Answer
$1.8\times10^8$ years
Work Step by Step
For an object in circular motion around mass M, there are two expression for the velocity; $v=\sqrt{\frac{GM}{r}}$ and $v=\frac{2\pi r}{T}$. Equate the two expressions and solve for $T$.
$$v=\sqrt{\frac{GM}{r}}=\frac{2\pi r}{T}$$
$$T=s\pi \sqrt{\frac{r^3}{GM}}=2\pi \sqrt{\frac{(3\times10^4ly\frac{(3\times10^8m/s)(3.16\times10^7s)}{1ly})^3}{(6.67\times10^{-11}Nm^2/kg^2)(4\times10^{41}kg)}}=5.8\times10^{15}s$$
$$=1.8\times10^8yr$$