Convert JPEG Logo to Vector

I have a single-colour JPEG logo that now needs to be reproduced as a crisp, fully scale-able vector for professional print work. I want the new file to mirror the current design exactly—clean edges, balanced... (Budget: $10 - $30 AUD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Design)