_Use_ III. But if it be enquired at what number of _Years_, it is an even Lay that a Person of any _Age_ shall die, this Table readily performs it; For if the _number_ of Persons _living_ of the _Age_ proposed, be _halfed_, it will be found by the _Table_ at what Year the said _Number_ is reduced to half by _Mortality_; and that is the _Age_, to which it is an even Wager, that a Person of the _Age_ proposed shall arrive before he _die_. As for Instance; A Person of 30 Years of _Age_ is proposed, the number of that _Age_ is 531, the half thereof is 265, which number I find to be between 57 and 58 Years; so that a Man of 30 may reasonably expect to live between 27 and 28 Years. _Use_ IV. By what has been said, the _Price_ of _Insurance_ upon Lives ought to be regulated, and the difference is discovered between the _Price_ of insuring the _Life_ of a _Man_ of 20 and 50. For Example; It being 100 to 1, that a Man of 20 dies not in a Year, and but 38 to 1, for a Man of 50 Years of Age. _Use_ V. On this depends the Valuation of _Annuities_ upon _Lives_; for it is plain, that the _Purchaser_ ought to pay for only such a part of the Value of the _Annuity_, as he has Chances that he is living; and this ought to be computed yearly, and the Sum of all those yearly Values being added together, will amount to the Value of the _Annuity_ for the _Life_ of the Person proposed. Now the present Value of Money payable after a Term of Years, at any given Rate of Interest, either may be had from Tables already computed; or almost as compendiously, by the Table of Logarithms: For the Arithmetical Complement of the Logarithm of Unity, and its yearly Interest, (that is, of 1,06 for Six _per Cent._ being 9,974694.) being multiplied by the number of Years proposed, gives the present Value of One Pound payable after the end of so many Years. Then by the foregoing Proposition, it will be as the number of Persons living after that Term of Years, to the number dead; so are the Odds that any one Person is alive or dead. And by consequence, as the Sum of both, or the number of Persons living of the _Age_ first proposed, to the number remaining after so many Years, (both given by the Table) so the present Value of the yearly Sum payable after the Term proposed, to the Sum which ought to be paid for the Chance the Person has to enjoy such an _Annuity_ after so many Years. And this being repeated for every Year of the Person's Life, the Sum of all the present Values of those Chances is the true Value of the Annuity. This will without doubt appear to be a most laborious Calculation; but it being one of the principal Uses of this Speculation, and having found some _Compendia_ for the Work, I took the pains to compute the following Table, being the short Result of a not ordinary number of Arithmetical Operations: It shews the Value of Annuities for every Fifth Year of Age, to the Seventieth, as follows.