Compounding Interest

$M(t)=P{\left(1+\frac{r}{n}\right)}^{nt}$

• $M(t)$ is money as a function of time
• $t$ is the time that we are observing the investment’s value
• $P$ is the principal/initial payment
• $r$ is the interest rate (indicated as APR, or annual percentage rate, in many sites)
• $n$ 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?

M(t)&=\$2000\left( 1+\frac{0.05}{12} \right)^{12\cdot50} \\ &=\$39871.91 \end{align}$$ ## [Desmos Calculator](https://www.desmos.com/calculator/ffqjnxl8dx)