Answer
$$\eqalign{
& {\text{Annual rate: }}9.50\% \cr
& {\text{Time to double: }}7.3{\text{ years}} \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Initial Investment: \$ 500}} \to {A_0} = {\text{\$ 500}} \cr
& {\text{For }}t = 10 \to A = \$ 1292.85 \cr
& A = {A_0}{e^{rt}}{\text{, }}t{\text{ in years}} \cr
& {\text{Therefore,}} \cr
& \$ 1292.85 = \$ {\text{500}}{e^{r\left( {10} \right)}} \cr
& {\text{Solve for }}r \cr
& {e^{10r}} = \frac{{1292.85}}{{500}} \cr
& 10r = \ln \left( {\frac{{1292.85}}{{500}}} \right) \cr
& r = \frac{1}{{10}}\ln \left( {\frac{{1292.85}}{{12500}}} \right) \cr
& r = 0.0949992 \cr
& r = 9.50\% \cr
& \cr
& A = {A_0}{e^{rt}} \to A = 500{e^{0.095t}} \cr
& {\text{The time to double is }}A = 2{A_0} \cr
& 1000 = 500{e^{0.095t}} \cr
& t = \frac{{\ln 2}}{{0.095}} \cr
& t = 7.2962 \cr
& t \approx 7.3{\text{ years}} \cr} $$
