Answer
$$\eqalign{
& {\text{Annual rate: }}3.46\% \cr
& {\text{Amount after 10 years: }}\$ 17667.53 \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Initial Investment: \$ 12,500}} \to {A_0} = {\text{\$ 12,500}} \cr
& {\text{Time to Double: }}20{\text{yr}} \to t = 20{\text{yr}} \cr
& A = {A_0}{e^{rt}}{\text{, }}t{\text{ in years}} \cr
& A = {\text{12,500}}{e^{r\left( {20} \right)}} \cr
& A = {\text{12,500}}{e^{20r}}{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{The time to double is }}A = 2{A_0} \cr
& A = 2\left( {{\text{\$ 12,500}}} \right) \cr
& A = {\text{\$ 25,000}} \cr
& {\text{Substituting known values into }}\left( {\bf{1}} \right) \cr
& {\text{25,000}} = {\text{12,500}}{e^{7.7520rr}} \cr
& {e^{20r}} = 2 \cr
& \ln {e^{20r}} = \ln 2 \cr
& 20r = \ln 2 \cr
& r = \frac{{\ln 2}}{{20}} \cr
& r = 0.0346 \cr
& r = 3.46\% \cr
& \cr
& {\text{*The amount after 10 years is:}} \cr
& A = {\text{12,500}}{e^{0.0346t}} \cr
& A = {\text{12,500}}{e^{0.0346\left( {10} \right)}} \cr
& A = \$ 17667.53 \cr} $$
