# Avg.: Varying Life Insurance: Geometric Progression In DetLifeInsurance: Life Insurance Premium and Reserves Valuation

## Description

Calculates the present value of a varying life insurance according to a geometric progression.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```Avg.( x, h, n, k = 1, r, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 ) ```

## Arguments

 `x` An integer. The age of the insuree. `h` An integer. The deferral period. `n` An integer. Number of years of coverage. `k` An integer. Fractions per year. `r` The variation rate. A numeric type value. `i` The interest rate. A numeric type value. `data` A data.frame of the mortality table, with the first column being the age and the second one the probability of death. `prop` A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). `assumption` A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). `variation` A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. `cap` A numeric type value. Amount insured for the first year/period.

## Value

Returns a numeric value (actuarial present value).

## References

Chapter 4 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.

## Examples

 ```1 2 3 4 5 6``` ```Avg.(33,0,5,1,0.8,0.04,CSO80MANB,1,"none","none",1) Avg.(26,2,4,1,0.4,0.04,CSO80MANB,1,"none","none",1) Avg.(25,0,15,2,0.25,0.04,CSO80MANB,1,"constant","inter",1) Avg.(37,10,10,4,0.05,0.04,CSO80MANB,1,"constant","intra",1) Avg.(40,5,20,6,0.04,0.04,CSO80MANB,1,"UDD","inter",1) Avg.(20,0,80,12,0.01,0.04,CSO80MANB,1,"UDD","intra",1) ```

DetLifeInsurance documentation built on July 8, 2020, 7 p.m.