What Is Continuous Compound Interest?
Continuous compounding calculates interest as if it compounds an infinite number of times per year. It uses Euler's number (e ≈ 2.71828) in the formula A = Pe^(rt). This produces the maximum possible return for a given rate and time period. While no bank compounds truly continuously, it represents the theoretical upper limit of compound growth.
The Formula Explained
A = Pe^(rt) where A is the final amount, P is the principal, e is Euler's number (≈2.71828), r is the annual interest rate as a decimal, and t is time in years. For example, $10,000 at 6% for 10 years: A = 10000 × e^(0.06×10) = 10000 × e^0.6 = $18,221.19.
Continuous vs Discrete Compounding
The difference between continuous and daily compounding is small but real. On $10,000 at 6% for 10 years: daily compounding yields $18,220.44 while continuous yields $18,221.19 — a difference of $0.75. The gap grows with higher rates and longer periods.
When to Use This Calculator
Use continuous compounding when analyzing theoretical growth models, comparing investment scenarios, studying financial mathematics, or evaluating instruments that advertise continuous compounding rates. It's also useful in options pricing models like Black-Scholes.