The federal government could raise $716m a year by applying a 15% loan fee to all student loans in an attempt to recoup the cost of subsidised interest rates, the Grattan Institute has found.

The move would hit postgraduates and commonwealth-supported undergraduates the hardest – they now pay no loan fees.

“Loan fees would contribute to budget repair, but leave per-student university funding unchanged, reduce pressure to cap student numbers, avoid upfront charges, and preserve protections for low-income graduates,” the report concluded.

The policy would reduce loan fees for full-fee paying undergraduates, who now pay 25%, and those on vocational education and training loans, who pay 20%.

Those taking out student loans under Hecs-Help pay a nominal rate of interest, meaning the government subsidises their loans. In 2016, that subsidy was worth a little more than $600m, but the Grattan Institute report, released on Monday, warns that the bill will top $1bn if interest rates return to historical averages.

The report, by Grattan’s education director Andrew Norton and senior associate Ittima Cherastidtham, found that the 15% loan fee would have raised a net total of $716m in 2016 (after accounting for reductions in existing fees), in effect wiping out the cost of the interest subsidy.

The 15% loan fee could prove an attractive alternative for the Coalition government, which tried to introduce real interest rates on student loans in the 2014 budget, only to back down in the face of a hostile Senate.

The Grattan report argued that loan fees were progressive compared with charging real interest, which would punish students who took breaks from work or earned low incomes. It said the differences in the current rates of loan fees “are unfair and lack a policy rationale”.

The report said loan fees would extend the time it took students to repay loans but leave annual repayments unchanged. “As a result, loan fees would have little impact on access to higher education,” it said.

The fee would add about a year’s repayments to pay back the loan for men and women alike.

Cash-poor students could continue to borrow with no upfront charges, and low-income graduates would still not have to repay until their income reached the $54,869 threshold, the report said.

Under the current system, women receive on average 17% of their original borrowing in interest subsidies while men receive 16%, showing that the 15% fee would almost entirely wipe out the subsidy.

But the Grattan Institute proposed that high-income graduates, who repaid their loans more quickly, would help cross-subsidise the cost of low-income graduates who repaid more slowly.

The report noted that even with a 15% loan fee, low-income graduates would still receive an interest subsidy to their loans. For example, the 15% fee would almost halve the subsidy of women earning $65,000 and cut a quarter of the subsidy for men earning that amount.

Men and women earning $95,000 would be disadvantaged because their current interest subsidy is less than 15%.

The Grattan Institute said the previous Coalition and Labor governments had attempted to reduce higher education costs, but the difficulty was in finding a saving consistent with economic and social goals. It has previously modelled lowering the loan repayment threshold to $42,000, a move that would save the budget at least $500m a year.