If an initial amount Ag of money is invested at an interest rate r compounded n times a year, the value of the investment after i years is A=A_{0}\left(1+\frac{r}{n}\right)^{n t}

If we let n → x, we refer to the continuous compounding of interest. Use l'Hospital's Rule to show that if interest is compounded continuously, then the amount after 1 years is