The 500k is funds that go 100% to the institutions
Hmmm, I read it as the 500k is a top off to the original hand out, which even thou was given to the institution, the institution was required to give at least half directly for student use.
And re the pell grant mentioned before, it seems like the amount given was based on pell and non pell students (75/25) but the top off is regardless as long as under 500k it is topped of to that amount.