The number of government-guaranteed loans to college students has soared this year, spurred by low, 9 percent interest rates for borrowers, large federal supplements for lenders and fears that the program would be sharply curtailed.

After considerable controversy, Congress decided two weeks ago against major cutbacks in the popular loan program, as the Reagan administration proposed, although some limits will be imposed Oct. 1.

Before Congress made up its mind, there was rush of loan applications, and officials said the surge is continuing.

"We're still up to our eyeballs in paperwork," said James Leamer, executive director of the Maryland Higher Education Loan Corp., which approved twice as many loans in July as it had a year earlier. "And the money is there. Most of the major banks are running wide open. They're getting a good return."

In Virginia, loan volume was up almost 70 percent, with $51.4 million in loans approved in July. In Washington, July loan disbursements tripled by the the city's largest maker of student loans, the Higher Education Loan Program, but the increase was from a relatively small figure a year ago when the program was starting again in the city after several years' interruption.

"It's an incredible deal, and people all over the country are taking advantage of it," said Robert Leider of Alexandria, author of a widely used guide to financing college costs, "Your Own Financial Aid Factory." "There's been an enormous amount of publicity given to the low-interest student loans and other interest rates have gotten so high. A lot of people are trying to get them to get in under the gun."

Nationally, the amount loaned students was up 63 percent in the first half of the 1981 fiscal year, according to the U.S. Education Department. It is projected to reach $7.2 billion to $8 billion by Sept. 30, when the fiscal year ends, compared to $4.8 billion in 1980.

This year's explosion in the size of the student loan program comes on top of sharp incrases in 1979 and 1980 after Congress removed all family income limitations on eligibility as part of the Middle Income Assistance Act.

In 1978, the last year the subsidized loans were limited to families earning less than $25,000 a year, the total amount borrowed nationwide was just under $2 billion. About 1.1 million students borrowed the funds, a number that rose to 2.3 million last year and is expected by the Education department to increase by another 800,000 this year.

Currently, college undergraduates and students taking post-high school vocational courses can borrow up to $2,500 a year with a limit of $12,500. Graduate students can borrow $5,000 a year with a maximum of $25,000 per borrower for both undergraduate and graduate loans.

Besides the 9 percent interest paid by borrowers, the federal government pays an interest supplement tied to the rate for 91-day Treasury bills. The total return to commercial lenders is currently about 19 percent, an attractive yield on loans that are virtually risk-free because the federal government insures against defaults.

As a result of the upsurge in lending and interest rates, the cost of student loans to the federal government rose from about $600 million in 1978 to $1.6 billion in 1980 and an expected $2.6 billion this year.

To try to hold it down, the Reagan administration proposed limiting all loans to the amount students need based on a formula involving college costs and family income and assets. The administration also sought to end a subsidy under which the government pays all interest costs until six months after a student graduates or drops out.

Even though the Carter administration proposed the same changes just before it left office last January, the cutbacks were strongly opposed by higher education groups and congressional Democrats.

Eventually, in the budget reconciliation bill Congress passed two weeks ago, the only major change was imposition of a needs test limiting the size of loans for families earning more than $30,000 a year. Congress also required students to pay a 5 percent loan origination fee on all loans, starting 10 days after President Reagan signs the bill, which he is expected to do next week.

The limits on borrowers earning $30,000-plus will become effective Oct. 1. The Education Department, which must set the limits, has yet to submit details of its plan to Congress, which can overturn the proposal by a vote of either house.

Because of the uncertainty, Leider said many students apparently are putting in loan applications now when no one's family income is considered.

Few lenders have collected income data on loan recipients for the past few years since it wasn't required. However, the Virginia Education Loan Authority, the largest student lender in that state, reported that 10,197 of its 39,211 loans last year were made to students from families earning over $30,000. Included were 3,771 loans to those earning more than $50,000 and 117 to those at $95,000 and above.

"Obviously, there are quite a few people out there who really don't need the loans," said Alexander Astin, head of the Higher Education Research Institute, "and are just putting the money into money market funds which pay 16 to 18 percent. But there are a lot of others who do need it because tuition has gone up so much."

Regardless, Astin said data from his annual nationwide survey of college freshmen indicates that the proportion getting student loans doubled from 10.4 percent in 1978 to 20.9 percent last fall. During that time the median contribution of parents to college costs declined from $565 to $447 despite inflation