Convert JPEG Logo to Vector

I have a finished logo that currently exists only as a JPEG. I need it redrawn from scratch as a fully-scalable vector so I can use it for print, large-format signage, and digital assets without quality loss... (Budget: $10 - $30 USD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Graphic Design, Illustrator, Logo Design, Photoshop, SVG, Vector Design)