Ulpian's life table is an ancient Roman annuities table. It is known through a passage, originating from the jurist Aemilius Macer, preserved in edited form in Justinian's Digest. The table appears to provide a rough outline of ancient Roman life expectancy. Although it is not clear what population the table refers to, or how its data was gathered, Richard Duncan-Jones has suggested that it refers to slaves and ex-slaves, who were often the object of testamentary maintenance grants. Aemilius Macer probably lived in the 230s AD. He records the table in his systematic commentary on the lex Julia de vicesima hereditatium, an Augustan law of 6 AD that put a 5 percent tax on inheritances. Despite its many numbers, the fragment does not appear to be afflicted by any serious textual corruption. Table Macer's text provides two figures: a forma, or schedule, presented by Ulpian (d. 223), and a customary (solitum est) schedule that antedates Ulpian's. The forma is described as a means of calculating tax for alimenta and usufructs. The age of the legatee is checked against the table; the figure recorded on the table is multiplied by annuity's annual value. Five percent of this last figure is what is owed in tax. Ulpian's life table gives figures broadly consistent with the Coale–Demeny Model West life table: female life expectancy at birth is 22.5 years, male life expectancy is 20.4. Its mortality figures are thus higher than those of most models, though the statistical flaws in the evidence itself has encouraged interpretative caution. Although, among moderns, "life expectancy" tends to mean "the average number of years lived after age x", the table figures probably represent median life expectancy (i.e., the number of years elapsed before half the selected population is dead). After childhood, the two figures are quite close, but childhood mortality causes the figures for the first years of life to diverge. The figures given are too high to represent the predicted market value of the annuity at a conservative rate of return on capital (assuming the annual rate of 4%, the present value of an annuity for a person with a lifespan of sixty years would be approximately twenty-three times the annual value of the annuity, compared to 30 given in the table for the first group). The table therefore most likely represents the rate at which the annual tax payment on the annuity was staggered: a