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Published online by Cambridge University Press: 18 August 2016
In the course of an actuary's practice, the question not uncommonly arises—What is the value of a life interest, accompanied by a policy of assurance on the same life ? The most obvious course for solving this question is to value the life interest and the policy separately—the former by the well-known formula 
. With regard to the policy, it is not so clear how it should be valued. If valued on the same principles as the life interest, the value of a policy for £1 would be 1 − (p + d) (1 + A); but this formula is quite inapplicable, for it gives a negative value for many years to a policy, and almost always a much smaller value than the surrender value allowed by the Office. There is, therefore, apparently no choice but to take the value of the policy at the latter amount.
*
This formula was first given by Mr. Griffith Davies: it coincides with the less elegant one given in Jones on Annuities, art. 246, 
, which may be reduced to the form in the text by the help of the formula 
. A proof of the formula, as well as of some very useful and practical extensions of it, is given by Mr. Jellicoe in the Assurance Magazine, vol. ii., p. 159.
† The value of a reversion, as given in Mr. Jellicoe's paper already referred to, is 1 – d (1 + A). In the case of a policy for £1, we must subtract from this value the cost of an annuity equal to the annual premium, or p (1 + A), giving the value of the policy as stated in the text, 1 – (p + d) (1 + A).