I'm gobsmacked at this post - it's been eye opening to me. I've looked after friends and neighbours cats multiple times for free. I'd never even considered charging them! To me it's just a neighbourly thing to do and it's 5/10 mins twice a day.
There was one neighbour who had 2 cats - they didn't get on so they put one cats stuff in their en-suite upstairs, and the other in the kitchen. I had to make sure the door was always shut. There were no cat flaps, so I had litter trays to deal with too (and one of the cats used to do really, really runny shits and always seemed to perch on the litter tray to do it outside of the tray for me to clean out - probably in protest to the situation! He was also a really nasty cat who attacked everyone for no reason) and despite all that I'd never have accepted payment for doing it.
We have a cat too, but we rarely go away so it's not as if we are doing tit-for-tat in terms of cat sitting.
My two youngest sons (10 & 14) absolutely love cats and beg me to come with me/let them do stuff for the cats - I like to think when they're old enough they'd cat sit for their friends/neighbours without wanting payment for it.
If I were the OP I'd look to find a friend or neighbour with cats too that you could do cat sitting for each other, if they don't want to pay out for someone to do it. Otherwise, I'd probably think around half of what you'd pay a professional cat sitter (because they won't have tax, insurance, etc to pay on top of it) would be a reasonable rate for a teenager looking for a bit of cash in hand.