Jailbreaking an iphone 5 for rogers?

I really want to jailbreak my phone cuz i'm sick and tired of rogers making me pay extra for a bunch of stuff i didn't even do. I have a bill of like $93 bucks and apparently if jailbreak it, it won't be seen that i didn't pay and i use other companies. Is this true? Like can someone explain to me what happens to your account with your main carrier (mine is rogers) when you jailbreak your phone and go to another carrier. Will you be charged or anything?

Jailbreaking won't change your carrier. You have to unlock it.

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