## A treatise on the valuation of life contingencies, Volume 1 |

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20 years hence A's death aged 20 aged 23 aged 30 aged 50 alive annual premium annuity of 200 annuity payable arranged Article assurance becomes beginning birth calculation claims column combinations compute the value Construct continue couples dead deferred differences discount divided endowment expectation expression formula four fraction function Give Give the formula given increase integral interpolation interval joint lives jointly lb lc letters limits logarithms multiplying natural nominees number of payments observe obtain occur paid payable 20 person now aged pla+1 present value previously purchase represent Required the annual Required the present Required the value result succession suppose survivors symbol taking the sum Thence third transactions true wherefore whole write

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Page 63 - Therefore, a written promise to pay a certain sum of money at the death of a party to the instrument, or at a limited time after the death of such party, or of a third person, is a valid Promissory Note ; because it must inevitably become due at some future time, since all men must die, although the exact period is uncertain.

Page 38 - NJ+,_I,J_I, and so on. = y, the second numerator must be 16. The present value of £l to be paid on the death of (.r), provided he die within n years after y. From the preceding result subtract the present value of £l payable at the death of (x), if (y) survive. (See No. 9.) 17. The present value of £(1) to be paid at the death of (x), if he survive (y). From the present value of an assurance on the life of...

Page 38 - ... value of £l payable at the death of (x), if (y) survive. (See No. 9.) 17. The present value of £(1) to be paid at the death of (x), if he survive (y). From the present value of an assurance on the life of (a;) subtract the result of (9), or the value of £l to be paid at his death, if y survive. 18. The present value of £l to be paid at the death of (x), if more than n years after the death of (y). From the present value of an assurance of £ 1 on the life of (x) subtract the result of (15)....

Page 125 - ... parts, as it is generally conceded that no matter when the death occurs we are entitled to the full year's cost for that policy year. Inasmuch as we are dealing with calendar years and not with policy years, let us look at the matter on that basis. Taking the whole year's deaths during the calendar year on the supposition of a uniform distribution of deaths during the year (which is in accord with mean reserve valuations) we can assume that one-half will die before the anniversary and one-half...