Have you ever had trouble doing arithmetic? You might take some comfort from an accountant's plight at Fidelity Investments, the world's largest mutual fund company.

Fidelity, in a letter to shareholders of the huge and venerable Magellan Fund, has finally offered up a detailed account of just why it had to renege last month on its estimate that Magellan shareholders would get $4.32 a share in a year-end payment.

An accountant, the letter now reveals, mistakenly omitted a minus sign while doing a tax calculation, turning a $1.3 billion loss into a $1.3 billion gain.

It's the kind of simple math error anyone could make, but that no one expects to occur at Fidelity, which manages $300 billion in funds with state-of-the-art computers and top investment managers.

"Some people have asked how, in this age of technology, such a mistake could be made," wrote J. Gary Burkhead, managing director of Fidelity Investments. "While many of our processes are computerized, the requirements of the tax code are complex and dictate that some steps be handled manually by our tax managers and accountants, and people can make mistakes."

"I think this is one of the reasons," said industry watcher Michael Lipper, "that there are erasers on pencils."

But if that mystery was solved, another remains: Why did Fidelity, known for its marketing savvy, wait so long to provide these details? When the error was discovered last month, Fidelity issued only a cryptic press release, sending the media and some industry analysts into a frenzied attempt to determine whether there was some larger systemic breakdown at the firm.

"It caused unnecessary anxiety," said Lipper, president of the research firm Lipper Analytical Services Inc. "I think it's a case study in public relations: that a series of incomplete facts without an ability to speak further suggests to many people that things are much worse."

The Fidelity letter, which was being received by shareholders this week, seemed to dispel the earlier concerns about the firm's internal systems and controls.

Magellan, the world's largest mutual fund with $36 billion in assets, has 3 million accounts. Because of its size and reputation -- established by legendary mutual fund guru Peter Lynch in the 1980s -- Fidelity has long been a lightning rod for attention in the business, and this case wasn't any different.

Some industry analysts wondered whether Fidelity had been lucky to avoid the kind of public relations fiasco that recently hit Intel Corp. when it continued to insist to customers that the bug in their computers' Pentium chip was not a problem that should concern them.

Fidelity said, however, that Burkhead's letter had been in the works for some time.

"As soon as it happened, we knew that we were going to communicate to our shareholders in writing," said spokeswoman Constance Hubbell. "A lot of people didn't understand fund distributions. There was a general lack of knowledge... . In some cases, particularly overseas, there were inaccurate and wrong stories."

Fidelity refused to identify the accountant or to say whether he or she still held a job at the company. But to some, the mere fact that a lonely pencil pusher had wreaked such havoc was almost endearing -- a triumph for those who failed at math, can't balance their checkbooks or figure out their taxes.

"There is some carrying over from Dickens's day," said John Coffee, a professor of securities law at Columbia Law School. "We still have that sense that somewhere up there, Bob Cratchit is still adding up a column of figures."