# axn: Annuity immediate and due function. In spedygiorgio/lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

## Description

This function calculates actuarial value of annuities, given an actuarial table. Fractional and deferred annuities can be evaluated. Moreover it can be used to simulate the stochastic distribution of the annuity value.

## Usage

 ```1 2``` ```axn(actuarialtable, x, n, i = actuarialtable@interest, m, k = 1, type = "EV", power=1,payment = "advance", ...) ```

## Arguments

 `actuarialtable` An actuarial table object. `x` Age of the annuitant. (can be a vector). `n` Number of terms of the annuity, if missing annuity is intended to be paid until death. (can be a vector). `i` Interest rate (default value the interest of the life table). (should be a scalar). `m` Deferring period. Assumed to be 1 whether missing. (can be a vector). `k` Number of fractional payments per period. Assumed to be 1 whether missing. (should be a scalar). `type` A string, either `"EV"` for expected value of the actuarial present value (default) or `"ST"` for one stochastic realization of the underlying present value of benefits. Alternatively, one can use `"expected"` or `"stochastic"` respectively (can be abbreviated). `power` The power of the APV. Default is 1 (mean) `payment` The Payment type, either `"advance"` for the annuity due (default) or `"arrears"` for the annuity immediate. Alternatively, one can use `"due"` or `"immediate"` respectively (can be abbreviated). `...` Arguments to be passed to `pxt()`.

## Details

When "ST" has been selected a stochastic value representing a number drawn from the domain of

a_{x}^{n}

is drawn. "EV" calculates the classical APV.

A numeric value.

## Warning

The function is provided as is, without any warranty regarding the accuracy of calculations. The author disclaims any liability for eventual losses arising from direct or indirect use of this software.

## Note

When either x=ω or n=0 zero is returned.

## Author(s)

Giorgio A. Spedicato

## References

Actuarial Mathematics (Second Edition), 1997, by Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J.

`annuity`, `Exn`
 ```1 2 3 4 5 6``` ``` #assume SOA example life table to be load data(soaLt) soa08Act=with(soaLt, new("actuarialtable",interest=0.06, x=x,lx=Ix,name="SOA2008")) #evaluate and life-long annuity for an aged 65 axn(soa08Act, x=65) ```