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1. While the tuition does not directly influence the qualifications of a school, it will rather proportionally effect the money the school has to spend on professors, facilities, and all the other things it needs to educate you better. Further, a pricey school is often a sign of desire or prestige which rightfully or not will impact your prospects during hire and your salary once hired.
Private schools aren't backed up by tax dollars, so they have to charge more. Price is not indicative of the quality of the education, facility, nor professors. There are terrible professors at ivy league schools just like there are terrible professors at state universities.
An expensive school isn't a sign of desire. Your performance is the sign of desire. Proving that you have what it takes in your classes, whether they're attended at ivy league or community college will speak volumes.
As for prestige, who cares? Working for an employer who gets giddy over a prospective hire only because of the school attended is probably someone you should avoid. Performance over prestige.
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2. As #1 alluded to, a better school means quicker hire out of college and increased salary. The money you'll gain will offset the added debt.
No, a better performance will. I hate to keep reiterating it, but the school doesn't make the individual. The individual makes himself. You get out as much as you put in, and more. I know people who spent tons on private education and didn't land jobs that immediately paid off their debts. It just doesn't always happen. That isn't to say it never happens, but more likely than not, you won't be landing that dream job simply because you went to a school that put you in the debt you're trying to get out of.
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The idea that CS101 at Podunk U will teach you the same things, just as well as CS101 at CMU is a fallacy. It is not a rock solid rule, but in education you do generally get what you pay for. Your college education is the most important investment you will ever make, and will influence 40+ years of income. Don't skimp on it.
Define "well." Are you speaking about the available resources? The professor qualifications? The faculty? The teaching assistants? Teaching isn't a 1-way operation. It requires work on the student's part as well. The availability of specialized classes may be lessened at local colleges, but they're still there. The fundamentals of Calculus do not vary depending on the price of the institution.
Overall though, you're right. You shouldn't skimp on your education. I don't mean economically, though, like you do. I mean it in the sense of effort. Go to college and
learn. Do the work, put in the effort, and you'll come out a skilled individual with a world of opportunity because you've shaped yourself into a knowledgeable person.
I just want to harp one last point. You get as much as you put in. It isn't all about money. It's all about you. No matter where you go, as long as the college offers an education that covers the entire scope of what you wish to achieve and as long as you put in the effort required to become a skilled individual, you're going to be in a good position.