A Perpetuity, Life Annuity, and Life Insurance Related to a Decomposition of 1

This note is about the historical development of the expression ... , where i is an annual interest rate and ... is a life annuity for a person age x. This expression has meaning in its own right, but it also equals ... , where ... is the expected present value of insurance of 1 unit paid at the end of the year of death. The equation ... provides a foundation for taxation in life estate and inheritance matters in which ... captures income from a life estate and ... represents the remainder. When ... is placed on the right side, the equation ... states that 1 consists of life annuity and life insurance components. Three problems play central roles in the development of the equation ... one problem is due to Abraham de Moivre (1667-1754), another to Thomas Simpson (1710-1761), and the third to Richard Price (1723-1791). Sections II and III discuss these problems after brief sketches of de Moivre, Simpson, and Price. Section IV is a conclusion. (ProQuest: ... denotes formulae/symbols omitted.)