Euro zone finance ministers sealed a second bailout for debt-laden Greece on Tuesday that will resolve its immediate financing needs but seems unlikely to revive the nation's shattered economy.

After 13 hours of talks, euro zone officials said ministers had finalized measures to cut Greece's debt to 120.5 percent of gross domestic product by 2020, a fraction above their original target of 120, after negotiators for private bondholders accepted bigger losses to help plug the funding gap.

Agreement on the 130-billion-euro ($172 billion) rescue package, subject to strict conditions, will help draw a line under months of uncertainty that has shaken the currency bloc, and avert an imminent Greek bankruptcy.

We have reached a far reaching agreement on Greece's new program and private sector involvement that would lead to a significant debt reduction for Greece and pave the way towards an unprecedented amount of new official financing ... to secure Greece's future in the euro area, Luxembourg's Jean-Claude Juncker, who chairs the Eurogroup of finance ministers, told a news conference.

The euro jumped almost half a cent, reversing earlier losses, after Reuters reported a deal had been struck.

A report prepared by experts from the European Union, European Central Bank and International Monetary Fund said Greece needed extra relief to cut its debts near to the official debt target given the ever-worsening state of its economy.

If Athens did not follow through on economic reforms and savings, its debt could hit 160 percent by that date, said the report, obtained by Reuters.

Given the risks, the Greek program may thus remain accident-prone, with questions about sustainability hanging over it, the nine-page confidential report said, highlighting the fact that Greece's problems were far from over.

The accord will enable Athens to launch a bond swap with private investors to help reduce and restructure its vast debts, put it on a more stable financial footing and keep it inside the 17-country euro zone.

Around 100 billion euros of debt will be written off as banks and insurers swap bonds they hold for longer-dated securities that pay a lower coupon, although it is not clear how many will take the deal.

Private sector holders of Greek debt will take losses of 53.5 percent on the nominal value of their bonds. They had earlier agreed to a 50 percent nominal writedown, which equated to around a 70 percent loss on the net present value of the debt.

Given the balanced agreement reached with the creditor group ... and the fact that the package delivers debt sustainability for Greece we expect a high participation rate, Juncker said.

The debt sustainability report delivered to ministers last week showed that without further measures Greek debt would only fall to 129 percent by 2020.

The IMF had said if the ratio was not cut to near 120 percent, it may not have been able to help finance the bailout, putting the whole scheme in jeopardy.

To help fill the financing gap, euro zone central banks will also play their part.

A Eurogroup statement said the ECB would pass up profits it has made from buying Greek bonds over the past two years under its emergency bond-buying program to national central banks for their governments to pass on to Athens to further improve the sustainability of Greece's public debt.

The ECB has spent about 38 billion euros on Greek government debt that is now worth about 50 billion euros.

Whatever its constituent parts, economists say the deal may only delay a deeper default by a few months. A turnaround in the economy could take as much as a decade, a prospect that brought thousands of Greeks onto the streets to protest against austerity measures on Sunday.

DOUBTS OVER COMMITMENT

Skeptics question whether a new Greek government will stick to the deeply unpopular program after elections due in April, and say Athens could again fall behind in implementation. That could prompt lenders to pull the plug once the euro zone has stronger financial firewalls in place.

While there are doubts in Germany and other countries that Greece will be able to meet its commitments, including implementing 3.3 billion euros of spending cuts and tax increases, the threat of contagion from a chaotic Greek default always made a deal more likely than not, no matter how tortuous the negotiations.

Greek Prime Minister Lucas Papademos, IMF Managing Director Christine Lagarde and ECB President Mario Draghi attended the Brussels talks, signaling they were likely to be decisive.

The private creditor bond exchange is expected to launch on March 8 and complete three days later, Athens said on Saturday. That means a 14.5-billion-euro bond repayment due on March 20 would be restructured, allowing Greece to avoid default.

It's a result that can be justified and that creates the preconditions to get Greece onto a sustainable return to economic health if the swap deal with private creditors is successful, German Finance Minister Wolfgang Schaeuble told reporters.

The vast majority of the funds in the 130-billion-euro program will be used to finance the bond swap and ensure Greece's banking system remains stable; some 30 billion euros will go to sweeteners to get the private sector to sign up to the swap, 23 billion will go to recapitalize Greek banks.

A further 35 billion or so will allow Greece to finance the buying back of the bonds. Next to nothing will go directly to help the Greek economy.

No one is pretending it will end Greece's problems. Figures last week showed its economy shrank 7 percent year-on-year in the last quarter of 2011, much more than expected, with further cuts likely to make matters worse.

The troika of European Commission, ECB and IMF, responsible for monitoring Greece's reform progress, carries out quarterly reviews and could decide Athens is not meeting its commitments at any one of them.

($1 = 0.7538 euros)

(Additional reporting by Luke Baker, Julien Toyer, Robin Emmott in Brussels, Daniel Flynn in Paris, Terri Kinnunen in Helsinki. Writing by Mike Peacock and Paul Taylor; editing by Elizabeth Piper)

Germany International Monetary Fund