If an initial amount $C$ of money is invested at an interest rate $i$ compounded n times a year, the value of the investment after $t$ years is

$A=C\left(1+\dfrac{i}{n}\right)^{n t}$

If we let $n \rightarrow \infty$, we refer to the continuous compounding of interest. Use l'Hospital's Rule to find the value of the investment if it is compounded continuously for $t$ years. Your answer may depend upon $C$, $i$, and $t$.