LaTeX
EAR=\left(1+\frac{r}{m}\right)^m-1Variables
- r: nominal annual rate
- m: compounding periods per year
- EAR: effective annual rate
How to use this formula
Converts a nominal annual rate compounded m times into an effective annual rate.
Important notes
- The nominal rate convention must be known.
- Continuous compounding uses e^r−1.
Quick example
A 12% nominal rate compounded monthly has EAR=(1.01)^12−1.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The nominal rate convention must be known.
- For the Effective Annual Rate, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Match the interest rate to the compounding period, convert percentages to decimals, and keep cash-flow timing consistent.
Worked example
A 12% nominal rate compounded monthly has EAR=(1.01)^12−1.
Common mistakes
- When copying Effective Annual Rate, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Effective Annual Rate with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Effective Annual Rate in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
EAR=\left(1+\frac{r}{m}\right)^m-1. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Effective Annual Rate used for?
Converts a nominal annual rate compounded m times into an effective annual rate.
Can I copy this formula as LaTeX?
Yes. Copy EAR=\left(1+\frac{r}{m}\right)^m-1 or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.