My wife and I are buying a new house but it doesn t have ac?

So we are purchasing a house that was stick built December 2014 and we found out it doesn t have ac which I think is ridiculous. Now the contractor accepted our offer for asking price but they are paying 6k in closing. Do you think it will honestly cost them that much? If not then do you think we could ask at closing for them to use the remainder towards an ac install? Also could we barrow more on our loan for the install since it is an fha? We really want ac and this is our first home if you can t tell. Thanks for answering, any advice would be greatly appreciated.

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