, DBS Multiplier require bill-pay / salary-credit conditions to hit headline rates); Malaysian ringgit savings pay 2.5-3.5% effective. After accounting for currency-strengthening risk (USD has been strong vs SEA currencies recently), holding USD savings in US accounts often produces the highest USD-equivalent yield. Singapore SGD savings are a reasonable hedge if you plan to return to Singapore long-term. For straight yield maximisation, US T-bills or money-market funds at 5%+ are hard to beat in 2026.
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