The Limit That Defines e

Tap a term to see what it means, or .

Calculate

Example: $1 invested at 100% a year, with interest compounded n times a year. Compounding every month (n = 12), what does it grow to in a year? And if n kept growing? Change the value to work out your own case.

Compounding periods per year n

Step by step

What each term means

Euler's Number (e): The constant e ≈ 2.71828, base of the natural logarithm and of the exponential function. It shows up whenever something grows at a rate proportional to its own size.
Limit (n → ∞): The value the expression approaches as n grows without end. No finite n reaches e, but it can get as close as you like.
Compound Interest ((1 + 1/n)ⁿ): $1 at 100% a year, split into n compounding periods of 1/n each. More periods earn more, but less and less more each time: the total never passes e.