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

After a marathon 12 hours of talks through the night, euro zone officials said ministers had agreed measures to cut Greece's debt to around 121 percent of gross domestic product by 2020, close to their original target of 120, after negotiators for private bondholders offered to accept a bigger loss to help plug the funding gap.

Agreement on a 130-billion-euro rescue package with strict conditions attached will help draw a line under months of uncertainty that has shaken the currency bloc, and avert an imminent bankruptcy.

"The financial volume (of the Greek package) is 130 billion euros and debt-to-GDP (will be) 121 percent. Now it's down to work on the statement," one official involved in the negotiations told Reuters. Another confirmed the two figures.

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

A report prepared for ministers by EU, European Central Bank and IMF experts, obtained exclusively by Reuters, said Greece would need extra relief to cut its debts near to the official debt target 2020 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.

"Given the risks, the Greek program may thus remain accident-prone, with questions about sustainability hanging over it," the 9-page confidential report said, highlighting the fact that Greece's problems are far from over.

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

Greece will have around 100 billion euros of debt written off as banks and insurers will swap bonds they hold for longer-dated securities that pay a lower coupon.

Private sector holders of Greek debt are expected to take losses of 53.5 percent or more on the nominal value of their bonds as part of a debt exchange that will reduce Greece's debts by around 100 billion euros.

Previously they had agreed to take a 50 percent nominal writedown, which equated to around a 70 percent loss on the net present value of the bonds.

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.

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

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Euro zone crisis in graphics http://r.reuters.com/hyb65p

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DOUBTS OVER COMMITMENT

Skeptics question whether a new Greek government will stick to the deeply unpopular program after elections due in April, and believe Athens could again fall behind in implementation, prompting exasperated 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, International Monetary Fund Managing Director Christine Lagarde and ECB President Mario Draghi all attended the Brussels talks in a sign 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.

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: 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 will allow Greece to finance the buying back of the bonds, and 5.7 billion will go to paying off the interest accrued on the bonds being traded in. Next to nothing will go directly to help the Greek economy.

Those numbers could change in the final analysis given the scramble to meet the overall objective of reducing Greece's debts from 160 percent of GDP to around 120 by 2020.

Earlier, euro zone sources said national central banks in the currency bloc could restructure Greek bonds held in their investment portfolios in the same way as private investors, cutting Athens' debt by 3.5 percentage points.

If the ECB were to forego profits on its Greek holdings, that would raise another 5.5 percentage points of GDP, the report showed.

The deal will provide immediate relief to Athens and financial markets but 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.