I understand the continuously compound interest formula and I've seen the proof that relates it to e but what I don't understand is how could someone think that e and $(1+1/n)^n$ are related? What is the intuition behind it?
2026-03-13 13:47:49.1773409669
How does the constant e relate to continuously compound interest?
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Assuming you've seen the actual proof, a good intuition for why $e$ and compound interest should be related comes from one of the most important properties that makes $e$ a special number: the fact the value of $e^t$ at a given $t = t_0$ is exactly the slope of the curve $e^t$ at $t = t_0$.
To get the intuition, consider what happens if, starting with $x(0) = 1\$$, you have a compound rate of $1$ with a given frequency of compounding $n$. What should happen when your frequency of compounding increases indefinitely? In other words, if you adjust the slope of $x(t)$ every time $x(t)$ changes, how should you adjust it?