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On the Determination of the Rate of Interest of an Annuity

Published online by Cambridge University Press:  18 August 2016

A. De Morgan
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Extract

This subject, as it left the hands of Simpson, Halley, Dodson, &c., is fully discussed in the appendices of Francis Baily's work on interest and annuities. These, with Milne's note on the subject (vol. ii., p. 680), Jones's notice of the problem, and the various modes of approximation announced in the pages of this Journal, give all I have found written about the matter in modern times. Referring to the citations in Baily for the history of the question subsequent to 1680, I give what I have found in previous time; and I add a few new formulæ for consideration. The problem is, I doubt not, of infrequent occurrence. It never occurred to myself to want more than a look at the tables would furnish; but it may be suspected that, as the requirements of business become closer, inverse problems will acquire more importance than they now possess.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 8 , Issue 2 , January 1859 , pp. 61 - 67
Copyright
Copyright © Institute and Faculty of Actuaries 1860

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References

page 61 note * The Scale of Interest; or, the use of decimal Fractions, and the Table of Logarithmes, in the most easy and exact Resolving of all Questions in Anatocism, or Compound Interest,.…together “with their use in the measuring of board, timber, …. for the use of the intended English Mathematical and Grammar School at Ross in Herefordshire. Also, a direction for Deans and Chapters …. in their Letting of Leases and Taking of Fines. By John Newton, D.D., and one of His Majesty's Chaplains. …. London, printed for Dixy Page … and Allen Bancks … 1668. 8vo.

page 63 note * John Stiles, the Cambridge carrier, is a person of note in the Macclesfield Correspondence. He takes the books backwards and forwards, returns with the money, and his name is a household word in the correspondence between Cambridge and London. He might have said to Newton. Ubi tu Jupiter. eao Mercnrius.

page 63 note † Interest Epitomised, both Compound and Simple. Very useful for every one that Lendeth or Borroweth; and for Purchasing and Selling of Annuities or Pensions, and Leases in Reversion. Whereunto is added, a Short Appendix for the Solution of Adfected Equations in Numbers by Approachment: performed by Logarithms. By Michael Dary, Philomath. London: Wm. Godbid, 1677. 8vo.

page 64 note * This is, I believe, the earliest manifestation now known of the temperament which afterwards put the world in some danger of never knowing Newton's discoveries.