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Every school caculates aid differently, in same cases, you will do better at Williams than its peers, in some cases (including yours, alas) worse. Considering both schools now require no loans at all, I am pretty surprised at the difference. But if you really want to attend Williams, don't let the aid offer stop you -- if you have a better offer at Amherst or MIT or anyplace else, definitely show that to the financial aid office and see if they will match -- they may well do so, and it's worth a shot. Don't view this as a final, unmaleable offer, again, especially if you have better offers from peer institutions.
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