Harvard's endowment is $32 billion. They can fund many students at $50,000 a year from the interest without touching the principle, and it's a major goal of theirs to do so. Yale, Princeton, and Columbia also have multi-billion dollar endowments and are aiming to do the same. They can afford it.

This is how the University of Chicago does it (from their website):

Thanks to an extremely generous gift of $100 million from an anonymous alumnus, we are now able to offer an even more competitive financial aid package to many of our students. The Odyssey program has allowed more students from modest backgrounds the ability to pursue all that the University has to offer without the worries of working to pay off loan debt. For students with family incomes below $75,000 a year, all expected federal student loans are replaced with Odyssey Scholarships. For students with family incomes between $75,000 and $90,000, half of their expected federal student loan obligation is replaced with Odyssey Scholarships. You must apply for need based financial aid in order to be considered for this need-based University funded scholarship.

Right, even Brown, one of the poorest Ivies, has more than $2 billion in endowments. And one of the methods they do to afford it is charging higher tuition: Christina Paxson, Brown's president, has (maybe not officially, but at least in private) has said that she wants tuition to work similar to a graduated-income tax. This would mean even children of rich ($150-200k/yr) parents would be eligible for some amount of financial aid (because $150k/yr isn't enough to be able to afford $60k/yr tuition), but they may end up paying the same tuition as everyone would normally, if there were no financial aid.

This is also a large part of the logic top-tier schools have used to justify their increased tuition to the federal government.

If Harvard really wanted that they could offer their education for free to all 21,000 students right now, cover the tuition with a 4 percent interest on their endowment and still have more than $5B left for other expenses.

Right, but why would you have everyone going for free, when you can get a guarunteed $60k/yr of revenue from ~30%+ of your students, without it presenting any hardship to them? Also, I'd be unsurprised if another reason for raising tuition was to raise the perceived value of the university. Which would help contribute to even higher donations.

>How long would the Ivy-league schools maintain those huge endowments if most spots were taken by students from poor background?

This logic is flawed imo. Yes the students are poor at the moment, but the endowments don't come from what students are now. They come from what they will be. "excellent students" plus excellent education strikes me as a pretty good recipe on that front.

> How long would the Ivy-league schools maintain those huge endowments if most spots were taken by students from poor background?

Pretty long, I’d wager. The endowments weren’t built on tuition, they were built on alumni giving. One might hope that formerly poor students would be more likely to give generously as wealthy alumni.