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On the Relation between the Theories of Compound Interest and Life Contingencies
Published online by Cambridge University Press: 18 August 2016
Extract
It has often occurred to me that but scant justice has been done to the application of the infinitesimal calculus to the theories of compound interest and life contingencies. This is, perhaps, in some measure due to the popular relegation of the differential and integral calculus to the realms of the so-called “higher mathematics.” There are, of course, two aspects of the case to be borne in mind. On the one hand, it is necessary to present the subjects in such a form as will be best suited to the student who is commencing to study them. For this purpose experience shows that a start should be made with particular cases, leaving the generalization until such time as the student shall have obtained a grasp of first principles sufficient to enable him to view the subjects in their general aspect. On the other hand, however, there is no doubt that to the reflective mind there comes a time when the desire is felt to invert the process and deduce the formulæ in their logical sequence from a fundamental general hypothesis.
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- Research Article
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- Copyright
- Copyright © Institute and Faculty of Actuaries 1907
References
page 308 note * n is, of course, not necessarily an integer.
page 311 note *
This agrees with the true value calculated by the formula 
page 313 note * The true value, to 3 places, is ·043.
page 313 note † The true value, to three places of decimals, is 5·363 %.
page 317 note *
For μ
x
should be substituted 
(see Addendum, p. 347).
page 319 note * It will be remembered that Messrs. E. M. Moors and W. R. Day made use of this fact in the calculation of the values of μx for ages under 12 based on their New South Wales and Victoria Table (J.I.A., vol. xxxvi, p. 175).