I keep seeing "e", can you explain what is it, and what is it for?

Question

I keep seeing "e", can you explain what is it, and what  is it for?

anonymous · Answer

$$e = \lim_{n \rightarrow \infty} (1 + \frac{1}{n})^n$$

solomonzelman · Answer

Infinite limits.... what is e and n in this expression.
I know it is limited to infinity, or unlimited.

anonymous · Answer

e is the thing I'm defining, since you asked what it was! :D
n is going to infinity.

solomonzelman · Answer

n is the limit, right?

anonymous · Answer

I don't quite understand what you're asking. Rephrase?

solomonzelman · Answer

Can you explain what is the n in this equation?

anonymous · Answer

n is the value that is approaching infinity

anonymous · Answer

I can't say $(1 + \frac{1}{\infty})^{\infty}$ because you can't actually compute that. So the form I wrote is used.

anonymous · Answer

Do you know the interest formula?

anonymous · Answer

Consider a loan with an annual interest rate $r$ and a principle $P_0$. 
After $t$ years the new amount $P_t$ is$$
P_t=P_0(1+r)^t
$$

anonymous · Answer

compounding interest.

solomonzelman · Answer

I did it last year, but totally forgot.

anonymous · Answer

Suppose instead of compounding yearly, it compounded monthly.
Then the monthly interest rate is $r/12$ and the number of times it compounds after $t$ years is $12t$.$$
P_t=P_0\left(1+\frac r{12}\right)^{12t}
$$

anonymous · Answer

Pert!

solomonzelman · Answer

P w/ a little t is the total

r is the difference or ration.

solomonzelman · Answer

what is P zero?

anonymous · Answer

the initial principle

anonymous · Answer

Can you follow so far?

solomonzelman · Answer

The initial amount of $ he/you/I  has/have?

anonymous · Answer

Yes

solomonzelman · Answer

yes, good!

anonymous · Answer

The initial amount of the loan, or account

solomonzelman · Answer

yep!

anonymous · Answer

Suppose it compounds every day: $$
P_t=P_0\left(1+\frac r{365}\right)^{365t}
$$

solomonzelman · Answer

can you explain the fraction of  r over 365
(I know what the r is)

anonymous · Answer

Suppose it compounds $n$ times: $$
P_t=P_0\left(1+\frac{r}{n}\right)^{nt}
$$

solomonzelman · Answer

OK

anonymous · Answer

The yearly rate is $r$ so the daily rate is $r/365$

solomonzelman · Answer

and why is it to the power of nt

anonymous · Answer

Because after a year it has compounded $n$ times.

anonymous · Answer

It compounds $nt$ times.

solomonzelman · Answer

I can see that....

anonymous · Answer

So you follow so far?

solomonzelman · Answer

think so, 
yep!

solomonzelman · Answer

Can we continue in 30 minutes or so?

anonymous · Answer

maybe

solomonzelman · Answer

I'll mention you!

solomonzelman · Answer

thank You and bye!