A confidential report commissioned by the government has proposed redrawing the terms of student loans taken out over the past 15 years, that would make them more expensive to pay back for 3.6 million borrowers in England alone.

The proposal to increase the interest rates on the £40bn worth of loans is the most controversial of a series of options contained in a Whitehall-commissioned study examining how the coalition could privatise the entire stock of student loans issued since 1998.

Increasing the amount that students would be forced to pay back would make the loans more attractive to buyers.

The document, prepared by Rothschild investment bank, was submitted to the business department in November 2011, but is understood to still be under active review. It has never been made public, or been seen by higher education professionals.

Any move to increase the interest rates on loans already taken out could add extra years of repayments even for those who left university long ago.

In the report, dubbed Project Hero, the authors suggest a script for ministers to persuade graduates to accept the worsening of their conditions. "We all live in difficult times," they suggest ministers argue. "You have a deal which is so much better than your younger siblings (they will incur up to £9,000 tuition fees and up to RPI+3% interest rates)".

A statement from the Department for Business, Innovation and Skills confirmed that ministers were still looking at how to privatise the pre-2012 student loan book. It noted: "The government has not made any changes to the pre-2012 loans interest rate terms … Work on the feasibility of selling the pre-2012 student loan book is ongoing."

Ministers already plan an auction of the remaining student loans issued between 1990 and 1998. Although they have a face value of £900m, they are expected to fetch a fraction of that amount. The real value lies in the loans issued after 1998, which are worth between £35bn and £45bn – many multiples more than all the state assets otherwise lined up for sale.

At the moment, the interest on all student loans taken out before 2012 is capped. Graduates pay interest at either the RPI measure of inflation or banks' base rate plus 1%, whichever is lower.

But in the privatisation study, Rothschild found that the rate-cap was a major deterrent to potential investors, who worried that if inflation outstripped the base rate they would lose out on returns.

In order to sell as much of the loan book as possible, the financiers advise that the government underwrite the risk with a financial instrument called a synthetic hedge, in effect using the public finances to guarantee returns to private investment.

Alternatively, they suggest dumping the cap on loan rates altogether. If that proves impossible, the team suggest "an 'offer of compromise', including a payment holiday, or an interest-free period or a different cap".

"The [financial] risk is best taken by government...; second best is it being taken by graduates...; and lastly by investors who want inflation protection."

Removing the cap would, however, burden graduates with years of extra repayments, lasting in some cases until the end of their working lives. At the moment, the cap on student debt taken out before 2012 keeps repayment rates at 1.5%. Lifting it would mean a rate of 3.6%, in line with RPI in March 2012. One indicative calculation suggests that an employee on £25,000 a year, with £25,000 of undergraduate loans taken out before 2012, could work until retirement without ever paying off their debt if the interest rate cap were removed.

Loans taken out since 2012 have interest rates fixed at RPI plus 3%.

The proposals were greeted with fury by lecturers' and students' representatives. "This government is showing that it's more concerned with helping investors make money than defending the interests of student and taxpayers," said Simon Renton of the University and College Union. "Students and taxpayers deserve better than a Hobson's choice between payday lending or another giant PFI."

Lifting the cap would also fly in the face of ministerial assurances that there would never be a retrospective change in terms. Speaking to a parliamentary select committee last June, universities minister David Willetts told MPs: "In the letter that every student gets there are some words to the effect that governments reserve the right to change the terms of the loans. That is a text that has always been there for students, but we have no plans to change the framework we have explained to the House of Commons."

The report was obtained by the False Economy website through a freedom of information request. Although over 90% of it was redacted, the blacking-out was light enough that virtually the entire report can be read. It was analysed for the Guardian by higher education analyst Andrew McGettigan.

"Many people have speculated about the problems associated with selling student loans," said McGettigan, author of The Great University Gamble. "This is the first authoritative confirmation we've had that the main impediment to sale is the interest rate protection in place for existing borrowers. Under these proposals, this government will get cash now but borrowers or future governments pick up the tab."

"The government must immediately rule out this outrageous suggestion," said Liam Burns of the National Union of Students. "Despite pushing them to establish in law that conditions on student loans could not be altered retrospectively the government refused and gave weak assurances that they had no plans to do so. Now we see their own advisers are suggesting that very move."