I recently missed a credit card payment by one day (my first one ever in my history of credit starting from over 10 years ago), and I called the credit card company to have the late fee waived. I reasoned that this was a mistake, that I have excellent credit history (my score is very, very good too), and that it won't happen again.

I pay off my entire amount every month, and the credit card company agreed to waive the late fee. However, I was charged an interest on the balance that I had because I had missed the payment. I had tried calling them to waive the interest charges but had no luck.

Are credit card interest charges negotiable to be waived? I know late fee and interest fees (not charges) can be negotiated, but I was told this charge could not be. From my perspective, my activity would be worth more if I stayed as a customer than to let such a minuscule amount drive me away from their service.

What can I do to successfully negotiate the interest charge if possible? Is this something dependent on the company itself or will I have to bite the bullet and live with the charge?