In 1692, Parliament set out to raise a million pounds for the war against France by selling survivorship shares in a government tontine: pay in, name a life, and collect a dividend that grew as other subscribers' nominees died. The same statute provided that if the million wasn't fully subscribed by its own deadline, anyone still willing to pay in could take a plain annuity instead: fourteen pounds a year for every hundred pounds advanced, for as long as a named life lasted, yours or anyone else's you cared to nominate. The statute set that rate and the paperwork for proving the nominee still breathed. It never asked how old that life was. A newborn nominated under it drew the same terms as a man of sixty, because nobody selling annuities in England had the numbers to do otherwise.
Far from the sea on the River Oder, near the border of Germany and Poland, the city of Breslau had been doing something London and Dublin had not: recording, month by month, the age of every person who died there. Those tables reached the Royal Society, and Edmond Halley set out to make sense of them. London's and Dublin's own bills of mortality were useless for the purpose, he explained: both cities drew so many strangers who died there that funerals routinely outran births, and a standard population needs people who die where they were born. Breslau lay so far from the sea, he noted, that few strangers came to it.
From five years of entries, Halley worked out that of 1,238 children born in Breslau in an average year, 348 died before their first birthday, and only 890 lived to see it. He then worked out how many of the city's own people were alive at every age, 34,000 in all, and read that standing population as a stand-in for a thinning generation, an assumption of his own that Breslau held roughly steady, births running only a little ahead of burials. From it he could finally answer a question nobody selling annuities in England had ever actually worked out: the odds that a person of a given age would survive the year. A twenty-year-old's odds of doing so, he wrote, were 100 to 1; a fifty-year-old's, 38 to 1. Turned into a single price paid up front, a ten-year-old's remaining life was worth nearly thirteen and a half years of the annuity; a thirty-six-year-old's was worth eleven.
Then Halley turned his own table on the government's fund, the one paying fourteen pounds a year, flat, for any life. At that rate, he worked out, a buyer was paying for only seven years of annuity, whoever's name went on the form, while his own numbers put a ten-year-old's true worth at better than thirteen. For a nominee that young, the fund charged barely half what Halley's table said the annuity was worth, and he wrote that up as a great advantage to anyone putting money in.
Until his table, Halley wrote, the value of an annuity had been set only by "an imaginary Valuation." The men who had studied London's and Dublin's bills before him had said themselves what those records lacked: how many people were alive, and how old the dead had been. Breslau's register recorded the ages, and from five years of them Halley could estimate the rest. A life can be priced only as well as deaths are counted.