How to convince my mom to get me Xbox Live....?

last year before i got banned on runescape i had a membership on there for about a year...for 5 bucks a month thats 60 bucks a year...and a 12 month xbox live gold card is 50 bucks so im tryin to get my mom to get me xbox live b'c before shes the one who paid for my runescape so i dont think she should hav any problems with xbox live....but at least she doesnt kno how much profanity and **** is on it sometimes but shes knos im a mature 13 year old so......any suggestions on gettin her to get me it?