LoL?...
To the OP : the game does not tell you how many turns are left for your peace deals. I agree it's very much lacking... They will obviously add a "current deals" tab in a future patch for this obviously lacking feature.
For now you can get one of the UI enhancing mods. One of them gives you a detailed breakdown of the "Reports" tab where a "Current Deals" is added and I believe the peace timers are displayed there, along with your Trade Deals, Alliances etc.