. Journal . Contributions to be made to an [April Following the same process as that by which we obtainedformula (3), we get the following formula for the value of thechildrens annuities which become payable at the decease of afunctionary of the age .r. ^x = y(CxCcx+Cx + \ + i) (6) Lastly, the process by which we obtained formula (4) gives us D. ^^ as the single premium which a functionary of age x muslpay, in order to secure, for each of his children who surviveshim, and is under 18 at his death, an annuity payable bymonthly instalments up to that age. For the annual premium payable in ad
. Journal . Contributions to be made to an [April Following the same process as that by which we obtainedformula (3), we get the following formula for the value of thechildrens annuities which become payable at the decease of afunctionary of the age .r. ^x = y(CxCcx+Cx + \ + i) (6) Lastly, the process by which we obtained formula (4) gives us D. ^^ as the single premium which a functionary of age x muslpay, in order to secure, for each of his children who surviveshim, and is under 18 at his death, an annuity payable bymonthly instalments up to that age. For the annual premium payable in advance during the lifeof the member, the formulas will be respectively— p _z;-42(C,W,) ^wx — and for a premium ceasing in 7i years n^tcx — • JNar+M-i ^X-\ + H-l If it should be further required that the premium shouldcease on the members invalidity, the annuity-value would haveto be calculated by a combined mortality and invalidity table. 77 Rai/yvays.: Ungraduated. S-hsche Pii d according to Stafishcs of the JVorwegHfiffaHwayi accordmgfo D graduated 1 according to the Norwegian Census I87Saccording to Statistics of . Bergisch fiirhschg f^seniTsfin 1906.] Annuity Fund for Widows and Children. 209 Table III. Probabilities of heing Married, and of having Children underAge 18; also Average Ages of Wives. Age of Member Probability of being Married (((!)x100 according to Probability of having Children under Age 18 (f) X100 according to Average Age of Wife according to SchjoU Belim SclijoU Behm Scbjoll(adjusted) Behm (1) (2) (3) (4) (5) (C) (7) 17 5 -1 20 18 1-5 -4 ... 21 19 30 1-5 22 20 5o •41 3-0 ■78 22 28 21 9-0 2-13 55 1-74 23 24 22 13-5 5-oO 9-5 3-84 24 23 23 19-5 10-65 15-0 7-44 24 24 24 27-0 18-66 22-0 12-41 25 ! 24 25 360 28-96 30-0 19-32 26 25 26 44-5 40-02 38-U 28-04 27 i 26 27 52-5 51-01 45-5 37-80 27 1 26 28 60-0 61-68 52-5 47-89 28 27 29 66-5 70-65 59-0 57-53 29 28 30 72-0 81-72 60-0 65-27 29 28 31 765 83-82 70-4 72-00 30 29 32 800
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