Compound Interest Intuition

Let’s talk about a different way to arrive at the equation for continuously compounded interest; a way that doesn’t explicitly evaluate \lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}. We’ll do this by writing an equation that relates the current amount of money you have to the amount you should have in the future after earning interest (it’ll actually be a differential equation.)/


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