Practical Lessons in Actuarial Science; An Elementary Text-Book, Containing, Also, All Mortality Tables That Have Ever Been Standard Anywhere, With Corresponding Commutation Columns
Practical Lessons in Actuarial Science; An Elementary Text-Book, Containing, Also, All Mortality Tables That Have Ever Been Standard Anywhere, With Corresponding Commutation Columns
Miles Menander Dawson
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(aj-,) ^ M The first part of this annual premium is also payable for life of X or for n years; the second part for the joint lives or n years. For an annuity certain of m + i payments, the first due at end of year in which x dies, add ,|A, and „|Px, re- spectively. In computing such premiums the numerator of the sec- ond part may be derived from one mortality table, repre- senting experience among annuitants, and the other factors from another mortality table representing experience among insur...ed lives. Digitized by CjOOQ IC CONVERSION FORMULAS, JOINT LIFE, SUC- CESSIVE LIVES AND SURVIVORSHIP ANNUITIES. We have seen that there are subtle relations between all of these benefits. It remains to gather them together as far as may be. Thus we have a = a^ 4- ay ~ a^ = a, + a,|y = a, — a,, a.l.or Ai, (a, ) = Al, (l.a,) + AL, (..a, ) Al,(|.a,) =Al,(a,)-A;,(Ja,) Ai,(Ja,)=Ai,(a,)-Ai,(l.a,) Pa. I, or Pi, (a, ) ^ K(\.^ ) + K (J*,) Pi,(l.a,) = P^(a,)-Pi,(Ja,) P.r(,|a,) = Pi.K)-Pi7(l.a,) The inter-relations : A=i.A + .|A I.A = A-.|A .|A = A-|.A P=I.P + .iP ' l.P = P-JP .|P = P-|.P Digitized by CjOOQ IC Practical Lessons in Actuarial Science.
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