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I'm new to this and trying to improve my credit and score. In general, how long will it take for me to see an improvement in my score? If I pay everything on time and my collection accounts are paid off, how many points can I expect my score to increase in let's say 6 months?
Very little. Paying collections won't help your FICO score and FICO really doesn't reward you for on-time payments, though you'll see improvements over time due to the aging. I don't think you'd see a noticable gain over 6 months.
Now if those collections disappeared, your score would spike.
Welcome to the forums!
I'd suggest reading the following:
Common Abbreviations
Credit Scoring 101 - great for knowing what is in your credit score and to see how your score is impacted.
What Steps Do I Take - great for learning the repair process.
and Example letters - PFDs, GWs, DVs, etc.