Answer
$$\eqalign{
& {\text{Annual rate: }}8.94\% \cr
& {\text{Amount after 10 years: }}\$ 1833.66 \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Initial Investment: \$ 750}} \to {A_0} = {\text{\$ 750}} \cr
& {\text{Time to Double: 7}}\frac{3}{4}{\text{yr}} \to t = 7.75{\text{yr}} \cr
& A = {A_0}{e^{rt}}{\text{, }}t{\text{ in years}} \cr
& A = {\text{750}}{e^{r\left( {7.75} \right)}} \cr
& A = {\text{750}}{e^{7.75r}}{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{The time to double is }}A = 2{A_0} \cr
& A = 2\left( {{\text{\$ 750}}} \right) \cr
& A = \$ 1500 \cr
& {\text{Substituting known values into }}\left( {\bf{1}} \right) \cr
& 1500 = {\text{750}}{e^{7.75r}} \cr
& {e^{7.75r}} = 2 \cr
& \ln {e^{0.055t}} = \ln 2 \cr
& 7.75r = \ln 2 \cr
& r = \frac{{\ln 2}}{{7.75}} \cr
& r = 0.0894 \cr
& r = 8.94\% \cr
& \cr
& {\text{*The amount after 10 years is:}} \cr
& A = {\text{750}}{e^{0.0894t}} \cr
& A = {\text{750}}{e^{0.0894\left( {10} \right)}} \cr
& A = \$ 1833.66 \cr} $$
