How do I figure out the remaining interest on this credit card that I paid off? Details below, please help!?

Balance of credit card was 5,775.00 on last statement. I paid $140 payment on 10-02-09 and paid the rest of the balance (5635.00) on 10-20-09. There are 2 different interest rates (one was promotional) so it gets tricky.

I received a bill for $69 in interest after I paid it off. I just want to check their math to make sure I'm not being ripped off because they are not figuring it right on purpose so they can make more money. It says that they are taking a "30 day cycle" and averaging the daily periodic rate from that.

Can someone explain to me how this works? I read the fine print on the back of the bill and it doesn't go into any detail on what happens when the balance is paid in full so I'm at a loss. It does say that when they average the daily balance new transactions are added "as of the transaction date, the beginning of the billing cycle in which they are posted to your account, or a LATER date of OUR CHOICE." (Emphasis is mine.)

I was told this "billing period" was from 9-22-09 till I paid it off, which was 10-20-09. That is not 30 days, it's 28. It seems to me that they are adding an extra 2 days which increases the finance charge.