This document summarizes compound interest formulas and applications. It provides the formula for compound interest when interest is compounded n times per year. As n increases, the balance approaches a limit of (1 + r/n)^nt, which is the formula for continuous compounding. Examples are given to compare balances with quarterly, monthly, and continuous compounding over 5 years at 5% interest. The document also introduces the logistic growth function used to model bacterial culture growth over time.