HVIDOVRE, Denmark — At first, Eva Christiansen barely noticed the number. Her bank called to say that Ms. Christiansen, a 36-year-old entrepreneur here, had been approved for a small-business loan. She whooped. She danced. A friend took pictures.

“I think I was so happy I got the loan, I didn’t hear everything he said,” she recalled.

And then she was told again about her interest rate. It was -0.0172 percent — less than zero. While there would be fees to pay, the bank would also pay interest to her. It was just a little over $1 a month, but still.

These are strange times for European borrowers, as if a wormhole has opened up to a parallel universe where the usual rules of financial gravity are suspended. Investors lent Germany nearly $4 billion this week, knowing they would not be fully repaid. Bonds issued by the Swiss candy maker Nestlé recently traded in the market for more than they will ever be worth.

Such topsy-turvy deals reflect the dark outlook for the region’s economy, as policy makers do whatever they can to revive growth, even taking interest rates below zero to encourage borrowing (and spending). In this environment, the simplest of banking tasks have become a curiosity.