The UK could face a bill of between €7.7bn and €10bn for its share of the EU officials’ pension and benefits funds, according to a comprehensive study of European finances.

However, EU officials may have been underfunding the pension scheme due to discrepancies between discount rates used to calculate liabilities and staff contributions, the study by Brussels-based think tank Bruegel said.

The figures are likely to be a major sticking point of the UK’s negotiations to exit the European Union.

Authors Zsolt Darvas, Konstantinos Efstathiou, and Inês Goncalves Raposo made the pension estimates as part of a broader study of the UK’s likely financial obligations towards the EU.

The UK’s estimated contributions relate to unfunded defined benefit plans for EU staff and a Joint Sickness Insurance Scheme, with combined liabilities of €63.8bn at the end of 2015.

Staff are expected to contribute one-third of annual pensions costs, with member states paying the balance. Based on this, the study’s authors estimated the UK’s bill for future pension payments at between €7.7bn and €10bn, depending upon whether the calculations take into account rebates from the EU to the UK.

However, the authors noted that the liability figures were “rather uncertain” – largely due to the discount rate issue. The 2015 liability figure was based on a 0.6% discount rate, an average of one-year interest rates across the euro-zone.

At the same time, staff contributions were measured using a discount rate based on a much longer-term average. This went from a 12-year historical moving average until 2012, when it moved to an 18-year average. This is set to increase gradually to a 30-year average by 2021, two years after the UK’s exit talks are expected to have concluded.

“Since nominal and real interest rates have fallen in many advanced countries in the past 30 to 40 years,” the authors wrote, “there was a big decline in the balance sheet discount rate after the euro crisis abated after 2012. This decline pushed up the present value of pension/sickness insurance liabilities. In contrast, since the length of the historical moving average used for the staff contribution calculations has gradually increased in recent years, that discount rate has in fact increased, contrasting with the global decline in interest rates.”

The authors argued the use of a long-term moving average was “unjustified”, as it had resulted in staff collectively contributing less towards annual pension costs than the one-third they are supposed to.

“This implies that EU staff have been underfinancing their pensions relative in the past years and will continue to underfinance for more than a decade to come, compared to the theoretical requirement,” the authors said.

If liabilities were calculated using a risk-free rate, as is common practice in the UK, then the figures could increase “substantially”, the authors added.

UK prime minister Theresa May officially served notice of the country’s intention to leave the EU yesterday.

EU leaders have made clear that the UK will have to pay its fair share of bills and obligations before it leaves. Newspaper reports have referred regularly to a rough estimate of €50bn in total, but the Bruegel study said the total bill could be more than double this figure.

“Depending on the scenario, the long-run net Brexit bill could range from €25.4bn to €65.1bn,” the authors said. “Upfront UK payments could reach €109bn, followed by significant subsequent EU reimbursements.”

Bruegel’s board is chaired by former European Central Bank president Jean-Claude Trichet, and includes academics, investment professionals, and current and former government ministers from across Europe.

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