FRANKFURT, Germany — Imagine a mortgage that pays you the interest, not the other way around. Or a savings account where it’s the bank, not the saver, who collects interest.

Welcome to the upside-down world of ultra-low and negative interest rates that is taking hold in many parts of the world where economic growth has been sluggish. Now more than a decade old, economists think it could be a feature of the global economy for years to come and change the way people save and invest.

“This will mean that we must save more, work longer, and expect less,” said Olivia Mitchell, an economics professor at Wharton Business School at the University of Pennsylvania.

The latest chapter is the drop in interest rates on some bank deposits below zero as central banks, particularly in Europe and Japan, try to support the economy amid uncertainty about trade by making borrowing cheaper to spur spending and investment. Official data released Friday showed that Germany’s growth ground to a halt at the end of last year.

Economists think there are also longer-term factors causing low rates, such as aging populations in rich countries and high rates of savings in China and other emerging economies.

Low rates first hit in the wake of the global financial crisis. The U.S. Federal Reserve, Bank of England, Bank of Japan, and European Central Bank slashed rates close to zero. In 2014, the ECB went negative.

Ultra-low rates have helped push up stock markets to record highs, as vanishing returns on safe assets lead to a search for returns elsewhere. Pushing people to invest in riskier assets is part of the stimulus effect central banks are trying to impart. But there are also fears that very low rates can cause markets to bubble up, and crash back down with painful consequences. So far, the dire predictions haven’t come true. The current bull market in U.S. stocks turns 11 years old March 9.

In Germany, some banks are now telling companies and others with large amounts of cash that they must pay a rate on large deposits instead of accruing interest. The penalty typically applies to big accounts, such as more than 500,000 euros ($555,000), according to financial website Biallo.de. Banks are doing this because they themselves have to pay a 0.5% penalty on deposits they hold at the European Central Bank. If banks can’t find a home for depositor money, it winds up in their ECB holdings and results in their being charged.

Small depositors like individual consumers are so far not being charged on savings. The idea is politically toxic, especially in Germany.

But the low rate environment raises questions about preserving wealth, especially for those trying to save for retirement. German newsmedia are full of stories about “penalty rates”and criticism of the European Central Bank for, as they put it, expropriating savers.

Gerhard Michel, a financial coach in Duesseldorf, says people need to be aware that inflation eats away at savings even in more normal times, though people may be less aware of it when rates are above zero.

“If you look at it historically, people with savings accounts never had any kind of interesting performance,” he said. “The inflation rate ruins any returns on the government bond market or the savings market — and it has always been that way historically. What shocks people now is that people must say the word zero, or even negative, interest.”

Michel, who is 53, teaches his coaches about value investing, a more time-consuming approach that analyzes financial statements to look for companies the market may be underestimating.

His approach with his own money: “I will buy stocks until the end of my days.”

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