EXPECTATION OF LIFE, in the doctrine of life annuities, is the ſtate, or number of years of life, which a perſon of a given age may, upon an equality of chance, expect to enjoy.
By the expectation or ſhare of life, ſays Mr. Simpſon (Seleſt Exercises, p. 273), is not here to be underſtood that particular period which a perſon hath an equal chance of ſurviving; this laſt being a different and more ſimple conſideration. The expectation of a life, to put it in the moſt familiar light, may be taken as the number of years at which the purchaſe of an annuity, granted upon it, without diſcount of money, ought to be valued. Which number of years will differ more or leſs from the period abovementioned, according to the different degrees of mortality to which the ſeveral ſtages of life are incident. Thus it is much more than an equal chance, according to the table of the probability of the duration of life which the ſame author has given us, that an infant, juſt come into the world, arrives not to the age of ten years; yet the expectation or ſhare of life due to it, upon an average, is near twenty years. The reaſon of which wide difference is the great exceſs of the probability of mortality in the firſt tender years of life, above that reſpecting the more mature and ſtronger ages. Indeed if the numbers that die at every age were to be the ſame, the two quantities above ſpecified would alſo be equal; but when the ſaid numbers become continually leſs and leſs, the expectation muſt of conſequence be the greater of the two.