Although the interest rate on the notes has remained constant, other things have changed. The road, called Central Avenue when it was built, is now known as Jerome Avenue after Churchill’s grandfather, Leonard W. Jerome.  The site of the racetrack, known as Jerome Park and in its day a magnet for all manner of society swells, is now a reservoir.  And the two towns that originally issued the bonds, Morrisania and West Farms, then incorporated villages outside the city limits, no longer exist, which is how New York City ended up holding the bag of debt after annexation.  As generation followed generation, the 100 or so outstanding notes with a combined face value of $66,000 have all but been forgotten, aside from an occasional newspaper account. But the Bank of New York Mellon, which administers the bonds for the city, has a record of the 39 bondholders who own them and has been mailing them interest checks twice a year.  Two of the active bonds are in the Museum of the City of New York, which has held them since 2001. They were a gift from Mr. Lebenthal, who had held them for 30 years after buying them through a broker from the Poughkeepsie Rural Cemetery. The cemetery had gotten them from Martha B. Jones in 1914. She took possession of them in 1881.  City officials declined to identify the other bondholders, citing privacy concerns, so it is hard to say how they have kept track of a flimsy piece of paper that would not pay off for several lifetimes.  But the difficulty of the task can be seen in the fact that city officials can no longer locate the heavy bound ledger in which, in neat Victorian script, their predecessors kept track of the bonds by serial number and purchaser name.  The ledger, which the city displayed as recently as 1980, became superfluous when record keeping for the bonds was transferred to computers.  Not all the ledgers are missing: “We do have some dating back to the early 1900s,” Regina Fleszar, the director of investor relations for the city comptroller, wrote in an e-mail message. “But at the moment cannot find the one containing the 1868 bonds.”  What is known about the bonds is that they were the handiwork of a wily 19th-century financier and a couple of cash-strapped towns that schemed to implement a public work at the expense of their wealthy, gleaming neighbor.  The financier, Mr. Jerome, was a successful Wall Street stock speculator and a pioneer of American thoroughbred racing at a time when harness racing was more popular. To cultivate his hobby, he built the track. To ensure its success, he concocted a plan to lure upper-crust New Yorkers to what was then the suburbs by naming races after them, including the banker and socialite August Belmont (yes, the Belmont Stakes was first run in the Bronx).  “Jerome wanted to bring horse racing back as the sport of kings,” said Lloyd Ultan, the Bronx borough historian. “To do that, he knew he had to attract his wealthy friends to the racetrack. And to do that, he needed a road from the upper part of settled New York — what is now Midtown Manhattan — to where the racetrack was.”  There was a catch: West Farms, where the track was, and Morrisania, which would share the road, could not afford the improvement. So the towns issued bonds, backed by Mr. Jerome, with unusually long maturities, gambling that their rapidly expanding neighbor would soon absorb them, and their debt.  “Everybody knew because of the shift of population northward, it was only a matter of time before the City of New York was going to annex the territory,” Mr. Ultan said. “So they issued these bonds with the date of redemption so far in the future because they figured that once the City of New York annexed their town, then the City of New York would assume the payment of the bonds — which is exactly what happened.”  At its peak, Jerome Park attracted thousands of spectators who traveled by horseback, four-in-hand coach or train to fill the park’s clubhouse, grandstands and the surrounding knolls and bluffs to watch horses pound around the kidney-shaped track. The city condemned the park in 1890 to make room for the Jerome Park Reservoir.  In addition to his fame as financier, sportsman and bon vivant — at one point, he was listed as a “considerable owner” of The New York Times, according to his obituary — Mr. Jerome was known for his three daughters, and particularly for his middle daughter, Jennie.  “She was known as an international beauty, and she did what the daughters of wealthier Americans did in those days,” Mr. Ultan said, marrying the son of an impoverished European aristocrat. “Her son was Winston Churchill.”  Since 2000, the Bank of New York Mellon has administered the bonds for the city. This decade, four of the bonds have matured — one every other March beginning in 2001 — but no one stepped forward to claim the money.  “Our concern when we took over the business was seeing the age of some of the securities,” said Michael Hieb, a vice president of the bank. “We were scratching our heads.”  The typical municipal bond sold currently matures in 30 years.  Today, the city pays the interest on the outstanding bonds for the Bronx road twice a year, on March 1 and Sept. 1, in increments of $35 or $17.50, depending on the denomination of the bonds, which have a face value of $1,000 or $500. The total cost is $4,620 each year.  The city comptroller is not certain how much debt was originally issued through the bonds, but a previous estimate put the figure at $278,000, reflecting the fact that hundreds of bonds were probably sold originally, some of them with shorter maturities. Today, nearly 100 of the bonds, with a face value of $66,000, have yet to mature. By the time they do, the city will have paid out nearly $1 million in interest.  That debt is not large by modern standards, when the city currently borrows about $7 billion a year and has an annual debt service of about $3.7 billion.  But in the early years after the Civil War, when money stretched further, $70 a year in interest was a substantial sum, enough for a down payment on a middle-class house of good construction, which cost about $300.  “People who bought the bonds might say: ‘This is really cool; generations of my family will benefit from this,’ ” said Richard Sylla, a financial historian and a trustee for the Museum of American Finance. “For the issuer, if you don’t have to pay back the principal for 100 or 200 years, that’s an advantage, too.”  A version of this article appears in print on , on Page A24 of the New York edition with the headline: That’s What You Call Investing for the Long Term. Order Reprints| Today's Paper|Subscribe
Some municipal bonds issued in 1868 to build a road to a long-vanished racetrack are only now coming to maturity; some others in the same offering won’t until 2147.