The last-ditch effort to save the banking system in Cyprus should bring a rally when U.S. stock markets open on Monday, according to several investment managers.

Cyprus and its international creditors agreed early Monday on key elements of a deal for a 10 billion euro ($13 billion) bailout. Cyprus’ second-biggest bank, Laiki, will be restructured, and holders of deposits exceeding 100,000 euros will have to take losses, a European Union diplomat said. The diplomat spoke on condition of anonymity pending the official announcement.

It was unclear just how big of a hit big depositors will have to take, but the tax on deposits was expected to net several billion euros, reducing the amount of rescue loans the country needs.

U.S. investors won’t care too much about who takes losses in Cyprus, as long as there’s a bailout that stops the run on banks in the Mediterranean island nation and keeps the eurozone stable, said Karyn Cavanaugh, market strategist at ING Investment Management in New York.

“If this works out, regardless of the terms, this is going to be good for the market,” she said Sunday night.

The tax on large deposits likely will be 10 to 20 percent, in order to raise about $7.5 billion, said Jack Ablin, chief investment officer for BMO Private Bank in Chicago. The move should be well received by U.S. investors because it’s the third bailout deal in the eurozone, including Greece and Spain, and in each case the countries have agreed to austerity plans.

“I suspect investors will take that news pretty well,” he said.

The Dow Jones industrial average dropped more than 90 points Thursday in part on fears that the crisis in Cyprus will intensify. But it rebounded and erased the loss on Friday.

Late Sunday, Dow Jones industrial futures were up 42 points to 14,501. The broader S&P futures added 6 points to 1,558.00 and Nasdaq futures rose fractionally as well. Japan’s benchmark Nikkei 225 gained 1.35 percent to 12,505.51 in early trading.

The European Central Bank had threatened to stop providing emergency funding to Cyprus’ banks after Monday if there is no agreement on a way to raise 5.8 billion euros needed to get a 10 billion euro rescue loan package from the International Monetary Fund and the other countries that use the euro currency.

If Cyprus fails to get a bailout, some of its banks could collapse within days, rapidly dragging down the government and possibly forcing the country of around 1 million people out of the eurozone. Analysts say that could threaten the stability of the currency used by more than 300 million people in 17 EU nations.

A plan agreed to in marathon negotiations earlier this month called for a one-time levy on all bank depositors in Cypriot banks. But the proposal ignited fierce anger among Cypriots and failed to garner a single vote in the Cypriot Parliament.

The idea of some sort of deposit grab has returned to the fore after Cyprus’ attempt to gain Russian financial aid failed this past week, with deposits above 100,000 euros at the country’s troubled largest lender, Bank of Cyprus, possibly facing a levy of up to 25 percent.

Monday’s deal between Cyprus, the International Monetary Fund and the European Commission still needs approval by the 17-nation eurozone’s finance ministers. The deal could still be scuttled if Parliament rejects the tax on depositors, said Dimitri Papadimitriou, president of the Levy Economics Institute of Bard College.

And Cavanaugh said any glitch that thwarts the deal could still cause U.S. markets to plunge later. She’s still concerned that the U.S. economy, with recent weak corporate earnings, may be hurt by economic troubles in Europe. She’s advising investors to be defensive, staying in the market but moving some of their portfolios into bonds.

However, Ablin said tiny Cyprus shouldn’t have much of an impact on U.S. markets short of a total default.

“We’ve been through a lot, and the euro has not yet fallen off the table,” he said. “I guess the conventional wisdom is the euro can sustain a big setback in Cyprus and still continue to move forward.”