Something More About De Moivre's Formula

1865 ◽  
Vol 12 (4) ◽  
pp. 232-233
Author(s):  
P. Gray
Keyword(s):  
Life Annuities ◽  
De Moivre’S Formula

Mr. Baron Maseres, in the preface to his cumbrous work on the Principles of the Doctrine of Life Annuities (1783, quarto), at p. xi., after referring to and commending for its utility the method for finding the value of an annuity on (x) in terms of that of an annuity on (x + 1), has the following:—“This method was first communicated to me by Dr. Price, but it was published in the year 1779, by Mr. William Morgan, the actuary to the Society for Equitable Assurances, near Blackfriars Bridge, in his Treatise on the Doctrine of Annuities and Assurances on Lives, pp. 56, 57; and it had been published before by Dr Price himself, in his Treatise on Reversionary Payments, Note 0 of the Appendix, and likewise by Mr. Thomas Simpson, in his book on Life Annuities, Prob. 1, Coroll. 7; which last book was published so long ago as the year 1742.

scholarly journals Mandatory annuitization and money's worth: evidence from Singapore

2021 ◽  
pp. 1-20
Author(s):  
Joelle H. Fong ◽  
Jackie Li
Keyword(s):  
Expected Value ◽  
Longevity Risk ◽  
Future Trends ◽  
The Past ◽  
The Future ◽  
Population Mortality ◽  
Mortality Improvement ◽  
Life Annuities ◽  
Compulsory Purchase ◽  
The Impact

Abstract This paper examines the impact of uncertainties in the future trends of mortality on annuity values in Singapore's compulsory purchase market. We document persistent population mortality improvement trends over the past few decades, which underscores the importance of longevity risk in this market. Using the money's worth framework, we find that the life annuities delivered expected payouts valued at 1.019–1.185 (0.973–1.170) per dollar of annuity premium for males (females). Even in a low mortality improvement scenario, the annuities provide an expected value exceeding 0.950. This suggests that participants in the national annuity pool have access to attractively priced annuities, regardless of sex, product, and premium invested.

On the Demonstration of Formulæ connected with Interest and Annuities

1854 ◽  
Vol 4 (4) ◽  
pp. 277-282
Author(s):  
De Morgan
Keyword(s):  
Actual Use ◽  
The Subject ◽  
Life Annuities

In most branches of mathematics, the actual use of fundamental processes in the form which the first definitions suggest, is often supplanted, either by processes of greater skill, or by the use of pure reasoning. In the subject of which this paper treats, there has not been much attempt to connect formulæ by reasoning. The actual exhibition of successive annual results has been the only method extensively employed; and it throws the required total result into a series of terms: this series is either algebraically summed, or calculated term by term for insertion in a table.The present paper is intended to show that this summation of algebraical series may be dispensed with, at least in questions of annuities certain : and also that common points of principle, which the ordinary methods leave altogether out of sight, will reduce many questions of life annuities to an absolute coincidence of form with the corresponding questions of ordinary annuities.

A Direct Proof of De Moivre's Formula

1916 ◽  
Vol 23 (10) ◽  
pp. 366 ◽  
Author(s):  
S. Lefschetz
Keyword(s):  
Direct Proof ◽  
De Moivre’S Formula
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