What is the value of a 2 carat loose diamond?

It completely depends upon the quality. There is no one value you can assign based upon the size. The "4 Cs" dictate value: Cut, Clarity, Color, Carat. You know one of the 4 Cs (carat) but the value can differ greatly based upon the other 3 Cs. The best way to determine value is to have it appraised.