The Mathematics of Compound Interest
Compound interest is the process where interest is credited on both the original principal and the previously accumulated interest. Albert Einstein famously referred to compound interest as the eighth wonder of the world.
1. The Universal Compound Interest Formula
For an initial principal $P$, annual rate $r$, compounded $n$ times per year over $t$ years with regular monthly contributions $PMT$:
$$A = P \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$2. Frequency Effects
The more frequently interest is compounded (e.g. daily vs annually), the higher the Effective Annual Rate (EAR) and the greater the final yield due to exponential compounding.