Understanding 'e' in the Compound Interest Formula for Students

[d.smith292]

Homework Statement

Here is the problem that made me confused at first, now I'm just annoyed. I know I got the right answer for this problem as seen below, but I'm annoyed by the fact that no one has explained what the heck "e" is. Will someone please explain to me what exactly "e" is, so I can get past this issue I have. Even though I can figure out the answer, I can't stop thinking about it until I figure out what it is and where it came from. Thank you, who ever helps me with this problem.

After 15 years, there is $10,000 in an account that was compounded continuously at 6%. How much was in the account originally?

Homework Equations

A = Pe^rt

The Attempt at a Solution

I'm searching for P, so I set my equation up like this:

10000 = Pe^.06*15

Then I get:

10000 = Pe^.9

Which leads to:

10000 = P(2.459603111) "Sorry I like to be as precise as possible until the end"

Leaving:

P ≈ 4065.70

 

[Mark44]

http://en.wikipedia.org/wiki/E_(mathematical_constant)

 

[HallsofIvy]

Mark, when I go to that page, I see "Wikipedia does not have an article with this exact name".

d.smith292, "e" is the base of the "natural exponential" function. It is called "natural" because one can show by Calculus that the derivative (rate of change) of the function $f(x)= a^x$ is a constant times $a^x$ itself. It happens that the constant is 1 if a is a specific real number that happens to be approximately 2.718... That is, e is defined as the real number such that the derivative of e^x is just e^x itself.

 

[Mark44]

Mark, when I go to that page, I see "Wikipedia does not have an article with this exact name".

Thanks! I didn't get all of the URL -- the final parenthesis was missing. I've fixed it now.

 

[jey1234]

e is a number that comes up a lot. It's used for math, bio, finance , etc... You will probably see it in more depth when you learn calculus. For now e is just another constant like π. We assign it a letter because its decimals are non repetitive and non terminating. It's actually very cool when you think about how one particular number is so significant in various different fields.