I don't think debt collection agencies charge interest like that do they?
If the outstanding debt was 3,000, then the bank will settle for a percentage of that amount in return (maybe 2,500 if the debt collector can collect the full 3,000) ignoring interest in the mean time. The bank's goal is to recover as much of their money as possible, not to keep adding to it. I.e. they have already given up on the full amount you owe them so it is pointless them looking for more.
The debt collector tries to get as much of the 3,000 back as possible in a reasonable enough time frame to make a decent return. In effect, the debt collection agencies interest is paid by what they keep from the collected amount, i.e. the bank pays what is effectively the interest not the person in debt.
This is just my take on it from dealing with them while I was in business and had cashflow problems.
If there are any debt collectors who can put me straight, feel free to do so...