aD {DetLifeInsurance}

Decreasing Life Annuities

Description

Calculates the present value of a decreasing life annuity.

Usage

aD(
  x,
  h,
  n,
  k = 1,
  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. Number of payments per year.

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. The annualized value of the first payment.

Value

Returns a numeric value (actuarial present value).

References

Chapter 2 of Life Contingencies (1952) by Jordan, chapter 5 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.

Examples

aD(27,0,3,1,0.04,CSO80MANB,1,"none","none",1)
aD(32,2,8,1,0.04,CSO80MANB,1,"none","none",1)
aD(35,8,15,4,0.04,CSO80MANB,1,"constant","inter",1)
aD(21,2,5,4,0.04,CSO80MANB,1,"UDD","inter",1)
aD(54,4,16,2,0.04,CSO80MANB,1,"constant","intra",1)
aD(20,10,15,3,0.04,CSO80MANB,1,"UDD","intra",1)