Editing Actuarial notation (section)

===Life annuities===
A life annuity is an annuity whose payments are contingent on the continuing life of the annuitant. The age of the annuitant is an important consideration in calculating the [[actuarial present value]] of an annuity.

* The age of the annuitant is placed at the bottom right of the symbol, without an "angle" mark.

For example:

<math>\,a_{65}</math> indicates an annuity of 1 unit per year payable at the end of each year until death to someone currently age 65

<math>a_{\overline{10|}}</math> indicates an annuity of 1 unit per year payable for 10 years with payments being made at the end of each year

<math>a_{65:\overline{10|}}</math> indicates an annuity of 1 unit per year for 10 years, or until death if earlier, to someone currently age 65

<math>a_{65:64}</math> indicates an annuity of 1 unit per year until the earlier death of member or death of spouse, to someone currently age 65 and spouse age 64

<math>a_{\overline{65:64}}</math> indicates an annuity of 1 unit per year until the later death of member or death of spouse, to someone currently age 65 and spouse age 64. 

<math>a_{65}^{(12)}</math> indicates an annuity of 1 unit per year payable 12 times a year (1/12 unit per month) until death to someone currently age 65

<math>{\ddot{a}}_{65}</math> indicates an annuity of 1 unit per year payable at the start of each year until death to someone currently age 65

or in general:

<math>a_{x:\overline{n|}i}^{(m)}</math>, where <math>x</math> is the age of the annuitant, <math>n</math> is the number of years of payments (or until death if earlier), <math>m</math> is the number of payments per year, and <math>i</math> is the interest rate.

In the interest of simplicity the notation is limited and does not, for example, show whether the annuity is payable to a man or a woman (a fact that would typically be determined from the context, including whether the life table is based on male or female mortality rates).
 
The Actuarial Present Value of life contingent payments can be treated as the mathematical expectation of a present value random variable, or calculated through the current payment form.