The letter e was chosen to name this number in honor of the mathematician Leonhard Euler (1707-1783), who discovered its importance.  The number e is irrational; its decimal expansion, like that of pi, is known to many decimal places.  Luckily, the number e has a value approximated to 2.71828, given here to five decimal places.

    Logarithms to the base e are sometimes called natural logarithms. They are less useful for computation than common logarithms but are used in calculation, frequently for calculating the annual yield of an investment that is compounded constantly.
 

 
    Lets say you have money in the bank, and the bank compunds your interest constantly.  The equation would be represented as: A=Pe^rt,  where A is the final amount, P is your initial quantity, r is your annual rate, and t is your amount of time.  Think of it as A=PERT.  It might help you remember the equation better.
 
 
Example
    Lets say you have $5,000 in the bank, and the bank coumpounds your 5% interest rate constantly for three years.  The equation would look like: A=5000e^1.05(3).  Hence leaving you with approximately $116,680.32 after three years. 1