The "natural" base appears in many places, both in the physical sciences and financial records of yore. In fact, it was clerks and bankers who first stumbled upon the fantastic number 2.718281... and how it was a very useful value to use when approximating increasingly compounded interest rates. For this and other reasons, it is now well entrenched as a fundamental value and given the designation of \(e\). Much like \(\pi\), \(e\) represents an infinitely non-repeating decimal number known as a transcendental number.

There are a few financial mathematical formulas for computing interest when the interest is compounded at different times than the rate is designed for. As an example, compounding interest monthly on a credit card with an annual percent interest rate is a very common practice amongst banks. 

Simple Interest Formula: \(A=P(1+r)^t\) where A is the future value, P is the "principle" aka initial value, \(r\) is the interest rate per unit of \(t\), time. 

General Compound Interest Formula: \(A=P\left(1+\frac{{r}}{{n}}\right)^{{nt}}\). In this case, \(n\) is the number of compounding periods per unit of time, \(t\). So, in the credit card example above, \(n=12\) since it is 12 times per year.

Continuously Compound Interest Formula: \(A=Pe^{{rt}}\). Here the interest is "always" accumulating and \(r\) is the rate per time period \(t\). This type of rate is also called the relative rate