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When my FICO updates to higher no. and I apply for a card the next day, will the CCC see the new or old score? (If old, how long do I have to wait for the CCC to see the new score?)
They will see the new one as the score was changed 2 or 3 days ago.
A Fico score is a fluid number and is constantly in motion since its based on a "snapshot" in time from the info in your CR. A new creditor would see a score based on the info in your report that very moment they request the score.