As given by the question
(a)
There are given that the initial payment is $500.
Now,
From the formula, the equation will be:
[tex]A=500(1+\frac{0.06}{12})^{12\times20}[/tex]Then,
[tex]\begin{gathered} A=500(1+\frac{0.06}{12})^{12\times20} \\ A=500(1+\frac{0.06}{12})^{240} \\ A=500(3.310) \\ A=1655 \end{gathered}[/tex]Hence, $1655 will you have in the account in 20 years.