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How can I determine if a FHA loan refinance offer is from a reputable lender
Start with the list of mortgage companies approved to work in your area. There are 80 within 10 miles of my house, and more than 100 in my county. Pick ones you know because they are established businesses in your area, region, or even nationally.   A good place to start might be with your current lender. The risk you seem to be worried about is a scam or a trick. In the recent past the scams were ones where the home owner didn't understand teaser rates, and the risk of interest only and pick-your-payment loans. The simpler the bells and whistles, the less likely you are to be embarking on a risky transaction. It can't hurt to ask an organization like the BBB or neighbors, but realize that many people loved their exotic mortgage until the moment it blew up in their face. So for 5 years your neighbor would have raved about their new mortgage until they discovered how underwater they were.  Regarding how smoothy the transaction is accomplished, is hard to predict. There is great variation in the quality of the loan officers, so a great company can have rookie employees. Unless you can get a recommendation for a specific employee it is hard know if your loan officer is going to give great service.   When getting a mortgage for a purchase, the biggest risk is getting a mortgage that results in a payment you can't afford. This is less of a risk with a refinance because you already have a mortgage and monthly payment. But keep in mind some of the monthly savings is due to stretching out the payments for another 30 years. Know what you are trying to do with the refinance because the streamlined ones cant be used for cash out.