COLLEGE admission notifications have begun to arrive. With every thrilling acceptance comes something far less welcome: the heart-stopping reality of what it all costs.

Tuition has risen almost 1,200 percent in the last 35 years, and the sticker price for many four-year private colleges and out-of-state public universities exceeds $250,000. Even at state universities, the average four-year cost for residents is more than $80,000 for tuition, room, board and expenses. But every college offers need-based financial aid, right? Well, sort of.

A college aid package can be made up of three elements: grants (sometimes called scholarships), loans and work-study programs. The biggest single source of aid is the federal government — but in the form of loans ($68 billion, 37 percent of all aid, in 2013). About 5 percent of aid comes from states and a large part from the college’s own resources. Much of the college’s contribution comes in the form of a discount from the school’s already inflated tuition, which, with a straight face, administrators call a grant.

When colleges compute their aid packages, they start with a student’s expected family contribution — that is, what the government expects a family to be able to contribute, not what the family expects. The E.F.C. is calculated by the federal government based on data submitted by the family on the Fafsa form (the Free Application for Federal Student Aid, which is mandatory if the student wants any sort of financial aid, even work-study jobs in the school cafeteria). The Fafsa’s complexity rivals that of a tax return, but it is less user friendly.