Banks, credit unions and other firms involved in the Guaranteed Student Loan Program are overpaid millions of dollars a year because the Education Department fails to check erroneous billings, a government study said Wednesday.

The General Accounting Office said an investigation found that during one three-month period in 1985 the Education Department overpaid to 16 lenders at least $1.8 million in interest subsidies on outstanding guaranteed student loans because the lenders submitted erroneous billings.Lawrence Thompson, a GAO assistant comptroller general, conceded the error rate for the 16 lenders cannot be projected to all 14,000 banks, savings and loan associations, life insurance companies and credit unions eligible to make loans to students at about 8,000 schools.

But he stressed "the extent of such errors in the department's billing procedures makes it likely that similar errors are made by many lenders."

Student loans are first guaranteed by one of 58 agencies, and ultimately by the government. The subsidies include all interest on loans while students are in school or during a grace period after they leave schools, and a smaller subsidy after students begin repaying their loans. Lenders also are paid in cases of default.

Thompson recommended that Congress authorize the Education Department to assess lenders interest on overpayments due to erroneous billings from the date of the overpayments and require lenders to verify their billings.