Growing Money
The Price of Money
When you borrow money, you get charged a yearly percent of the amount you owe (the decimal interest rate r), and you get charged that interest maybe every day, week, or month. This is how often you compound interest (n times per year).
e's Interest in Money
To determine the amount you owe after t years just multiply how much you borrowed by (1+r/n)nt. Now this is where e comes in. If you let how often you calculate and add in the interest to the loan become so frequent that you are doing it all the time, you end up with something called continuously compounded interest.
This is what banks use when you take out a loan of money. Bernoulli found that if you let n go all the way to infinity, that formula above becomes simply ert.
So for example, if you earned a yearly interest rate r of 100% (ie double your money) and you wanted to continuously compound that interest all day and every day for that year, you would end up with e times what you started with.