I was delinquent in paying a debt to XXXX XXXX XXXX XXXX for an emergency ambulance ride. Incidentally, I did call the Fire Department directly shortly after the date of service and attempted to pay over the phone. At that time, they did not have an electronic system in place to accept payment via debit/credit card and requested that I send in a check, which I did not do. I called back last month and attempted to pay the debt directly to them and they advised that they had already sent the account to collections with National Business Factors. 
As the debt was sent to National Business Factors , Inc., I was contacted via writing by them. Within ten days of receiving their collection letter, I contacted National Business Factors , Inc. directly and paid the original debt in its entirety. I refused to pay the interest as I did not enter into a contract with National Business Factors , Inc. and felt I had paid the bill completely. The bill from XXXX XXXX XXXX XXXX was for {$350.00} and on XXXX/XXXX/2015, this amount was paid to National Business Factors , Inc. 
I continued ( and still do ) to receive phone calls and letters from the collection agency threatening to ruin my credit if I do not pay the interest, which they report continues to accrue daily. 
I have contacted the collection agency on numerous occasions citing my belief that legally I do no owe this debt as I have not entered into a contract with them, therefore they can not charge me this interest. I have consulted the internet and state laws to learn that I am not legally responsible for this debt. They are aggressive with me when I attempt to communicate with them and continue to threaten my credit worthiness. 
The amount in question is only {$25.00}, though that compounds daily so is likely higher at this point. I am protesting out of principle, certainly not out of inability to pay the amount. I disagree with their collections tactics and do n't feel I owe this debt. 
Is it legal for a XXXX party collection agency to hold me responsible to them for their interest after the debt has already been paid off completely? And continue to compound the debt after the original debt has been paid? 

I 've attempted to attach supporting documents such as the original bill as well as evidence of payment and letters from National Business Factors but this system will not allow PDF files to be uploaded - I tired XXXX times and it freezes the system. I 'm happy to provide documentation if requested via email attachment.