Hello and thank you for your question.
When your credit provider 'sold' your debt' the purchaser acquires all the rights to interest, etc under the original credit card agreement, this is why they are able to charge interest on your debt. Just make sure there calculations are correct and that they have included ALL the payments you have made to either the original credit card company and the debt collector.
Generally credit card contracts contain clauses allowing the credit provider to terminate the line of credit at any time and then call in the loan, at which time you wil lose the ability to draw on further funds, but are still liable to repay and pay interest your debt to that point.
The interest they appear to have been alleging you have acquired over the period does seem high, so again you need to check your figures, but if your credit card debt was $20,000 in 2011, you may have been incurring something in the order of $4,000 a year in interest on your debt (credit cards often charge something in the order of 20% per year interest), so if it took you the full 5 or so years of regular payments to pay back $20,000, a further $10,000 or so in interest would have accrued on top of the original amount, and it would be more, if most of your repayments occurred later rather than earlier.
I trust the above assists your understanding.
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