Compounding Interest
#Math
$\displaystyle M(t)=P\left( 1+\frac{r}{n} \right)^{nt}$
- $\displaystyle M(t)$ is money as a function of time
- $\displaystyle t$ is the time that we are observing the investment's value
- $\displaystyle P$ is the principal/initial payment
- $\displaystyle r$ is the interest rate (indicated as APR, or annual percentage rate, in many sites)
- $\displaystyle n$ is how often the payment compounds
E.g.: How much is a 50-year long investment worth if $2000 was initially invested, the APR is 5%, and it compounds monthly?
$$\displaystyle \begin{align}
M(t)&=$2000\left( 1+\frac{0.05}{12} \right)^{12\cdot50} \\&=$39871.91
\end{align}$$