Practical Lessons in Actuarial Science Volume 1; Text

by Miles Menander Dawson

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 ... net premium, including the first year. Designating this cost by F and the corresponding annuity by f, we have for a life Net premium after ist year SP, = P, + f Net premium ist year 'P, = P, + f--F This plan appears to answer all the requirements. The cost of collection and renewal offers no difficulties, being a function, which we will designate as k, of the premium after the first year; but as it will really need to be a function of the gross premium, we defer it for a moment. The cost of management may be added to the net premium as a fixed amount (c), each year including the first The values of P, F, f and c are, then, determined in advance, and we have the following requirements 'P', (gross premium ist year) = P', (gross premium thereafter). 'P, (net premium after ist year) = P, + f 'P, (net premium ist year) = 'P,--F = P, + f--F F = f (i+a,). From these, remembering that the premium when loaded with other costs must be loaded by k per cent of itself for cost of collection and renewal, we P', = ('P, + c) (i + k) = (P, + f + c) (i + k) 'P'. = ( 'P, + F + c) f i + k) =( 'P, + c) (i + k) = (P, + f + c) (i + k) When net premiums are made by an ultimate table and reserves are computed by this net premium but by a select table otherwise, the effect is to allow the present value of all the salvage from mortality, by the select table over the ultimate table, as an offset to initial expenses. ENDOWMENTS AND INSURANCES WITH RETURN OF NET ANNUAL PREMIUMS, CONTINUOUS THROUGHOUT TERM. Suppose an insurance for life with return of all net annual premiums. Designate the net annual premium by the symbol n, used in the English notation to signify any special or unusual annual premium. The value of this insurance is plainly separable into two p...

60 pages, Paperback

Published May 19, 2012