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Matt wants to know if he should pay down (or completely pay off) the amount associated with the judgment to increase his credit score and to appear more creditworthy to lenders.
Paying down or paying off the amount associated with the judgment will have no impact on the credit score. While the judgment may now be reported as satisfied on his credit report, the fact that he even had a judgment in the past (satisfied or not) still negatively impacts his credit score. The data shows that consumers with derogatory information (such as a judgment) on their credit history have higher future credit risk compared to consumers with no previous derogatory patterns.
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Once the judgment is no longer reported (legally, it must be removed from the report after 7 years), it will no longer have any impact on the score. Matt may try and work with the lender to see if they will delete the judgment if he satisfies it in full (this is sometimes referred to as a "pay for delete" agreement), but there are no guarantees the lender will agree to that (and there is no requirement they do so).
Even though a satisfied judgment does not have a positive impact on score, a lender may consider it a good sign of willingness to pay and may override the score and grant the credit Matt may seek in the future.
Image: walknboston, via Flickr.com