My "preferred lender" who does FHA financing tells me that it's very difficult to get a loan for less than 50K. I have certainly closed many properties in that range, however! It's easier with cash, but doable with financing, and 50K is the mark to shoot for--that's a 50K loan, not purchase price.
Good evening Jennifer, depending on your credit and use of the home it should not be an issue. If you are trying to buy to flip, it could be an issue. As noted, best to contact a local loan officer but if its primary and you have good credit , I dont see an issue for a fha or conventional loan. Good luck Steve Busse CRS, GRI