This may be a good read.
As Nina mentioned, plenty of art schools put you in a whole lot of debt through their programmes, and it really doesn't matter which school you go to, so long as you have a good portfolio when you're looking for a job. Employers generally don't care about paper qualifications, either.
Teaching yourself to be a good artist is certainly possible, but it requires lots of dedication and planning, because it's way too easy to get overwhelmed looking at all the art tutorials and references online. Procrastination is probably your biggest enemy here too, though. It's way too easy to just slack off when you're not being hammered with deadlines.
I've been fortunate enough to get a formal art education at a fraction of those costs. Personally, I don't think it's necessary, but if you can get one without putting yourself in a huge debt, I think it's worth it, especially if you find yourself lacking direction when it comes to art.
In my opinion, an art course provides you with the guidance needed to learn the basic fundamentals and then later on the more specialised skills needed to survive in the industry. Of course, you'd still have to learn a lot on your own, because there probably won't be enough time to cover everything in the course, but it gives you enough knowledge that you won't be completely lost when looking for improvement.
Oh, and there's also lecturers (and peers) around to offer you professional critique. It's not always you can find constructive criticism online, so it's nice to have someone you can talk to for advice and help. One-to-one chats are the best!
An art course also lets you build connections and get contacts for future job endeavours in the industry, too. It's not to say that you can't do this on your own through forums or attending seminars or anything, but it's a lot easier to get contacts when your entire class is (probably) going to be in the same industry as you are. That way, when a classmate leaves for the industry, there's a chance they could recommend you for a job if you're good enough.
And of course, an art course is definitely going to showcase your work if you're good enough, which gives you the exposure every artist looking for a job needs.
Anyway, those are just some of the perks of going to an art course. Everything an art course has to offer you can find elsewhere, but it's just there in one convenient location in an art programme. It's not all doom and gloom, I guess, but it's definitely not a bed of roses either. You'd have to be committed to staying in the course, and that means being prepared to lose hours of sleep because of deadlines and other assignments.
Ultimately, it's best to decide whether you want to take art as a job, or whether you want to pursue it as a hobby. The life of an artist isn't the most financially stable, so you could try taking art on the side if you want a more lucrative career. I mean, it's possible to get into art later on. There are freelance artists who did art on the side before moving onto doing it full-time once they were able to sustain their lives with it alone.
Regardless, I'd consider looking up some online courses as an alternative. There are many online schools floating around, some of which are mentioned in the link above, like
Watt's Atelier and
CGMA.
Schoolism is a fairly new online school, too. If you're like me, though, and you like getting things for free, there's sites like
Ctrl+Paint and channels on Youtube like
Proko's, and
Sycra's, too.
Hope this helps. :)
(I'm having lots of fun in my course.)