Answer
$$\eqalign{
& {\text{Time to double: }}12.60{\text{ years}} \cr
& {\text{Amount after 10 years: }}\$ 31,198.55 \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Initial Investment: \$ 18,000}} \to {A_0} = {\text{\$ 18,000}} \cr
& {\text{Annual Rate: 5}}\frac{1}{2}{\text{% }} \to r = 0.055 \cr
& A = {A_0}{e^{rt}}{\text{ }}\left( {\bf{1}} \right){\text{, }}t{\text{ in years}} \cr
& {\text{The time to double is }}A = 2{A_0} \cr
& A = 2\left( {{\text{\$ 18,000}}} \right) \cr
& A = \$ 36,000 \cr
& {\text{Substituting known values into }}\left( {\bf{1}} \right) \cr
& \$ 36,000 = {\text{\$ 18,000}}{e^{0.055t}} \cr
& {e^{0.055t}} = 2 \cr
& \ln {e^{0.055t}} = \ln 2 \cr
& 0.055t = \ln 2 \cr
& t = \frac{{\ln 2}}{{0.055}} \cr
& t = 12.60{\text{ years}} \cr
& \cr
& {\text{*The amount after 10 years is:}} \cr
& A = {A_0}{e^{rt}} \cr
& A = {\text{\$ 18,000}}{e^{0.055\left( {10} \right)}} \cr
& A = \$ 31,198.55 \cr} $$
