Capital One--Canceled, but not gone

I just called and cancelled my Cap 1 card because they were changing the terms of agreement.
My current interest rate is 5%, and it was increasing to 13%. If I opted out of the new terms, my card would be cancelled., but my current rate will apply while I pay off my card. This sounds almost too good to be true--that I can keep the 5% rate. I'm holding on the the written notice, in case my rate does go up.
My new goal is to pay off the card by Oct. 15. This sure is taking longer than I thought!