Is Penn Foster School of Online Study accredited in America, and does it allow you to go to a university?

Short answer: Yes and yes.

I couldn’t find a school with that exact name and capitalization, but Penn Foster, the for-profit online high school — formerly a “correspondence” (by mail) school dating back to the 1890s — is accredited by the Middle States Association of Colleges and Schools, coincidentally the very same regional accrediting body that covers the high school I graduated from. And as my credential indicates, I did go to university. So the first yes is a strong yes.

As for the second part of your question… it’s still a yes, but with a lot of caveats. I would draw your attention to this fine print at the bottom of the web page about Penn Foster’s high school program:

You are solely responsible for ensuring that the program and program award satisfy the education requirements of potential employers, desired postsecondary institutions, and all other relevant agencies. Neither job placement nor postsecondary admission are guaranteed to graduates upon program completion.

The school aims to prepare students for the workforce, college, or the military — all three of which tend to like people with high school diplomas and pay them better than those without. “The workforce” is probably the most expected destination, given that some vocational prep courses for things like auto repair or veterinary technician are offered.

The core curriculum is very basic by American high schools standards. Two “general math” courses and one “consumer math” course are, well, better than no math at all. You can get two algebra courses and a geometry course as electives. But that puts you where I was at the end of 10th grade. There’s no trigonometry, no pre-calculus, no calculus. No “honors” track for smart-ish kids, and absolutely no “advanced placement” track. In an ordinary American high school, this is the curriculum for kids who can’t handle anything harder.

So you could get into extremely non-selective universities, probably for-profit ones or perhaps religious universities, sure. You are absolutely not (see that fine print) guaranteed admission, or indeed anything short of derisive laughter, from your desired postsecondary institutions, whatever they may be. Don’t expect “good” universities to be impressed by your diploma from Penn Foster — if you want to go to one, do two years in a community college with a 2+2 program that gets you an associate’s degree and (with decent grades) guaranteed acceptance to a state university system for the final 2 years of your bachelor’s degree.

If you are a teenager and can go to an ordinary physical high school to earn your diploma, for less than $1,000-$1,500… please do that. Especially if you’re smart enough to handle anything other than the most basic curriculum. You’ll be far better off.

But if you’re too old for high school, or there’s no free public high school near you? Well, the answers to both parts of your question were “yes.”