(Reuters) – Markets around the world are set to rally on Monday in response to European governments’ agreement on a massive financial safety net for Greece, though the country will still struggle to resolve its debt crisis.

After two previous announcements this year failed to calm the markets, euro zone finance ministers on Sunday overcame deep political divisions and revealed a plan that appears generous and detailed enough to ease fears of a Greek debt default.

The ministers approved a mechanism for their countries to extend up to 30 billion euros ($40 billion) of emergency loans to Greece. Athens has not decided whether to apply for the aid, but many analysts think it will have to do so.

Together with at least 10 billion euros expected from the International Monetary Fund in the first year, Greece may receive the biggest multilateral financial rescue ever.

“I think it will be a big boost to all markets, not only Europe but in Asia and here in the U.S. as well,” said Alan Lancz, president of Alan B. Lancz & Associates, an investment advisory firm in Toledo, Ohio.

“It was one of the clouds that prevented the U.S. (stock market) from breaking through to new highs, so lifting this barrier will be a big positive. We have a lot of money on the sidelines globally and this could be a big catalyst to bring some of that money in.”

The existence of the safety net for Greece will help remove concern about a potential “domino effect” on other countries with fiscal problems, Lancz added. Debt prices of some weaker euro zone states such as Portugal have come under pressure.

The size of the package is on the high side of market expectations, and could prompt a violent rebound in Greek bond prices and bank shares this week because some financial institutions had been selling them short.

BOND YIELDS

The yield on Greece’s 10-year government bonds could plunge to near 6.5 or even 6.0 percent this week from 7.25 percent on Friday, analysts said.

Some predicted the euro, which has been hurt for months by concern that an eventual Greek default could force the country out of the single currency zone, might rebound to near $1.40 in coming weeks from $1.35.

Mark Waggoner, president of U.S. firm Excel Futures in Bend, Oregon, said the aid plan would help increase liquidity in Greek debt by making traders feel safer, and might make U.S. investors more willing to buy Greek bonds. He predicted global commodity prices would benefit.

Including the money expected from the IMF, the size of the aid package would be large enough to cover the remaining borrowing needs that Greece has declared for this year.

In fact, if the announcement of the package pushes Greek yields down sharply, Athens may be able to squeeze through a tricky period of debt refinancing over the next six weeks without actually accessing the package; it must raise about 11 billion euros by May.

A test of this will come on Tuesday, when Athens plans to sell 1.2 billion euros of Treasury bills.

LONG TERM

In the long term, however, markets are likely to remain worried about Greece’s ability to tackle its 300 billion euro debt mountain, which exceeds its annual economic output by a quarter — especially given the country’s deep recession.

This may make accessing the aid package inevitable, and leave Greek assets vulnerable to fresh speculative attacks if Athens seems to be failing to meet budget deficit-cutting targets agreed with the European Union.

“Having the program on the table may be enough to shore up confidence, but without the amount of cash needed, it’s just a matter of time before they have to ask to use it,” said Koon Chow, a strategist at Barclays Capital.

European Economic and Monetary Affairs Commissioner Olli Rehn said the three-year euro zone loans would carry an interest rate of about 5 percent.

While that is well below the current rate of about 7 percent that Greece would have to pay to borrow three-year money from the market, it is still several percentage points above the rates that healthy euro zone countries have to pay, and the additional interest cost is a major burden for Athens.

Marco Annunziata, chief economist at UniCredit Group, said Greece seemed likely to meet the EU’s fiscal targets for 2010 — but it would end this year in a deeper recession, with a still-high budget deficit close to 9 percent of gross domestic product, and having done little to restore its competitiveness.

“The challenge of combining robust economic growth with draconian fiscal adjustment, both essential to reach debt sustainability, remains a formidable one,” he wrote.

Another factor that may continue to worry euro zone markets, and prevent any extended rally by the euro, is structural weaknesses in the zone that have been exposed by the Greek crisis: sharp divergences in countries’ economic performances, and the difficulty that governments had in agreeing on a strategy to handle the crisis.

EU finance ministers will discuss ways to reduce divergences and improve coordination of economic policies at a meeting in Madrid late this week, but given their political differences and the complexity of any reforms to the zone’s rules, they may not make much progress.

(Additional reporting by Jan Strupczewski and Christopher Sanders; Editing by Andrew Torchia)