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Published online by Cambridge University Press: 18 August 2016
The following collection of problems is intended to serve two purposes—first, as a continuation of a former article, published in vol. x. of this Magazine, under the title of “Solutions of the Compound-Survivorship Assurance Problems,” which treats of cases involving three lives only; and secondly, as an introduction, or preliminary step, to a complete exposition of the writer's method of constructing mortality and annuity tables upon Mr. Gompertz's celebrated hypothesis, a brief account of which method will be found in the eighth and ninth volumes.
page 65 note * It is, I believe, sometimes the practice, in making the periodical valuations of an Assurance Office, to substitute for half-yearly and quarterly premiums the corresponding annual payments. But as these half-yearly and quarterly policies, one with another, will become renewable at the expiration of one-half of the interval of renewal, it follows, from the circumstance above mentioned, that this substitution is not only unnecessary, but absolutely incorrect. The proper course is, to take the sum of the payments due in the year on each policy, whether one, two, or four, and value them as if they were payable altogether at the expiration of half a year. Of course, these remarks do not apply when the exact period at which the next premium becomes due, on each policy, is taken into account. In that case, the substitution referred to would be quite correct.
page 68 note * This formula is given by Mr. Gompertz, in his Analysis Applicable to tie Estimation of Life Contingencies.