Well first off tell them that a cat won't be that much work. just clean the litter box and they aren't too much work. they are cute, fun and playful a great pet to have around the house. I have a cat he's really not too much work at all.
I had the same problem with a dog. Tell them that you will take full responsibility for the cat and that you will put lots of time into it, and commit to your promise. Also, save up some money to help them lay for the cat because a cage, cat, food, and supply prices can add up fast. Tell them that you are old enough and very responsible. Best of luck and don't forget to follow me! :)
Don't push you're parents too far, but if you really want one then help your parents a bit around the house maybe? Think again of what you're getting your parents into; pets cost alot of money its like 200$ each shot and that x4 shots every year.. It's a lot of money.. Ask for it for you're birthday might help(: Hope this comment helps!!! Good luck!
Your parents know the finances of your family. Food, vet bills, extra litter... They also know how hard it is to fight the pet fur war! (I can't win a battle, let alone the war). We rescue cats. 9 right now. People keep dumping them, because they can't handle their care. Relax. Enjoy the cuties you have. And, be glad your family is being responsible. If you never get overwhelmed beyond your means or temperament/tolerance, you will never dump a sweet soul. P.S. The humane society is humane. Dumping is horrid.