Algebra/Natural Logarithms and e

A special form of logarithms, called natural logarithms, use a constant number known as e, which is approximately 2.718. Like pi, this number appears in many real-life situations, and will be used from algebra through calculus. For now, think of it as

$e=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\cdots$

The exclamation point stands for the factorial of the number.

Compound Interest

Interest earned on a savings account usually compounds, meaning that if you put $100 in an account that compounds at 5% yearly, after one year you would get $100 * 1.05 = $105, but next year you would get $105 * 1.05 = $110.25. Although 25 cents seems trivial, when millions of dollars are invested, this adds up.

How about if 5% yearly interest were compounded monthly? Weekly? Daily? Continuously? It turns out that 5% interest on a continuously compounding investment of $100 makes 105 * e^x dollars, where x is the number of years passed. If you continue learning math until Calculus, you will eventually see more characteristics of e. Template:Subject