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Published online by Cambridge University Press: 22 April 2013
I Have endeavoured to draw together one or two of the popular arguments for ascertaining the sum which ought to be given now, in consideration of another sum, say of £1 or £100, to be paid at death; or, in the language which is peculiar to the Actuarial profession, to determine the Single Premium for the Assurance of £1.
The systems of Life Assurance calculation which were in practice when Price, Baily, and Milne brought forward their most valuable volumes, have in a great measure been superseded by a different but a more powerful arrangement, thanks to the labours of Barrett, Davies, and Jones; and here permit me to follow these illustrious names with that of David Chisholm. But while by this system a saving of time and mental exertion is afforded to the Actuaries of the present generation, I very much fear that a knowledge of first principles is less likely to be attained by the student under that cabalistic system, than if trained under the simpler system of Milne. The columnar or commutative system of calculation facilitates the expertness of the calculator at the expense, if I may use the expression, of his understanding; while the other system is much more apt to bring under his notice the exact nature of the problem, and the reasons involved in his formula for determining its solution.
page 61 note * These formulæ ought to be retained in the student's memory.
page 68 note * As this is the first time v is introduced, it may be as well to state that v is an abbreviated symbol for 
and represents the present value of £1 (discounting at interest only) due at the end of one year; or the sum which, when put out at i interest, will amount to £1 at the end of one year; and that (1–v) is the discount upon the £1, or the interest upon v for a year, and is equal to iv.
page 69 note * The formula for the present value of a temporary annuity for n years, of which the first payment is to be made at the end of one year, is, by the Institute's notation, 
This symbol may be easily retained in the memory by considering that the term, the n, is on that side of the perpendicular line which is nearest to the a. If the annuity is deferred, the n is on the further side of the line = 
If the annuity is temporary for n years, but deferred m years, the symbol would be 
When in advance these may be symbolised by a different form of the same letter, thus—
= Temporary annuity for n years, first payment being due, = 
Temporary annuity for n years, first payment being due in m–1 years, = 
See Institute of Actuaries notation—Life Tables, 1872, p. 245.
page 70 note * These formulæ ought also to be indelibly fixed upon the student's memory.
page 99 note * It will be observed that the annual premium for a temporary assurance follows one of the forms of the annual premium for a whole life assurance 
and that the annual premium for an endowment assurance follows another, of these forms 
by merely substituting the corresponding temporary for the whole life annuities, in the same way as was pointed out in single premiums.