My wife's business is trying to get some documents printed and want to put their logo on them. The logo was designed 20+ years ago and all she has are printed copies. The printer is asking for a vector EPS file. I offered them a Photoshop EPS file I created by scanning the paper copy of the logo using Photoshop Elements, but they tell me what I've created is a rasterized image, which they cannot use.

Is there a way to scan this logo and create a vector EPS file? What software would I need to have to do so? Adobe Illustrator?

The only graphics software I have currently is Adobe Photoshop Elements.