Effective Annual Rate Calculator

Convert nominal APR to EAR with daily, monthly, quarterly, semi-annual, and continuous compounding. Compare frequencies, calculate real rate after inflation, and find equivalent nominal rates.

Effective Annual Rate (EAR)
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Difference from Nominal —
Effective Monthly Rate —
Extended More scenarios, charts & detailed breakdown ▾
EAR
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vs Nominal —
Professional Full parameters & maximum detail ▾

Effective Rates

Effective Annual Rate (EAR) —
EAR Including Fees —
Real EAR (after inflation) —

Equivalent Rate Conversion

Equivalent Nominal Rate at Target Freq —

Dollar Impact

Annual Interest on Principal —

How to Use This Calculator

  1. Enter the nominal interest rate and select the compounding frequency to instantly see the EAR.
  2. Use Compare Compounding to see EAR at all frequencies for the same nominal rate.
  3. Use Continuous to find the theoretical maximum EAR.
  4. The Professional tier adds fee-adjusted EAR, real rate after inflation, and equivalent nominal rate conversion.

Formula

EAR = (1 + r/n)^n − 1
Continuous EAR = e^r − 1
Real EAR = (1 + EAR) / (1 + Inflation) − 1
where r = nominal rate, n = compounding periods per year

Example

Example: 6% nominal rate, monthly compounding. EAR = (1 + 0.06/12)^12 − 1 = 6.168%. Daily = 6.183%. Continuous = 6.184%. Real EAR at 3% inflation = 3.076%.

Frequently Asked Questions

  • APR (Annual Percentage Rate) is the nominal rate before compounding effects. EAR (Effective Annual Rate) is the actual rate earned or paid after accounting for compounding within the year. For example, 6% APR compounded monthly = 6.168% EAR.
  • The more frequently interest compounds, the higher the effective rate. Daily compounding produces slightly more than monthly, which produces more than annual. For a 6% nominal rate: annual = 6.000%, monthly = 6.168%, daily = 6.183%.
  • Continuous compounding is the theoretical limit of increasing compounding frequency to infinity. The EAR formula is e^r − 1. For a 6% nominal rate, continuously compounded EAR = 6.184%. It's used in options pricing and academic finance.
  • Use EAR when comparing products with different compounding frequencies — it gives an apples-to-apples comparison. APR is the legal disclosure standard in the US for loans. For savings accounts and CDs, look for APY (which equals EAR).
  • Fees increase the effective cost of borrowing. The Professional tier adds annual fees to the interest to show the true EAR including fees, which can be significantly higher than the stated APR for small loans with flat fees.

Related Calculators

📋 APR Calculator 📈 Compound Interest Calculator 💰 Interest Calculator 🏦 CD Calculator
Sources & References (5) ▾
  1. CFPB — APR vs. Interest Rate — Consumer Financial Protection Bureau
  2. Federal Reserve — Selected Interest Rates (H.15) — Federal Reserve
  3. FDIC — Deposit Account Interest and APY — Federal Deposit Insurance Corporation
  4. Truth in Lending Act (Regulation Z) — APR Calculation Rules — Consumer Financial Protection Bureau
  5. FINRA — Understanding APY and Effective Annual Rate — Financial Industry Regulatory Authority