LaTeX
CAGR=\left(\frac{V_f}{V_i}\right)^{1/n}-1Variables
- V_i: initial value
- V_f: final value
- n: years
How to use this formula
Finds the constant annual growth rate connecting an initial and final value.
Important notes
- CAGR hides volatility between endpoints.
- Both values should be positive for the standard real-valued formula.
Quick example
Growth from 100 to 121 in two years gives 10% CAGR.
Applicability, worked calculation, and verification
Assumptions and domain checks
- CAGR hides volatility between endpoints.
- For the Compound Annual Growth 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
Growth from 100 to 121 in two years gives 10% CAGR.
Common mistakes
- When copying Compound Annual Growth Rate, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Compound Annual Growth Rate with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Compound Annual Growth 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
CAGR=\left(\frac{V_f}{V_i}\right)^{1/n}-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 Compound Annual Growth Rate used for?
Finds the constant annual growth rate connecting an initial and final value.
Can I copy this formula as LaTeX?
Yes. Copy CAGR=\left(\frac{V_f}{V_i}\right)^{1/n}-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.