I think they will ask you to pay a certain amount or purchase the book and bring the new copy in.

It sounds like in this case it will be cheaper to pay what the library is asking .

From what I remember there is a limit that they can charge you.

If you pay this off before racking up late fees, then find the book later, you can bring it in and (at least at my local branch) they give you the price of the book back minus the actual late fees.

So, whatever you do, take care of it asap because the late fees are what get you in the end