Zakaat on a lost gold ring

Q: My wife took out her gold ring to make wudhu at home and then forgot where she left it. This happened last week. 

We searched high and low for it, in the cupboards, drawers, and in every part of the house (in the kitchen, under the sofa, or any other place possible). 

After searching extensively, we have now lost hope of finding it, and we now suspect the helper may have snatched it. Will my wife need to pay zakaat on the ring?