_{0}of money is invested at an interest rate

*r*compounded

*n*times a year, the value of the investment after

*t*years is

A = A

_{0}(1 + r/n )

^{nt}

if we let n->infinity 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

*t*years is

A = A

_{0}e

^{rt .....i dont understand how to get from the first amount to the second using l' hospital's rule}