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On the Construction and Use ov a Series ov Select Mortality Tabls to be Employd in Combination with the Institute HM(5) Tabl.(Continued)

Published online by Cambridge University Press:  18 August 2016

Extract

In Part I ov this paper I gave (vol. xxi, page 246) a tabl ov the finally ajusted probabilitys ov deth in the first five insurance years, for quinquennial ages at entry from 20 to 75. I gave also specimen mortality tabls for each ov those ages at entry, so ajusted as to join on, after the laps ov five years, to the Institute HM(5) Tabl; also values ov anuitys at 3 and 4 per-cent during the first five insurance years for lives entering at the same ages; and, lastly, commutation tabls calculated at 3 and 4 per-cent interest. I hav since found that ther is a misprint in the tabl ov the probabilitys ov deth, as q [35]÷3 shoud hav been printed ·010177 insted ov ·010077. This, however, is a mere misprint and dos not afect the other tabls. (It wil be notist that, insted ov riting q 35+3, as in the first part ov this paper, I now always enclose the age at entry in square brakets, thus [x].)

In order to make the new tabls practically useful, it is necesary to hav results, not merely for quinquennial ages at entry, but for every age. The first step to be taken for this purpos is the calculation ov the probabilitys ov dying in the first five insurance years, for every age at entry. These calculations wer made by means ov the formula explaind in my paper in the number ov this Jurnl for last July, in which I gave (see page 280) the actual work ov interpolating between q [30]+3 and q [40]+3. But for the two quinquennial intervals at the beginning and at the end ov the series, namely, from age 20 to 30 and 65 to 75, I uzed constant fifth differences insted ov fourth differences as explaind in my paper. Whenever the calculated probability exceeded that acording to the HM(5) Tabl, the latter was substituted.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1881

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References

page 408 note * Mr. Spens has givn only the anuitys; but it is so simpl a proces to deduce the premiums from them, that I think I may properly speak ov the premiums as being calculated by Mr. Spens.

page 433 note * We shoud hav got a closer agreement if, insted of taking the value ov V([36]).[35]+1) at .00495 according to Tabl 10, we had taken the more correct value, .004955