lated at 5 percent, the value of £100 nett annual income is as follows, for the ages specified: Annexed will be found complete tables of the values of annuities and reversions at 3 and 5 percent interest, and of annual premiums at 3 percent. A comparison of these with Mr. Brown's tables will, I think, show that sufficient reason exists for my having called attention to the subject. TABLE I, showing the Probabilities of Dying, also the NumbersLiving and Decrement, according to the Observations by the late Rev. John Hodgson, M.A., on 5088 Clergymen, Incumbents of Livings, &c., in England and Wales, of whom 3122 had Died. TABLE II.-Values of Annuities on Single Lives at 3 and 5 percent Interest. (First payment due at end of the Year.) TABLE III.-Present Values of an Unit payable at the end of the Year in which a Single Life may fail, at 3 and 5 percent Interest. TABLE IV.-Annual Premium for the Assurance of an Unit payable at the end of the Year in which a Single Life may fail, at 3 percent Interest. [We thought it right to communicate the above paper to Mr. Brown, and he has favoured us with the following letter on the subject.-Ed. J. I. A.] REV. JOHN HODGSON'S CLERGY LIFE TABLES. To the Editor of the Journal of the Institute of Actuaries. SIR,-In reply to Mr. Bowser's remarks on the above Tables, I beg to offer a few words of explanation. 1. That in Table 1, Col. 6, “Number rated to be under Observation during the year of age," Mr. Hodgson appears to have taken great pains to ensure accuracy-even tracing the Lives by months of observation. Mr. Bowser has employed the usual method, which we adopt when the facts are not so minutely given; but I think it would be nearer the truth to add half the number of deaths to the number in Col. 6 for the corrected number subject to mortality at the beginning of the year of age. 2. The force of mortality computed from the average of the decennial groups of ages, would very nearly represent the force at the exact ages 30, 40, 50, . . and the "probability of dying in the year" deduced by the formula, would consequently be for the age 29 to 30, 391 to 401, .... I was induced to put it on to the completed ages 30, 40, 50, .... without further correction, in consideration of the evident tendency in the original observations to show a diminishing rate of mortality in the present century. To keep strictly to the whole observations for 1760 to 1860, it would no doubt have been more correct to have taken the average of the two successive ages 291 to 311, . . . . ... 3. In regard to my rough method of graduation, I have found that for official purposes it makes a better table for use than more scientific methods frequently do, as any one may discover who tries to use the new Tables of the Institute for Short Periods and Survivorships. I have always regretted that Mr. Makeham's method was not adopted for these Tables, likely to be so extensively employed in office calculations. My plan follows the fluctuations of the original Table of Observations, and makes use of all the facts to obtain the averages. It merely assumes for the intervals, what nearly all Mortality Tables seem to indicate, that under ordinary circumstances the rate of mortality increases or diminishes by geometrical progression. I am, Sir, your obedient Servant, 11 Lombard Street, SAMUEL BROWN. |