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I'd definitely hit Penfed before NAVY. You look like your in a OK place for both CU's by looking at your scores. Don't let your fear of denial stop you from getting what you want. Everyone will eventually be denied for something. Even those with the best scores.
I agree with the others - PenFed first as they are more inquiry sensitive. Navy doesn't seem to mind lots on inquiries, but they are HP happy (e.g. a HP for membership and then generally one HP for each additional credit product).
From my experience PENFED pulls Equifax for account and credit cards while NFCU pulls Trans Union for account and credit cards. If you ask for CLOC NFCU pulls Equifax. So as long as you stick to credit cards it shouldn't matter the order.
I appreciate tbe insight! Should I be worried about the number of new accounts ive opened recently when applying to PenFed? Because I was also looking into the AMEX everyday card that I was prequalified for a few weeks ago. I just want to be sure I make the best decision and dont waste a hard pull because these are going to be my last two applications and then im gardening for at least a year. Thanks for the advice!
IME, Navy pulls EQ for membership and TU for credit products and CLIs. Navy is all over the map on credit pulls though. Penfed does one EQ pull for everything and more conservative than Navy. This is why I recommended Penfed first. Amex pulls EX. Amex won't have any bearing on the other two. Unless you wait for it to report to all three CBs.
Inqs aren't permanent, neither are new accounts. The accounts will age together and in 12 months the inquiry will hold no weight.