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How can I determine if a FHA loan refinance offer is from a reputable lender
In my book if it comes in the mail with official looking envelopes, language and seals to try and get you to open it, the company isn't trust worthy enough for my business. I get a pile of these for my VA loan every week, I imagine FHA loans get similar junk mail. Rates are very low at the moment so it is likely that rates from reputable lenders are 1 to 2%  lower than say a year or 2 years ago.  In general if a lender gives you a GFE the numbers on it are going to be pretty accurate and there isn't a great deal of wiggle room for the lender so the concerns with reputation should focus on is this outfit some type of scam and then reviews on how good or bad their customer service is. Chances of running into a scam seem pretty low but the costs could be really high. As far as checking if an unknown lender is any good it is kind of tough to do. There is a list of Lenders on HUD's site. Checking BBB can't hurt but I wouldn't put a lot of stock into their recommendations. Doing some general Google searches certainly can't hurt but aren't fool proof either. Personally I would start by checking what prevailing rates are for your current situation. You could go to your proffered bank or to any number of online sites to get a couple of quotes.