Eurozone finance ministers have agreed on a formula to reduce Greek debt to 124 percent of GDP by 2020, with Athens having to come under even greater fiscal scrutiny but with the opportunity of seeing its debt reduced even further in the next few years.

The third meeting of the Eurogroup in two weeks produced a result after about 12 hours of talks as the euro area ministers and International Monetary Fund managing director Christine Lagarde agreed on a set of measures that would immediately cut Greece’s debt by 20 percentage points and then set it on a path that would see it drop below 110 percent of GDP by 2022.

The agreement means that Greece will also receive 34.4 billion euros by the end of the year – 23.8 billions is to complete the recapitalization of Greek banks - but the remainder of the bailout loans (9.3 billion euros) it was expecting next month will be paid in three tranches at the beginning of next year.

“This is not about money,” said the head of the Eurogroup, Jean-Claude Juncker, after the meeting.

“This is the promise of a better future for the Greek people and for the euro area as a whole, a break from the era of missed targets and loose implementation towards a new paradigm of steadfast reform momentum, declining debt ratios and a return to growth."

“This was a test for the eurozone and we simply could not afford to fail,” said European Union Economic and Monetary Affairs Commissioner Olli Rehn, who said that further steps to reduce Greek debt would be considered in the future.

“This agreement is possible because Greece has shown it is serious about reforms,” he said. “Greece has come a long way and the Eurogroup has recognized that.

Lagarde also reaffirmed the IMF’s commitment to the Greek program but said that the Washington-based fund would wait until a bond buyback scheme to reduce Greek debt has been carried out before deciding to release its share of bailout funding.

“Once progress has been made on specifying and delivering on the commitments made today, in particular implementation of the debt buybacks, I would be in a position to recommend to the IMF Executive Board the completion of the first review of Greece’s program,” she said.

Prime Minister Antonis Samaras gave a brief statement to journalists in Athens. “Everything went well,” he said. “All Greeks fought together. A new day begins tomorrow for all Greeks.”

Greece’s lenders agreed on a package of measures to reduce Greek debt by 40 billion euros, cutting it to 124 percent of gross domestic product by 2020.

In a significant new pledge, ministers committed themselves to take further steps to lower Greece's debt to “significantly below 110 percent» in 2022 -- the most explicit recognition so far that some write-off of loans may be necessary from 2016, the point when Greece is forecast to reach a primary budget surplus.

“When Greece has achieved, or is about to achieve, a primary surplus and fulfilled all of its conditions, we will, if need be, consider further measures for the reduction of the total debt,” German Finance Minister Wolfgang Schaeuble said.

To reduce Greece's debt pile, ministers agreed to cut the interest rate on official loans, extend their maturity by 15 years to 30 years, and grant Athens a 10-year interest repayment deferral.

They promised to hand back 11 billion euros in profits accruing to their national central banks from European Central Bank purchases of discounted Greek government bonds in the

secondary market.

They also agreed to finance Greece to buy back its own bonds from private investors at what officials said was a target cost of around 35 cents in the euro.

“The initiatives include Greek debt buybacks, return of Securities Market Programme (SMP) profits to Greece, reduction of Greek Loan Facility (GLF) interest rates, significant extension of GLF and European Financial Stability Facility (EFSF) maturities, and the deferral of EFSF interest rate payments,” said Lagarde.

“Taken together, these measures will help to bring back Greece’s debt ratio to a sustainable path and facilitate a gradual return to market financing,” the IMF chief added.

“The debt ratio is expected to decrease to 124 percent of GDP by 2020 through significant upfront debt reduction measures of 20 percent of GDP. In addition, I welcome the commitment by European partners to bring back Greece's debt to substantially below 110 percent of GDP by 2022, conditional on full implementation of the program by Greece. This represents a major debt reduction for Greece relative to its current debt trajectory.”