buffalo said:
You then hide the bill and never use it in front of the parents??? Doesn't sound like a great plan to me.
I tried that, when I got my first laptop

I was just starting my first full time job after graduating from university, and still living at home at that point. Of course it wasn't a parental permission thing, but I thought I'd just not say anything about it and see how long it would take for someone to notice.
... It took not even a day. The following day after I placed the order from work, I got home and my mother said I had a message on the answering machine. "Hello, this is Dell Canada calling to confirm your purchase ...."
As for Mammoth, I know how you feel. When I first started working and suddenly had disposable income, I felt like I "just had to have" everything. That Dell laptop was just the first drop in the bucket. When 2 years later I got laid off from that job, I found myself having to sell off all my toys... and by then I had gone through 3 laptops, 3 camcorders, 3 digital cameras, 2 tablet PC's, 3 different PDA's, a box of home automation gear, 2 older Macs, .... I've since learned to be more realistic about what I buy, as tempting as some of those toys are. You really need to learn to step back and REALLY think about whether you REALLY need something. There will always be new toys.
I teach and mentor young guys your age, but feel free to ignore me.

However, based on what I read in this thread, I think your best option to "proving yourself" is to NOT keep asking. Drop the subject for a while (by this I mean months, not just days..) Use the iMac. If you really want to make a statement about your lack of admin privileges, then find a number of legitimate things to do with the iMac, then ask (politely) for your mom to enter her admin password whenever she needs to. Don't hint, don't nudge, don't say it in an annoyed tone of voice, just ask her to come and enter her password, politely and casually, each and every time. This is the bed she made, so she gets to sleep in it.
You can find software to help you with school, or take up a hobby (buy a GPS unit and start geocaching, or learn guitar or piano). Get some good software or tools to support the interest. Do NOT fill up the hard drive with junk. And get your software legally. Your mom will see, over the coming months, that you are excited about using your iMac for enriching and educational purposes (and willing to spend money for good software or tools).
You're counting on her soon tiring of always entering her admin password. DON'T ASK OR HINT... not immediately... let her get the message. She will. If she feels you are ready for an admin account, she may bring it up, or you could casually ask about it at some point, months down the road.
Demonstrating you are responsible enough for your own admin account on your iMac is a first step toward being responsible enough to own your own computer. At the same time you are also demonstrating your maturity in being able to set long-term goals and being willing to work with your mom's restrictions (and eventually compromise with her when she feels you are ready) without pestering her and being annoying
However, you do have to look at things from her perspective too. I really think parents do need to know what their kids are doing on their computers, especially online. This may just be her way of keeping tabs on you and seeing what you're up to. The best way to counter that, I think, is not to make it an "us versus them" thing, but involve her in a positive way. Be very open about what you do, what files you're creating, who you're talking to. "Mom, come check this out!" and so on.
If you can learn to be very open and non-confrontational about your use of the iMac, this is the best way to prove to her that you are mature, trustworthy, and capable of doing more than she's currently letting you do.
Besides, if you wait a few more months, something even better than a MacBook is sure to come soon.
