My Brother's Battle with the Credit Card Company

For something different (let’s call it an engagement gift), I am giving my brother a forum to share his rant. I should preface this by writing that my brother does not back down from an argument. He once contacted KDKA’s Wayne Van Dine because he didn’t want to share his Social Security number with Duquesne Light to get electricity. He actually made it on the air and won. He has also had several lengthy confrontations with Verizon. Today’s battle (obsession?): the credit card company:

Can anyone in cyber land explain to me what is the "Effective APR"?
After going around and around with my credit card company we were able to decipher this: it is "your total finance charges - including transaction fees such as cash advance and balance transfer fees expressed as a percentage" What is the world does this mean? I'm a math person, so please just give me an equation to figure it out. Any way that I figure it on my statement it does not come up as the number presented. Yes I asked several people to help me calculate it but they can't. I was able to attain one example problem for 1 month, not the entire year, which apparently is how this thing is calculated. Additionally "it is automatically generated by the computer" is not a sufficient answer as well. Someone, somewhere in your company tells the programmer what to put into the computer, which means someone has an answer.

I have been told that the "Effective APR" does not factor into what I am paying. This appears to be accurate, but I'm not really sure why it is on there, and the 6 people I have spoken with only said "it is required by law". I know that our government officials come up some crazy and stupid laws, but what is up with this? Federal laws are designed to protect the people. This to me means it protects the consumer, company and/or the government itself. So who is this "Effective APR" protecting and why? I know that there is more to it so someone needs to fess up. If this does not factor into what I am paying, what is it used for? Who uses it and why? Please someone tell me.

If anyone can help my brother, please leave a comment. Personally, he lost me in the first few sentences, so I asked for clarification:

I have been told that I am not being billed differently. There are 3 essential questions that have not been answered. 1) How do I calculate it -- and why can't anyone tell me. 2) What is it used for -- and why can't anyone provide an answer 3. Who uses the Effective APR -- if it is not used then why are credit card companies legally bound to display it? It has to serve some purpose, but it does not seem like anyone can identify why.