15 5 Introduction
Total Disability Benefit in Life Insurance © 1913
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INTRODUCTION
After his publication of some ordinary Commutation Columns,
for use in computing the extra premiums for Total Disability
Benefits, by the method of comparison of premiums, the author
joined in the search for a more direct means of obtaining them.
This had been forecast as early as the year 1900 in a paper
read before the Third International Congress of Actuaries at
Paris, France, by M. Expedite Hamza, then actuary of a Russian
Insurance Company at St. Petersburg. The suggestions con-
tained in this paper were followed up in the year 1910 by Mr.
Franklin B. Mead, an American actuary, in a paper read before the
Actuarial Society of America and published in the Transactions
of that Society. He had also availed himself of material collected
by Messrs. Landis and Eldridge from the experience of the Knights
of the Maccabees, a fraternal order in the United States of America,
which had granted such benefits for many years.
In his paper, he published tables adjusting this experience in
connection with the American Table of Mortality, for the purpose
of making direct calculations of the extra premiums required for
Total Disability Benefits, and prepared formulae to be used in
connection therewith.
The author became convinced, however, that shorter and
simpler methods were necessary, and that formulae could be found,
analogous to those used in life insurance, as had been stated by
M. Hamza.
After numerous computations and trials the author hit upon
the device of a new Commutation Column for the purpose, the
origin and development of which will now be explained.
THE NEW COMMUTATION COLUMN
The formula given by M. Hamza for the value of an annuity,
the first payment payable at the end of the year in which an
active life now aged x becomes totally disabled, and to continue
thereafter as long as he lives, is
a”=a,-ar+^|(a,-ay
i
