Deriving the Present Value and Future Value of an Annuity Immediate

Below is the derivation of the present and future value of a unit annuity immediate, or a series of $1 cash flows that occur at equal intervals of time at the end of each period.  I originally wrote this document as a review for myself in preparation for actuary exam FM/2.  The majority of questions on the exam, despite the wide array of topics covered, come down to solving for the value of some annuity.  Granted, it likely won’t be a case as simple as the one below, but many problems about loans, bonds, yield rates, and even financial derivatives biol down to an annuity problem.

Annuity_Derivation

About schapshow

Math & Statistics graduate who likes gymnastics, 90s alternative music, and statistical modeling. View all posts by schapshow

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