LaTeX
A=Pe^{rt}Variables
- A: final amount
- P: initial principal
- r: annual rate as a decimal
- t: time in years
How to use this formula
Models continuously compounded growth of a principal amount.
Important notes
- The rate and time units must match.
- Real financial products may include fees and discrete posting rules.
Quick example
At P=1000, r=0.05, t=2, A≈1105.17.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The rate and time units must match.
- Map every symbol to the modeled quantity and verify units, domain restrictions, and simplifying assumptions.
Worked example
At P=1000, r=0.05, t=2, A≈1105.17.
Common mistakes
- Before substituting values into Continuous Compound Interest, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Verify the result of Continuous Compound Interest with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Continuous Compound Interest 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
A=Pe^{rt}. - 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
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Continuous Compound Interest used for?
Models continuously compounded growth of a principal amount.
Can I copy this formula as LaTeX?
Yes. Copy A=Pe^{rt} 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.