Effective Annual Rate (EAR) Calculator
Compute the Effective Annual Rate (EAR) — true cost of borrowing including compounding. Compare loans with different compounding schedules.
Effective Annual Rate Calculator
The Effective Annual Rate (EAR) is the true cost of borrowing once compounding is factored in. Two loans with the same nominal APR can have different EARs depending on how often interest compounds. EAR is the right apples-to-apples comparison metric for loans with different compounding schedules.
Worked example — interest on a USD 10,000 / 1-year balance
EAR at every standard compounding frequency
| Frequency | n / year | EAR |
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How to Use the EAR Calculator
Find the nominal APR on your loan
Every US loan discloses APR per TILA. Mortgage Loan Estimates list it prominently; credit card statements show it as "Annual Percentage Rate"; auto loan contracts show it on the financing disclosure form.
Pick the compounding frequency
Mortgages typically compound monthly. Credit cards compound daily. Auto loans typically monthly. Bi-weekly mortgage programs (covered separately by some lenders) compound bi-weekly. Check the loan agreement.
Read the EAR vs APR gap
The compounding premium tells you how much higher the true effective rate is than the disclosed APR. At low rates (5-7%) the gap is small (5-15 bps). At credit-card rates (22-28%) the gap is meaningful (250-350 bps).
Use EAR to compare loans with different compounding
If you're comparing a 7.0% APR monthly-compounded loan vs a 6.95% APR daily-compounded loan, raw APRs say the second is cheaper. EAR proves it: 7.000% → 7.229% vs 6.950% → 7.196%. Daily wins by 3.3 bps annually.
Effective Annual Rate — Why the APR On Your Loan Isn't the Real Cost
The Hidden Mathematics of Compounding
The Annual Percentage Rate (APR) you see on a US loan disclosure is, by federal convention, a nominal rate — it doesn't include the compounding effect within the year. The Effective Annual Rate (EAR) is what you actually pay once you account for the fact that interest accrues on previously accrued interest. The formula is the same as for APY on savings accounts: EAR = (1 + i/n)^n − 1, where i is the nominal rate and n is the number of compounding periods per year. The difference is which side of the transaction you're on — EAR is the borrower's true cost; APY is the saver's true yield.
On a 6% APR mortgage with monthly compounding, the EAR is 6.168% — a 16.8 basis-point premium over the disclosed APR. On a 22.99% credit card APR with daily compounding, the EAR is 25.83% — a 284 basis-point premium. The gap widens with both the nominal rate and the compounding frequency. This is why credit cards specifically are far more expensive than they look: the daily compounding compounds 365 times per year on a high nominal rate, making the effective burden meaningfully higher than the headline APR suggests.
Where EAR Matters Most in Practice
Credit cards (daily compounding, high APR): EAR is consistently 250-350 bps above APR. If you carry balances regularly, the disclosed APR understates your true cost. Use EAR (or our Credit Card Min Payment Trap tool) for honest cost comparison.
Bi-weekly mortgages: Some US lenders offer bi-weekly payment programs that effectively compound the loan bi-weekly. At 7% APR, the bi-weekly EAR is 7.246% vs monthly EAR of 7.229% — a 1.7 bp difference that adds up over 30 years. Bi-weekly programs also typically include an extra payment per year (26 half-payments = 13 monthly equivalents), which is the real lifetime-interest reduction; the compounding-frequency angle is secondary.
CDs and savings accounts (where the rate works for you): The same math, but in your favour. A US high-yield savings account at 4.5% APR with daily compounding has APY of 4.603% — that's an extra USD 10.30 per USD 10,000 per year compared to monthly compounding. Compounding frequency is one of the levers banks compete on (alongside the headline rate) when chasing depositors.
"On a 22.99% credit card APR with daily compounding, the EAR is 25.83% — that's USD 284 extra per year per USD 10,000 balance, hidden in the gap between APR disclosure and true cost."
EAR vs APR vs APY — The Federal Disclosure Tangle
Three terms, three federal regimes, one underlying math. APR is required by the Truth in Lending Act (1968) on loan disclosures, but doesn't include compounding by US convention. APY is required by the Truth in Savings Act (1991) on deposit accounts, and does include compounding. EAR is the academic-finance term that's equivalent to APY when applied to loans — but it's not federally required on loan disclosures, so US borrowers rarely see it on documents.
The EU is more consistent: the Consumer Credit Directive (2008/48/EC) requires APRC (Annual Percentage Rate of Charge) on every consumer credit product, and APRC is computed using effective-rate methodology — closer to US EAR than US APR. EU borrowers therefore get a more honest cost number on day one. For US borrowers, using this calculator to compute EAR from the disclosed APR is the equivalent step.
10 Facts About Effective Rates
EAR formula: (1 + i/n)^n − 1, where i = nominal rate, n = compounding periods/year.
US credit cards compound daily — at 22.99% APR, the EAR is 25.83% (a 284 bps premium).
US mortgages compound monthly — at 7% APR, the EAR is 7.229% (only 23 bps premium).
The EAR gap widens with both nominal rate and compounding frequency — high-rate daily-compounded products have the biggest gap.
Continuous compounding (e^r − 1) is the mathematical ceiling — never used on US consumer loans but common in academic finance.
The EU Consumer Credit Directive requires APRC (effective-rate basis), so EU borrowers see EAR-equivalent numbers on disclosures by default.
US TILA (1968) requires APR (nominal). TISA (1991) requires APY (effective). EAR is neither — but mathematically identical to APY.
Bi-weekly mortgage payments save more from the extra-payment-per-year effect (26 half-payments = 13 monthly equivalents) than from the compounding-frequency change.
At 10% nominal rate, monthly EAR is 10.471%; daily EAR is 10.516% — a 4.5 bp difference, mostly negligible at mortgage-rate levels.
Quick approximation: EAR ≈ APR + (APR² / 24) for monthly compounding. At 7%, that's 7% + 49/24 ≈ 7.20% (actual 7.229%).
Frequently Asked Questions
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EAR is the true effective annual interest rate once compounding within the year is factored in. The formula EAR = (1 + i/n)^n − 1 — where i is the nominal rate and n is compounding periods per year — converts any nominal-with-compounding rate to a single annual effective rate. Two loans with the same nominal APR but different compounding frequencies have different EARs, and EAR is the right apples-to-apples comparison number.
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Mathematically identical. EAR is the term academic finance and loan-comparison contexts use; APY (Annual Percentage Yield) is the term US federal regulation requires on deposit accounts under the Truth in Savings Act. Both compute the same number from the same formula. Different audiences use different labels — borrowers comparing loans usually use EAR; savers comparing accounts usually use APY.
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TILA (Truth in Lending Act, 1968) requires APR disclosure — a nominal rate that includes most fees amortised across the loan life but ignores intra-year compounding by federal convention. EAR isn't federally mandated for US loan disclosures. The EU equivalent, APRC under the Consumer Credit Directive 2008/48/EC, uses effective-rate methodology — closer to EAR — so EU borrowers see a more honest number by default. For US borrowers, this tool converts the disclosed APR into EAR so you have the same transparency.
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Depends on the nominal rate and compounding frequency. At 5% APR with monthly compounding, EAR is 5.116% — a tiny 11.6 bp gap. At 25% APR with daily compounding, EAR is 28.39% — a meaningful 339 bp gap. The gap widens both with the rate and with the compounding frequency. Generally: at low rates with infrequent compounding, EAR ≈ APR. At high rates with frequent compounding, EAR can be 2-4 percentage points above APR.
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Because interest accrued in earlier periods accrues additional interest in later periods. With monthly compounding on a 12% loan, the first month's interest (1%) gets added to principal, and the second month's interest is computed on the new balance — so you pay interest on interest. With daily compounding, this happens 365 times per year instead of 12. More frequent compounding produces more interest-on-interest, raising the effective cost.
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For loans, less frequent compounding is cheaper to you. Monthly compounding produces a lower EAR than daily compounding for the same nominal APR — so two loan offers with the same APR but different compounding mean the monthly-compounded loan is the cheaper one. For savings, the opposite: you want more frequent compounding because it boosts your APY. Always read the fine print to find the compounding schedule, then run the EAR/APY comparison.
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Continuous compounding is the mathematical limit as n → ∞. The formula simplifies to EAR = e^APR − 1, where e ≈ 2.71828. It produces the highest possible EAR for any given APR. Continuous compounding is rarely used in retail finance — daily compounding is the practical maximum on US credit cards and savings accounts. But it shows up everywhere in academic finance and derivatives pricing (Black-Scholes uses continuous discounting). For retail comparison, treat daily as the cap.
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Yes, but mostly NOT because of compounding. The big saving from bi-weekly payment programs is the extra payment per year: 26 half-payments = 13 monthly-equivalent payments, vs 12 in a standard monthly schedule. That extra payment per year applied to principal saves substantial interest over a 30-year mortgage. The compounding-frequency angle (bi-weekly vs monthly) is real but small (~2 bps). If you can't enroll in a formal bi-weekly program, sending in 1/12 extra principal each month achieves nearly the same effect.
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Singapore's MAS requires Effective Interest Rate (EIR) disclosure on most consumer credit, which is the same concept as EAR. Malaysia's BNM requires Effective Lending Rate (ELR). Both are conceptually equivalent to US EAR and computed on the same formula. Indonesia and Philippines have less formal effective-rate disclosure — some bank products quote "flat rate" interest computed on the original principal rather than reducing balance, which can be 50-80% lower than the equivalent EAR. If you're comparing ASEAN-market offers, always convert flat-rate quotes to reducing-balance EAR before using this tool.
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Three things. First, US auto loan APRs are typically lower than ASEAN equivalents (5-8% vs 6-12%) but the same effective-rate math applies — compute EAR if you're comparing offers across geographies. Second, US auto loans use monthly compounding (standard), so the EAR-vs-APR gap is small. Third, US credit unions typically offer 0.5-1.5pp lower APRs than commercial banks, and EAR-based comparison makes that gap even more favourable to credit unions. If you have <2 years US credit, dealer financing is usually significantly worse than what HSBC, Citi, or credit unions specialising in newcomer/expat lending will offer — always pre-shop before the dealer.
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