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Since you are planning to app/re-fi, I would pay the fingerhut balance now. The usage will keep the account open even if it doesn't report a statement balance. While you are at it, you might as well pay the other small balances off. The % of cards reporting a balance is a small factor with FICO 08. None the less, no need to leave points on the table.
I will stand by my earlier post. Re-fi the card and apply for 1 or 2 cards at the same time. Do the app's before the new account hits and potentially lowers your score. If Chase denies you, no big deal. INQs aren't a big deal if you are going to be in the garden for the next 12 months. However, I would think about a second card you might want to apply for at the same time. It would be good for you to have three regular, unsecured credit cards. A personal fav' of mine is Discover IT for thin files. However, Discover is unpredictable if you would be approved. You can find many other choices for "average" credit.
Good Luck!
@CreditDunce wrote:I think you could get away with adding one more account without hurting your score that much. One more TL should not drop your AAoA below the 1 year mark. When you are ready to re-fi (I am assuming you are waiting to pretty up your credit report before the re-fi), apply for the freedom or slate. Just in case Chase denies you for 5/24, I would have a backup card to apply for. Something like Barclay rewards card, Discover IT, etc. If you get denied, it isn't a big deal. Just hang out in the garden for a year and try again.
Note: By pretty-up, I mean all but one credit card report zero balance. The one with a balance should have less than 10% utilization showing.
I completely disagree (If you are saying it is ok to apply for the card before refi) and am feel like the default advice sometimes is to "go for it". given the short timeframe, regardless of what "might" happen, the prudent thing is to wait. If one cannot wait 30days to apply for a credit card in order to ensure they are in the best possible place for a refi I would question their overall credit judgement.
While we can all sit here as potificate that 1 more inquiry will not hurt, the OP is the one that has to deal with the consequences. What if that 1 inquriy for the CU meant the difference between a 6% loan and a 10% loan.
OP, while you may get it and it may not hurt you just never know. The Chase cards will always be there. Don't risk your ability to get that 19% APR down and save yourself some cash....