ESRI left off a lot of simple tools that you would think should be there - but developers and users, as always, come to the rescue!
There is, in fact, a tool (several) for this exact operation. Go to ESRI's support/downloads/ArcMap site and search for "document path" "path date" or other such search string. I found one called: "Document Path Date and Time" that I use all the time.
Also plan on spending some more time perusing the site. There is a wealth of addon tools, scripts, etc. to make your life with ArcMap easier.