This is a future value annuity problem.
The future value annuity is given by the formula:
[tex]\begin{gathered} FV=P\times(\frac{(1+r)^n-1}{r}) \\ \text{where P:Periodic payment} \\ r\colon\text{Rate} \\ n\colon\text{Time(years}) \end{gathered}[/tex]
From the question, we are provided with the following;
[tex]\begin{gathered} P=\text{ \$1000} \\ r=9\text{\%} \\ n=8\text{years} \end{gathered}[/tex]
Thus, the future value annuity is:
[tex]\begin{gathered} FV=1000\times(\frac{(1+\frac{0.09}{12})^{8\times12}-1}{\frac{0.09}{12}}) \\ FV=1000\times(\frac{(1+0.0075)^{8\times12}-1}{\frac{0.09}{12}}) \\ FV=1000\times(\frac{(1.0075)^{96}-1}{0.0075}) \\ FV=1000\times(\frac{2.0489-1}{0.0075}) \\ FV=1000\times(\frac{1.0489}{0.0075}) \\ FV=1000\times139.856 \\ FV=\text{ \$139,856.16} \end{gathered}[/tex]
Hence, Beth will have $139,856.16 at the end of 8 years
