Sallie Mae, the giant student-loan company, miscalculated the payments for about 800,000 of its borrowers and is telling them they will have to pay more each month to pay off their loans on time.

Correcting the error, which company officials ascribed to a computer-programming mistake, will raise borrowers' monthly payments by $40 or less in most cases, though the increase could exceed $100 in some others.

"We take full responsibility for the error, and we are keenly aware of the inconvenience it will cause some of our borrowers," said Sallie Mae spokeswoman Kathleen deLaski. The company plans to send letters to affected borrowers between now and the end of May explaining the situation.

The mistake involves only 10-year, variable-rate, federally guaranteed loans that are already in repayment. These include Stafford loans for students and Plus loans for parents. Current students and recent graduates who have not started repayment are not affected. Neither are those who have consolidated their government loans into a fixed-rate note, nor borrowers who have private loans handled by Sallie Mae. The company has 7 million student borrowers.

The mistake was discovered after a number of borrowers who were approaching their loan payoff dates realized that the amount of principal left on their loans was larger than the sum of the principal portion of the remaining payments. These borrowers began making inquiries to Sallie Mae last fall, and it took the company several months to set up a new program to recompute the payments and work out a policy on how to handle the situation.

The underpayments of principal allowed the borrowers to hold their money for slightly longer than they would have if the payments had been correct, so in theory they should owe additional interest. The company figured that such interest would total about $8 million for the loans involved but said it would not seek to collect it.

The problem was first reported by the Chronicle of Higher Education. Borrowers with questions can call a toll-free line, 800-890-9798.