Financial Math Peer-Reviewed & Code-Verified

The Mathematics of Compound Interest: Continuous vs. Periodic Compounding

An algebraic derivation of compounding formulas, the impact of compounding frequencies, and how continuous compounding relates to Euler's number (e).

OL
Osvaldo Luna
Last Updated: August 14, 2026 ⏱️ 8 min read

Periodic Compounding Formula

A = P (1 + r/n)nt

Continuous Compounding and Euler's Number (e)

Taking the limit as the frequency of compounding approaches infinity yields the continuous growth formula: A = P * e^(rt).

About the Author & Editorial Standards

OL

Osvaldo Luna

Lead Web Architecture & Software Security Specialist

Osvaldo Luna is a software engineer and web specialist with over 8 years of experience in high-performance client-side web applications, in-browser cryptography, and data privacy.

Have technical feedback or questions about this article? Reach out through our Contact Page.