Several weeks ago, a senior official issued a statement saying: “The president got massive depreciation and tax shelter because of large-scale construction and subsidized developments. That is why the president has always scoffed at the tax system and said you need to change the tax laws. You can make a large income and not have to pay large amount of taxes.”

On Saturday, after further inquiries from The Times, a lawyer for the president, Charles J. Harder, wrote that the tax information was “demonstrably false,” and that the paper’s statements “about the president’s tax returns and business from 30 years ago are highly inaccurate.” He cited no specific errors, but on Tuesday added that “I.R.S. transcripts, particularly before the days of electronic filing, are notoriously inaccurate” and “would not be able to provide a reasonable picture of any taxpayer’s return.”

Mark J. Mazur, a former director of research, analysis and statistics at the I.R.S., said that, far from being considered unreliable, data used to create such transcripts had undergone quality control for decades and had been used to analyze economic trends and set national policy. In addition, I.R.S. auditors often refer to the transcripts as “handy” summaries of tax returns, said Mr. Mazur, now director of the nonpartisan Urban-Brookings Tax Policy Center in Washington.

In fact, the source of The Times’s newly obtained information was able to provide several years of unpublished tax figures from the president’s father, the builder Fred C. Trump. They matched up with Fred Trump’s actual returns, which had been obtained by The Times in the earlier investigation.

If the new tax information does not offer a new narrative of Mr. Trump’s career, its granular detail gives a precise accounting of his financial failures and of the constantly shifting focus that would characterize his decades in business. Here are some key takeaways.

1. Mr. Trump was deep in the red even as he peddled deal-making advice

“Trump: The Art of the Deal” came out in 1987. It became a best seller — and a powerful vehicle for the self-spun myth of the self-made billionaire that would ultimately help propel him to the presidency.

Mr. Trump has long attributed his first run of business reversals and bankruptcies to the recession that hit three years later, in 1990. But the new tax information reveals that he was already in deep financial distress when his master-of-the-universe memoir hit the shelves.

For Mr. Trump, the 1980s were a frenzy of acquisition and construction, buoyed by hundreds of millions of dollars of borrowed money. In 1985, for the first time, Forbes’s “rich list” included Mr. Trump individually, independent of his father. But his estimated net worth according to the magazine, $600 million, included the real estate empire Fred Trump still owned.

With Mr. Trump’s vast debt and other expenses on his properties — among them Trump Tower and the Grand Hyatt hotel in Manhattan, and two Atlantic City casinos — his fortunes were already on the way down. In 1985, his core businesses reported a loss of $46.1 million; they also carried over a $5.6 million loss for earlier years.

Because those businesses were generally created as partnerships, they did not pay federal income taxes themselves. Instead, their gains, and their losses, flowed onto Mr. Trump’s ledger. To put his results in perspective, The Times compared them with detailed information that the I.R.S. compiles on an annual one-third sampling of high earners. Most of them appeared, like Mr. Trump, to be businessmen who received what is known as pass-through income.

For 1985, the I.R.S. information indicates this: Only three individual taxpayers in the sampling reported bigger losses than Mr. Trump.

2. In multiple years, he appears to have lost more money than nearly any other individual taxpayer

The tax results for the years that followed trace an arc of continued empire building — and gathering loss.

He bought the Eastern Airlines shuttle for $365 million; it never made a profit, and he spent more than $7 million a month to keep it flying. His new Trump Taj Mahal Hotel and Casino, opened in 1990 with more than $800 million in debt, sucked revenue from his other casinos, pulling them along into the red.

And so, year after year, Mr. Trump appears to have lost more money than nearly any other individual taxpayer, according to the I.R.S. information on high earners — a publicly available database with taxpayers’ identifying details removed. Indeed, in 1990 and 1991, his core businesses lost more than $250 million each year — more than double those of the nearest taxpayers in the sampling for those years.

The tax code allows owners of commercial property to write down the cost of their buildings — a valuable tax shelter known as depreciation. In “The Art of the Deal,” Mr. Trump cited one of his Atlantic City casinos to show how it works. Built for $400 million and depreciated at a rate of 4 percent a year, he said, it could allow him to shelter $16 million in taxable income annually. But Mr. Trump’s example, meant to demonstrate the magic of depreciation, shows something else: Depreciation alone cannot account for the hundreds of millions of dollars in losses he declared on his taxes.

3. He paid no federal income taxes for eight of the 10 years

Business owners like Mr. Trump may also use their losses to avoid paying taxes on future income. Over the years, those losses rolled into a $915.7 million free pass, known as a net operating loss, that appeared on his 1995 tax returns, pages of which were mailed anonymously to The Times during the 2016 campaign.

The new tax information shows how Mr. Trump’s net operating losses snowballed, reaching $418 million in 1991. That was fully 1 percent of all the losses that the I.R.S. reported had been declared by individual taxpayers that year.

And the red ink continued to accumulate apace. In all, Mr. Trump lost so much money that he was able to avoid paying any federal income taxes for eight of the 10 years.

4. He made millions posing as a corporate raider — until investors realized he never followed through

For a time, Mr. Trump was able to stave off his coming collapse with the help of a new public role: He traded on his business-titan brand to present himself as a corporate raider. He would acquire shares in a company with borrowed money, suggest publicly that he was contemplating a takeover, then quietly sell on the resulting bump in the stock price. An occasional quote from a high-profile associate helped burnish the myth.

“He has an appetite like a Rocky Mountain vulture,” his stockbroker, Alan C. Greenberg, told The Wall Street Journal in 1987. “He’d like to own the world.”

From 1986 through 1989, Mr. Trump declared $67.3 million in gains from stocks and other assets bought and sold within a year.

But ultimately, the figures show, he lost most, if not all, of those gains after investors stopped taking his takeover talk seriously.

5. His interest income spiked in 1989 at $52.9 million, but the source is a mystery

Amid the hundreds of figures on 10 years of tax transcripts, one number is particularly striking: $52.9 million in interest income that Mr. Trump reported in 1989.

In the three previous years, Mr. Trump had reported $460,566, then $5.5 million, then $11.8 million in interest.

The source of that outlier $52.9 million is something of a mystery.

Taxpayers can receive interest income from a variety of sources, including bonds, bank accounts and mortgages. Hard data on the workings of Mr. Trump’s businesses is hard to come by. But public findings from New Jersey casino regulators show no evidence that he owned anything capable of generating that much interest. Nor is there any such evidence in a 1990 report on his financial condition, prepared by accountants he hired at his bankers’ request.

Mr. Trump’s interest income fell almost as quickly as it rose. By 1992, he was reporting only $3.6 million.

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