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Edmond Halley (1656-1742) was a remarkable man of science who made important contributions in astronomy, mathematics, physics, financial economics, and actuarial science. Halley was fortunate to have been born into a wealthy family and to have had a father who provided for a first-rate education for his son. Halley enrolled in Oxford University at age 17, stayed for three years and, without a degree in hand, set sail for St. Helena in the south Atlantic to observe and catalogue stars unobservable from Europe. The voyage took two years and, upon his return to London, he was elected to the Royal Society at age 22 for his St. Helena work. Halley became the editor of Philosophical Transactions (the journal of the Royal Society), an Oxford professor from 1704-20, and Astronomer Royal at Greenwich from 1720 to his death. Isaac Newton and Halley were friends, and he urged Newton to write what became the Principia Mathematica and assisted financially and editorially in its publication. Halley plotted the orbits of several comets. In particular, he conjectured that objects that appeared in 1531, 1607, and 1682 were one and the same comet that would reappear approximately every 75 years. He correctly predicted that the comet would return in 1758, and it was posthumously named in his honor after its reappearance at the predicted time. Halley made two forays into financial economics, demography, and actuarial science. The second work (1705, 1717) was on compound interest. He derived formulae for approximating the annual percentage rate of interest implicit in financial transactions and annuities. His first contribution (1693) was seminal and is the topic of this note. In this work, Halley developed the first life table based on sound demographic data; and he discussed several applications of his life table, including calculations of life contingencies.
Halley obtained demographic data for Breslau, a city in Silesia which is now the Polish city Wroclaw. Breslau kept detailed records of births, deaths, and the ages of people when they died. In comparison, when John Graunt (1620-1674) published his famous demographic work (1662), ages of deceased people were not recorded in London and would not be recorded until the 18th century.1 Caspar Neumann, an important German minister in Breslau, sent...