If you just refinance what's owed, and don't take any cash out, then the current appraised value can be used to determine your financing options. However I didn't realize the scores were that low, if I was you I'd send a goodwill letter in to the company you had the late payment with and see if they'd remove it. If they do, that should not only increase the scores but help you qualify for FHA. Mortgage options are more limited these days, without 20% equity (gotta figure in the new loan amount would have closing costs) FHA is going to be your best option. FHA is looking for clean credit for 12 months, I was going to say with an automated underwriting approval it can be OK with negatives in the last 12 months, but with low 500 scores the odds aren't good for an automated underwriting approval. Priority #1 would be to get that late removed.
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