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You never know in your future quests for credit when the issue of having an unpaid, delinquent debt may come up.
If they wont do a PFD, then consider what your expected credit needs will be between now and when the CO will become excluded from your credit report.
It might still be beneficial to pay, even though you will get no score boost, if you will be applying for credit, such as a mortgage loan, that traditionally requires the satisfactin of any unpaid, delinquent debt before their approval of a mortgage loan.
For the determination of when it will become excluded from your credit report should you do nothing, you need to know the DOFD that preceded their charge-off, and then add the exclusion period of no later than 7 years plus 180 days.
After that point, credit report exclusion will become moot, and you can likely get an even lower settlement agreement.
Purely from a credit history perspective, it is preferable to pay in full UNLESS you can get a settlement AND their agreement not to report paid/settled for less.
Neither will remove the derogs from your credit report, so wont direclty improve your score.
However, both will discharge the debt.
If you settle for less, they have the option of reporting that fact to the CRA by way of a settled for less special comment.
That is never a favorable comment in your credit report, as it informs others that you have a past practice of not paying your entire obligated debt.
That means the prior creditor took a loss in dealing with you, and that could affect any decision as to whether to extend new credit.
If you cannot obtain a PFD, next best thing is to obtain a settlement for less along with their agreement not to make any reporting of settled for less to the CRAs.
The account will then look the same in a manual review as if it had been paid in full.