The Doctrine of Life-annuities and Assurances, Analytically Investigated and Practically Explained: Together with Several Useful Tables Connected with the Subject |
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Common terms and phrases
aged 40 aged 46 alluded annual payments assurance bability cent collateral series consequently COROLLARY decease deduced deferred annuity denote the value determine the value died last Diff different events divided Example expectation of receiving expression extent of human extinction find the value formula found equal give the expectation given sum payable given term joint lives aged l x l y l z lives aged 20 lives fail living as observed longest lx ly lz lxı ly₁ method Moivre Morgan multiplied by sv Northampton number of lives number of persons oldest Parcieux preceding Prob probabilities of living problem purchase quantities Ques Question rate of interest receiving the sum reckoning interest reversionary annuity SCHOLIUM Simpson single payment SOLUTION table of observations temporary annuity three given lives three joint lives three lives total present value unity added utmost extent value required values of annuities whence the following
Popular passages
Page 269 - But this is too gentle a censure. There is reason to believe that worse principles have contributed to their rise and support. The present members, consisting chiefly of persons in the more advanced ages, who have been admitted on the easiest terms, believe that the schemes they are supporting will last their time, and that they will be gainers. And as to the injury that may be done to their successors, or to younger members, it is at a distance, and they care little about it.
Page 272 - ... of the churchwardens and overseers of the poor for the time being, by the direction of the vestry or select vestry, for the benefit of the parish, in the manner herein-after provided.
Page 20 - When the contrary happens, as is generally the case in towns, they give the probabilities of living too high. But tables formed from the latter of these data, are subject to no errors. They must be correct, whatever the fluctuations are in a place, and how great soever the inequalities may be between the births and burials.
Page 15 - ... present work, in order to prevent any misunderstanding in the terms which are occasionally made use of. § 2. The probability of the happening of any event is to be understood as the ratio of the chances by which that event may happen, to all the chances by which it may either happen or fail, and it may be expressed by a fraction, whose numerator is the number of chances whereby the event may happen, and whose denominator is the number of chances whereby it may either happen or fail. Thus if...
Page 16 - ... expected by the fraction which represents the probability of obtaining it. Thus, if a person has a chances of obtaining, and b chances of losing a certain sum of money, the present value of which is equal to s, then will * X --—, denote his expectation of receiving such sum, and will be the true value of his interest therein*. * These principles m.iy be more familiarly explained by the following example.
Page 151 - ... tickets are already sold for this year, the season tickets are sold. By the time the Commissioner comes down to testify, it will be before you pass the bill which I am sure will be passed. He will come down here and throw statistics at you, and then you will pass the bill and it will look fine after the end of the first year, but at the end of the second or third year he can use this as a crutch for pay-TV.
Page 275 - I have had any information concerning them, they are founded on plans equally inadequate, hiving been formed just .as fancy has dictated, without any knowledge ,of the principles on which the values of re•versionary annuities ought to 'be calculated. The motives which influence the contrivers of these institutions, may be laudable ; but they ought, I think, to have informed themselves better.
Page 165 - But since the same lives are not involved in the same contingencies, I shall (in order to prevent any misunderstanding on this subject) prefix his own statement of the problem. " To determine the value of a given sum payable on the contingency of C's surviving B, provided the life of A shall be then extinct.
Page 18 - Two Events are independent, when they have no connexion one with the other, and that the happening of one neither forwards nor obstructs the happening of the other. Two Events are dependent, when they are so connected together as that the Probability of cither's happening is altered by the happening of the other.
Page 150 - To determine the value of a given sum payable on the decease of A or B, should either of them be the second or third that shall fail of the three A, B, and C.