ON ANNUITIES. Ipl 



answer the questions what is the value of an annuity 

 to be paid so long as A shall live,, and what is the 

 value of an annuity to he paid so long as A and B 

 shall both be ?live, but to cease when either of them 

 dies. The authorities upon the subject have been 

 already mentioned ; namely, Mr. Milne * for the Car- 

 lisle tables., and Dr. Price f and Mr. Morgan J for the 

 Northampton tables. Besides these we have the work 

 of Mr. Baily ,, now completely out of print; in con- 

 nexion with which must be mentioned the treatises || 

 on interest and on leases by the same author, which are 

 also out of print and scarce. The work of Mr. Davies ^[ 

 contains, in connexion with the Northampton tables, a 

 very considerable amount of results^ not elsewhere pub- 

 lished. The work of Mr. Baily on insurances has 

 lately been translated into French.** The results of 

 the Carlisle and Northampton tables have been lately 

 published on one large sheet, by Mr. M'Kean.ft All 

 the preceding are valuable works, and very much sur- 

 pass, in useful application, all that has been done in 

 any other country, or in all countries put together. 



I now give such a brief abstract of the results of the 

 Carlisle and Northampton tables as is consistent with 

 the plan of this work, in regard to annuities upon 

 single lives, and upon two joint lives. 



* A Treatise on the Valuation of Annuities and Assurances, &c. &c., by 

 Joshua Milne. London. Longman and Co. 1815. 



t Observations on Reversionary Payments, &c. &c., by Richard Price, 

 D.D. F.R.S.; seventh edition, edited by William Morgan, F.R.S. London. 

 Cadell and Davies, 1812. 



t The Principles and Doctrines of Assurances, Annuities, &c., by Wil- 

 liam Morgan, F.R.S. London. Longman and Co. 1821. 



$ The Doctrine of Annuities and Insurances, &c., by Francis Baily. 

 London. Richardson, 1816. 



The Doctrine of Interest and Annuities, &c., by Francis Baily Lon- 

 don. Richardson, 1808. 



Tables for the purchasing and renewing of Leases, &c.,by Francis Baily 

 London. Richardson, 1807, (second edition). 



If Tables of Life Contingencies, &c., by Griffith Davies. London. Long- 

 man and Co., and Richardson, 1825, 



** Theorie des Annuite? Viageres, &c., traduit de 1' Anglais par Alfred 

 de Courcy. Paris. Bachelier, 1836. 



tf Practical Life Tables, by Alex. M'Kean. London. Richardson, Butter- 

 worth, &c., 1S37. The annuities on two lives are given for every difference 

 or age ; whereas, in the works of Messrs. Morgan and Milne, they are only 

 given for multiples of five years, and the rest must be supplied by inter- 

 polation. This sheet is a beautiful specimen of typography. 



