The latest progress comes in the wake of two days of talks in Athens between Greece’s political leadership and Charles Dallara of the Institute of International Finance, the bankers’ lobby representing most investors.

Bankers and officials involved in the discussions who were not authorized to speak publicly say that bondholders have made significant concessions with regard to the interest rate, or coupon, that the new Greek bonds would carry. Having insisted previously on an average rate above 4 percent, creditors now seem willing to accept a rate below 4 percent for the 30-year bonds — perhaps as low as 3.6 percent.

The discussions are expected to continue through the weekend, and officials said some type of announcement could come Saturday or Sunday.

Talks have broken down twice before, largely because the International Monetary Fund and European leaders have pushed for a larger debt reduction in light of Greece’s worsening economic outlook, so there is the possibility that these negotiations will founder, too.

Technical talks are continuing with regard to a lump-sum payment of some sort that may be included in later years if the Greek economy improves.

On top of the 50 percent nominal loss, or haircut, already agreed, the lower coupon would produce a total loss for bondholders of more than 70 percent.

It is a tense time for Greece. Officials from the three institutions that are keeping the near-bankrupt nation financially afloat — the European Commission, the monetary fund and the European Central Bank — are demanding another round of spending cuts and reforms to justify a release of as much as 30 billion euros ($39 billion) in the months ahead.

A private sector debt deal is seen as a strict condition to Greece’s securing its next bailout installment.

Officials expect that the deeper bond loss will allow Greece to meet its goal of having a debt-to-gross-domestic-product ratio of 120 percent by 2020, a significant drop from the current ratio of 160 percent.

The recent collapse of the economy has made it more difficult for Greece to hit this number.

Though a debt agreement may spur Greece’s next bailout installment, the deeper loss being inflicted on bondholders carries the risk that many investors, in particular hedge funds that in recent months have loaded up on cheap Greek bonds in hopes of a payday this March, will refuse to participate in the deal.

Greece will try to impose the terms on all investors by writing collective-action clauses into the contracts of its old bonds. By doing this, the hope is that the holdouts, estimated to sit on 10 percent to 15 percent of the 206 billion euros ($272 billion) in outstanding securities, will exchange their old bonds for new bonds — preferring the new discounted bonds to their old ones, which may become worthless.

Some hedge funds that have bought at rock-bottom prices may decide to pursue legal action, although such a process could take years with small certainty of success.

Also undecided is what the European Central Bank, which owns 55 billion euros of Greek bonds, will do. Despite public pressure that it, along with investors, accept a loss on its bonds, the bank has not budged.

Greece and European officials continue to discuss a plan that would allow the central bank to swap its Greek bonds for another form of Greek debt that, unlike the bonds it now holds, would not be eligible for a haircut.

If such a swap were to occur, the central bank would not be affected if Greece were to invoke the collective-action clauses and force a loss on all bondholders.

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