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I would say that it should take around 30 days for the FHA streamline refinance. Since you have all your information together from the last lender you should be able to easily give that information to another lender if you wish to do so. [self promotion deleted by Zillow moderator.
You probably wont even have THAT loan long enough for you to recoup the money that you paid upfront! It would take more than 5 years for you to recoup the difference. 90% of homeowners refinance within the first 5 years. What I see mostly of, however, is 2 to 3 years! At least 1% lower would be good to refi to.