APPENDIX TO CHAPTER XVI 411
course the present value of the chance of receiving the insur-
ance, less the present value of the chance of paying the
premiums. Thus, for a man aged 30, who was insured 10 years
before, the chance of his death at the age of 35 will be about
4335 or .869%, since of 84,720 living at age 30, about 732 die
in their 36th year. Hence the present value of the chance of
receiving his insurance of $1000 in that particular year is
one, or $7.07, assuming the rate of interest to be 49. In
like manner we may determine the present value of the similar
chance for every other year of possible life, and the sum total
of these present values will be the total present value of the
chance of receiving the insurance, $287.66. From this must be
deducted the present value of the chance that he will pay
premiums. Thus, the chance of his paying the premium in the
above-named year, when he is 35 years of age, will be the
chance that he will be living at that time, which is.958. This
multiplied by his premium and discounted gives the present
value of this possible premium payment ; this added to the like
sums for every other year will give the total present value of
his obligation to pay premiums, $222.86; this, in turn, sub-
tracted from the present value of the prospective insurance
just obtained, namely $287.66, will give the present mathe-
matical value of his property, $64.80, called the value of his
insurance, or the “reserve” on his policy.
The true “commercial value,” or the value which he is will-
ing to pay, will be somewhat higher. For, in this case, the
coefficient of caution operates to increase, not to diminish, the
value of the property, as insurance tends, not to make a risk,
but to reduce it.
The calculation of mathematical values of life insurance has
been very perfectly worked out. The reader who is interested
will find the most complete explanations in the Institute of
Actuaries’ Text-book, 2 vols., London (Layton), 1901.
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