# I Realized What e Was For
I realized that abstract nonsense highly scattered my brain. I hav
e seriously thought that e was to make a^x have eigenvalue 1 for t
he differential operator... That's not logically wrong, but not th
e original purpose.
The original purpose of e was this:
If you compound an interest, that means (APY) -> (APR). Then the n
ew APY is
(New APY)
= [1 + (APR)/n]^n - 1
-> e^(APR) - 1
as n->inf. n is the number of compounding in a year.
This shows why compounding is good. (Old APY) = O(n) but (New APY)
= O(a^n).
## Examples
(10% APR) = exp(.1) - 1 = .1052 = (10.52% APY)
(50% APR) = exp(.5) - 1 = .6487 = (64.87% APY)
(100% APR) = exp(1) - 1 = 1.7183 = (171.83% APY)