02:19
Calculus of a Single Variable
Compound Interest The formula for the amount $A$ in a savings account compounded $n$ times per year for $t$ years at an interest rate $r$ and an initial deposit of $P$ is given by
$$A=P\left(1+\frac{r}{n}\right)^{n t}$$
Use L'Hopital's Rule to show that the limiting formula as the number of compoundings per year approaches infinity is given by $A=P e^{r t} .$