What You ACTUALLY Pay or Earn
EAR reveals the true annual interest rate when compounding is factored in. Banks advertise 22.99% APR on credit cards, but you pay 25.67% because interest compounds daily. That 2.68% gap costs $267 per $10K annually.
Why This Matters for Your Finances
Why: APR is the nominal rate lenders advertise; EAR is what you actually pay. Credit cards compound daily, so a 22.99% APR becomes 25.67% EAR. Mortgages compound monthly — 6.5% APR becomes 6.70% EAR. Always convert to EAR when comparing loan offers.
How: Enter the nominal rate (APR), select compounding frequency (daily for credit cards, monthly for mortgages), and optionally add principal to see dollar impact. Click examples to load credit card, mortgage, or savings scenarios.
- ●22.99% APR credit card compounded daily = 25.67% EAR — you pay 2.68% more than advertised.
- ●6.5% mortgage APR monthly = 6.70% EAR. The gap widens with more frequent compounding.
- ●For savings, APY = EAR — banks already reflect compounding in APY.
- ●Continuous compounding (e^r - 1) is the mathematical limit — highest possible EAR for a given nominal rate.
🏦 Sample Scenarios — Click to Load
EAR vs APR Comparison
Compounding Frequency Impact
Growth at Different Frequencies
APR-EAR Gap
⚠️For educational purposes only — not financial advice. Consult a qualified advisor before making decisions.
💡 Money Facts
22.99% APR credit card compounded daily = 25.67% EAR. $267 extra per $10K annually.
— CFPB
6.5% mortgage APR monthly = 6.70% EAR. Small gap, but compounds over 30 years.
— Federal Reserve
For savings, APY already IS the EAR. Banks use APY because it shows the higher rate.
— FDIC
6% nominal: annual=6%, monthly=6.17%, daily=6.18%. More compounding = higher EAR.
— Truth in Lending Act
The Effective Annual Rate reveals what you ACTUALLY pay or earn — banks advertise 22.99% APR on credit cards but you actually pay 25.67% because interest compounds daily. The difference? $267 more per $10,000 annually. The Truth in Lending Act requires APR disclosure, but EAR tells the real story. This calculator converts any APR to its true effective rate.
EAR vs APR: The Key Difference
APR (Annual Percentage Rate) is the nominal rate—what lenders advertise. EAR (Effective Annual Rate) is the actual rate after compounding. Credit cards compound daily, so a 22.99% APR becomes 25.67% EAR. Mortgages compound monthly, so 6.5% APR becomes 6.70% EAR.
How Compounding Frequency Affects EAR
More frequent compounding = higher EAR. Annual compounding: 6% stays 6%. Monthly: 6% becomes 6.17%. Daily: 6% becomes 6.18%. Continuous compounding (e^r - 1) is the mathematical limit—the highest possible EAR for a given nominal rate.
EAR for Credit Cards
Credit cards typically compound daily. A 22.99% APR compounded daily = 25.67% EAR. You pay 2.68% more than advertised. On a $10,000 balance, that's about $267 extra per year. Always convert APR to EAR when comparing credit card offers.
EAR for Savings Accounts
For savings, APY (Annual Percentage Yield) = EAR. Banks use APY because it already reflects compounding and shows the higher rate. A 5.00% APY = 5.00% EAR. Use APY/EAR to compare savings products.
Continuous Compounding EAR
Continuous compounding uses EAR = e^r - 1. A 10% nominal rate = 10.52% EAR. It represents the theoretical maximum—interest compounded infinitely many times per year. Used in finance for options pricing and certain investments.
EAR Formulas
Regular compounding: EAR = (1 + r/n)^n - 1, where r = nominal rate (decimal), n = compounding periods per year.
Continuous: EAR = e^r - 1, where e ≈ 2.71828.
When to Use EAR
- Comparing credit cards with different compounding frequencies
- Evaluating loan offers (mortgage, auto, student)
- Comparing savings accounts and CDs
- Investment return analysis
Frequently Asked Questions
What is the Effective Annual Rate (EAR)?
The Effective Annual Rate is the true annual interest rate you pay or earn when compounding is factored in. Unlike APR (nominal rate), EAR accounts for how often interest compounds—daily, monthly, etc. A 22.99% APR credit card compounded daily has a 25.67% EAR, meaning you pay 2.68% more than advertised.
What is the difference between EAR and APR?
APR (Annual Percentage Rate) is the stated nominal rate before compounding. EAR (Effective Annual Rate) is the actual rate after compounding. APR is required by the Truth in Lending Act for disclosure, but EAR shows the real cost. For credit cards with daily compounding, EAR is always higher than APR.
How does compounding frequency impact EAR?
More frequent compounding increases EAR. A 6% nominal rate compounded annually = 6% EAR, but compounded monthly = 6.17% EAR, and compounded daily = 6.18% EAR. Continuous compounding (e^r - 1) represents the mathematical limit—the highest possible EAR for a given nominal rate.
What is EAR for credit cards?
Credit cards typically compound interest daily. A 22.99% APR compounded daily becomes 25.67% EAR—you pay 2.68% more than the advertised rate. On a $10,000 balance, that's about $267 extra per year. Always convert APR to EAR when comparing credit card offers.
What is EAR for savings accounts?
For savings accounts, APY (Annual Percentage Yield) is the same as EAR—it already reflects compounding. A 5.00% APY = 5.00% EAR. Banks use APY for deposits because it shows the higher, more attractive rate. Use EAR/APY to compare savings products.
What is continuous compounding EAR?
Continuous compounding uses the formula EAR = e^r - 1, where e ≈ 2.71828 and r is the nominal rate in decimal form. A 10% nominal rate with continuous compounding = 10.52% EAR. It represents the theoretical maximum—interest compounded infinitely many times per year.