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Each company will be different. For example, my company will go as low as $50,000 for a conventional loan... but even with that exceptions can be made.
50k is about the minimum. some have even higher minimums
Well I can tell you for a fact that Quicken Loans will go as low as $44,770 as that is the total price of the townhouse I am buying with my down payment included. My suggestion to you would be to just call 5 or 6 trustworthy mortgage companies and ask them this and any other questions you may have. Hope you get a house in the near future and that I close on mine on time
My loan was also FHA.