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Effective Annual Rate
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Sources & Methodology
Calculations use the standard EAR formula from CFA Institute curriculum and the Fisher equation as defined by the Federal Reserve's monetary policy framework.
Federal Reserve — Nominal and Real Interest Rates
Federal Reserve framework for nominal vs real interest rate relationships and Fisher equation methodology
CFA Institute — Fixed Income & Interest Rate Analysis
Standard formulas for EAR, nominal rate conversion, and compounding frequency analysis
Methodology: EAR = (1 + r/n)^n − 1 where r = nominal rate, n = compounding periods/year. Continuous: EAR = e^r − 1. Nominal from EAR: r = n[(1+EAR)^(1/n) − 1]. Real rate (Fisher): real = (1+nominal)/(1+inflation) − 1. Approximate Fisher: real ≈ nominal − inflation. All outputs rounded to 4 decimal places.
⏱ Last reviewed: April 2026
How to Calculate Nominal and Effective Interest Rates
The nominal interest rate is the advertised annual rate — the number you see on a loan offer or savings account. The effective annual rate (EAR) is the actual rate you earn or pay after accounting for compounding within the year. When compounding occurs more than once per year, EAR is always higher than the nominal rate.
Core Formulas
EAR = (1 + r/n)^n − 1
r = nominal rate (as decimal) | n = compounding periods per year
Example: 12% nominal, monthly compounding
EAR = (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 = 12.68%
Example: 12% nominal, monthly compounding
EAR = (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 = 12.68%
Real Rate = (1 + nominal) / (1 + inflation) − 1
Fisher Equation — exact form
Example: 7% nominal, 3% inflation
Real = (1.07 / 1.03) − 1 = 1.03883 − 1 = 3.88% real return
Example: 7% nominal, 3% inflation
Real = (1.07 / 1.03) − 1 = 1.03883 − 1 = 3.88% real return
Impact of Compounding Frequency — 12% Nominal Rate
| Compounding | Periods/yr | EAR | Difference from Nominal |
|---|---|---|---|
| Annual | 1 | 12.00% | +0.00% |
| Semi-annual | 2 | 12.36% | +0.36% |
| Quarterly | 4 | 12.55% | +0.55% |
| Monthly | 12 | 12.68% | +0.68% |
| Daily | 365 | 12.75% | +0.75% |
| Continuous | ∞ | 12.75% | +0.75% |
APR vs APY — Why Lenders and Banks Use Different Rates
Banks strategically choose which rate to advertise. For savings accounts, they advertise APY (Annual Percentage Yield) — the EAR — because it looks more attractive than APR. For loans and credit cards, they advertise APR (Annual Percentage Rate) — the nominal rate — because it looks lower than the actual effective rate. This is why a credit card with "24% APR" compounded monthly actually has an EAR of 26.82%, not 24%. Always compare like with like: APY to APY, APR to APR.
💡 Quick Reference: For a 6% nominal rate, monthly compounding gives EAR of 6.168%. For 8%: EAR = 8.300%. For 10%: EAR = 10.471%. For 24% (credit card): EAR = 26.824%. The higher the nominal rate, the bigger the gap between nominal and EAR. This is why comparing APR on high-interest debt is so important.
Frequently Asked Questions
The nominal rate is the stated annual interest rate before adjusting for compounding frequency or inflation. It is also called APR (Annual Percentage Rate) for loans. A 24% APR credit card has a 24% nominal rate, but with monthly compounding the effective rate (EAR) is 26.82% — noticeably higher.
Nominal is the stated rate (APR). Effective (EAR/APY) accounts for compounding within the year. They are equal only with annual compounding. With monthly compounding, 12% nominal = 12.68% EAR. The more frequent the compounding, the larger the gap between nominal and effective rate.
EAR = (1 + nominal/n)^n − 1, where n = compounding periods per year. For 12% monthly: EAR = (1 + 0.12/12)^12 − 1 = 12.68%. For daily: EAR = (1 + 0.12/365)^365 − 1 = 12.75%. For continuous: EAR = e^0.12 − 1 = 12.75%.
APR (Annual Percentage Rate) = nominal rate, used on loan advertisements. APY (Annual Percentage Yield) = effective annual rate, used on savings account advertisements. Banks use APY for savings (makes rate look higher) and APR for loans (makes rate look lower). For true comparison, convert everything to EAR/APY.
The real rate adjusts nominal for inflation: real = (1+nominal)/(1+inflation) − 1 (Fisher equation). Approximate: real ≈ nominal − inflation. If a savings account pays 5% and inflation is 3%, real return ≈ 2%. The real rate shows purchasing power gained or lost, not just the dollar return.
More frequent compounding increases EAR above the nominal rate. At 12% nominal: annual = 12.00%, monthly = 12.68%, daily = 12.75%, continuous = 12.75%. The difference grows with higher rates — at 24% nominal, monthly compounding gives EAR of 26.82%, a 2.82 percentage point gap.
Continuous compounding is the mathematical limit of compounding infinitely many times per year. EAR = e^r − 1, where e = 2.71828. For 12% nominal: EAR = e^0.12 − 1 = 12.749%. This is the theoretical maximum effective rate for a given nominal rate, representing the upper bound of any compounding frequency.
In 2026, competitive high-yield savings accounts offer 4%–5% APY. Traditional bank savings accounts often offer under 0.50%. Money market accounts and CDs range from 4%–5.5%. The federal funds rate strongly influences savings rates — when the Fed rate is elevated, savings rates generally follow.
Nominal from EAR: nominal = n × [(1+EAR)^(1/n) − 1]. Nominal from real: nominal = (1+real) × (1+inflation) − 1. EAR from nominal: EAR = (1+nominal/n)^n − 1. All formulas use rates as decimals (e.g., 12% = 0.12).
The Fed sets the nominal federal funds rate (the headline number). But economic decisions respond to real rates — borrowing costs after inflation. When inflation is high, the Fed raises nominal rates aggressively to ensure real rates stay positive, discouraging excess borrowing. When inflation is low, even modest nominal rates can represent high real rates.
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