The only treatise of any value on this subject that I am acquainted with is a paper by Mr. Peter Gray, in vol. xiv of the Journal of the Institute of Actuaries. Considering the magnitude of the pecuniary interests frequently involved in transactions of the nature referred to, it is somewhat surprising that Mr. Gray's valuable labours have not, ere this, been followed up by contributions from other writers on the doctrine of Interest and Annuities. This, I think, is much to be regretted,—and must form my apology for the following attempt to add something to what Mr. Gray has given us.