Tables and Formulae for the Computation of Life Contingencies: With Copious Examples of Annuity, Assurance, and Friendly Society Calculations. Second Issue, with an Addendum ...
C. & E. Layton, 1870 - Annuities - 168 pages
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Tables and Formulae for the Computation of Life Contingencies: With Copious ...
Oliver Peter Gray
No preview available - 2016
9 Diff addends amount annuity application arithm Barrett cards Carlisle Table colog combination of lives commence common logarithmic Commutation Table complete mean duration computation consequently construct a table continual addition curtate mean duration Davies's Form deduced denote the present differences employed equal error example expression figures foregoing Formation of Column formula function give given logarithm Hence increased initial values interpolation inverse joint lives labour last place Log Log 1+x Log Log(l Log Log(l+ log.a log.B log.v Log(l+ lx+n manner method Milne mode Morgan mortality mortality table multiplication natural numbers number of lives obviously og.vpx oldest tabular age pair of lives passing to logarithms payments Penny Cyclopaedia portion present value Problem quantity rath required log requisite respect Scholium seven-figure shown single lives specified age subsist survive tabular argument tabular result tabular value tion type of operation unity verification whole number younger age
Page 36 - ... the application of the theory of computing the average duration of human life after any given age is founded on two assumptions. " Of these the first is that the experience of the future will accord with that of the past ; that is to say, that what ratio soever may have been found to exist in times past between the number surviving and the number dying in a given time, out of a specified number of individuals observed upon, the same ratio will be found to subsist in time to come between the number...
Page 80 - B dedepends ; if, moreover, TT denote the probability of a payment of B being received in the first year, and II the probability of the single life, or of all the lives, on which that benefit depends, surviving a year ; — then will the following equation always subsist : — For, if the benefit...
Page 69 - Expec." at a specified age, considered as a term of years, is more likely than any other term to be the actual duration of that life ; and another is that it denotes a term of years which the life in question is as likely to survive as not. Neither of these notions is correct. The first would imply that the year in which a life is most likely to fail is that in which its
Page 189 - All the entries of the same kind — direct and inverse — are brought together, the whole of the logarithms being found before a single natural number is taken out. We consequently proceed right through the table; and as we proceed, we find two, three, four, and even as many as six and eight entries on the same opening. At the close, moreover, the taking out of the numbers may, if necessary, be turned over to an assistant. On the other hand, when the common tables are used, direct and inverse entries...
Page 90 - I.) the present value of £1 to be received at the same time provided (x) be then alive, the difference between these two is evidently the present value of £l to be received a year hence if (x) be then dead.
Page 1 - All mathematical tables consist of two series of corresponding values, each value in either series having a value corresponding to it in the other.
Page 119 - XI. —To find the present value of a life assurance of £ 1 on (x) ; that is, of £1 to be received at the end of the year in which (x) dies, whenever that event may happen.
Page 101 - ... to be paid at the end of the year in which (x) dies, provided he shall have been survived by (y). This is the benefit whose present value is denoted by h^—, (192).
Page 69 - ... term, to be the actual duration of that life; and another is, that it denotes a term of years which the life in question is as likely to survive as not. Neither of these notions is correct. The first would imply that the year in which a life is most likely to fail is that in which its " expectation