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If you refinance is done right (i.e. not make you worse off), all other things equal, yes your credit score will eventually move in the right direction.
@youdontkillmoney wrote:If you refinance is done right (i.e. not make you worse off)
Can you explain how a refinance is done right?
A refinace is done "right" it it meets your objectives, typically money savings in the form of less interest pai dout over the long run. The interest savings is used to pay down other debt as you stated.
Payment of the current debts will not result in the removal of any derogs that have been reported under your payment history by the creditor or any debt collector, or the removal of any public record derogs. It wont improve your score in payment history unless you obtain a PFD acceptance, and thus deletion of reported derogs.
However, if the unpaid debt is under a revolving account, it is most likely still being included under your % util category scoring, and thus hurting the scoring of % util of revolving credit.
Paying will, if it is still being included in your revolving % util, reduce that util, and thus help scoring.
On the non-scoring front, payment is likely to help should you app for new credit where the creditor does a manual review of your credit report.
Seeing unpaid, delinquent debt can be a factor in denail of new credit, regardless of your credit score.