WASHINGTON, Dec. 21 - Nearly one-third of all the savings in the final budget bill comes from student aid, the Congressional Budget Office said Wednesday.

Under the bill, college students would pay higher interest rates on loans.. Many banks will receive lower subsidies. And the Education Department will work with the Internal Revenue Service to ferret out students and parents who underreport incomes on financial aid applications. The budget bill is estimated to save $39.7 billion over the next five years. Student aid accounts for $12..7 billion of the savings, or 32 percent.

Not since 1997 has Congress made such an ambitious effort to slow the growth of benefit programs. The legislation includes these changes:

States would have sweeping new authority to impose premiums and co-payments on millions of low-income people covered by Medicaid. States can also scale back benefits for many recipients.

For the elderly, it would be more difficult to qualify for Medicaid coverage for nursing home care if they transfer assets to their children or other relatives for less than fair market value.

Medicare would freeze payments for home health services and reduce payments for medical imaging.

Welfare recipients would be subject to stricter work requirements. States would be subject to new financial penalties unless they put more people to work or further reduce the number of families receiving assistance.

Aid that helps states collect child support from absent parents would be reduced.

The Bush administration worked closely with Republicans in Congress on provisions that affect student aid. But Education Secretary Margaret Spellings declined to comment until the bill cleared a final hurdle on Capitol Hill.

Republican negotiators said virtually all the cuts in student aid would be borne by banks and other lenders, an assertion sharply disputed by Democrats and college administrators, who said that two-thirds of the savings would be at the expense of students and their families.

Even as it makes those cuts, Congress is creating a new program for students from low-income families who are eligible for Pell grants. The amount of aid will not be based on financial need. To qualify, students would have to be United States citizens, have completed "a rigorous secondary school program of study" and be taking courses full time at a "degree-granting institution of higher education."

The student would have to maintain "a cumulative grade point average of at least 3.0." Juniors and seniors will be eligible only if they have declared a major in the physical or life sciences, computer science, mathematics, technology, engineering or a foreign language deemed critical to national security.

College and university groups, as well as most Democrats, opposed the overall bill.

"This is the biggest cut in the history of the federal student loan program," said David Ward, president of the American Council on Education, an umbrella group for public and private colleges and universities.

A lobbyist at the council, Becky H. Timmons, said, "Students will be paying higher interest rates than they are currently paying."

The rate would be fixed at 6.8 percent for students and 8.5 percent for parents. The current rates, which vary with market conditions, are several percentage points below those levels.

The new aid for freshmen and sophomores is known as academic competitiveness grants. Freshmen would be eligible for $750 grants, and sophomores for $1,300 grants. Juniors and seniors would be eligible for $4,000 a year in what Congress calls Smart grants. The name is an acronym for "science and mathematics access to retain talent."

The Senate majority leader, Bill Frist, Republican of Tennessee, said the new support for math and science education would increase America's ability to compete in a global economy.

"China and India are generating scientists and engineers at a furious pace while America lags dangerously behind," Mr. Frist said.

The bill would not change the maximum Pell grant, which has been $4,050 for several years. President Bush had proposed a $100 increase. The bill would increase the maximum amount of subsidized loans, to $3,500 and $4,500 for first- and second-year students, from $2,625 and $3,500.

Senator Edward M. Kennedy, Democrat of Massachusetts, said the math and science program would abandon the Pell grant principle that the neediest students should receive the most help.

"Under this proposal," Mr. Kennedy said, "a single mother who can attend college only part time because she has to work 40 hours a week to put food on the table will not be eligible for a penny in new grant aid."

Republicans said the budget bill squeezed far more savings from banks than from students. Representative John A. Boehner, the Ohio Republican who is chairman of the Committee on Education and the Work Force, said the bill would increase benefits for some students while saving money for taxpayers.

"Vast increases in federal student aid" have coincided with a decade of tuition increases, Mr. Boehner said.

He suggested that federal investments in higher education had contributed to "the college cost explosion that is squeezing the budgets of low- and middle-income families."

Representative George Miller, Democrat of California, said the Republican proposals would make it even harder for many families to pay for college. About 70 percent of the savings in student aid "come off the backs of students and their families," Mr. Miller said.