% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/multilife_ch12.R
\name{multilife_pure_endowments}
\alias{multilife_pure_endowments}
\alias{nExy}
\alias{nExybar}
\title{Multi-life pure endowments}
\usage{
nExy(x, y, n, i, tbl = NULL, model = NULL, ...)

nExybar(x, y, n, i, tbl = NULL, model = NULL, ...)
}
\arguments{
\item{x}{Age of the first life. May be scalar or vector.}

\item{y}{Age of the second life. May be scalar or vector.}

\item{n}{Nonnegative integer term. May be scalar or vector.}

\item{i}{Effective annual interest rate. May be scalar or vector.}

\item{tbl}{Optional life table object.}

\item{model}{Optional parametric survival model.}

\item{...}{Additional parameters passed to the survival model.}
}
\value{
A numeric vector of actuarial present values.
}
\description{
Computes pure endowment actuarial present values for joint-life and
last-survivor statuses for two independent lives.
}
\details{
\code{nExy()} computes an \eqn{n}-year joint-life pure endowment, payable
at time \eqn{n} if both lives survive.

\code{nExybar()} computes an \eqn{n}-year last-survivor pure endowment,
payable at time \eqn{n} if at least one life survives.


The joint-life pure endowment is
\deqn{
{}_nE_{xy}
=
v^n\,{}_np_{xy}.
}

The last-survivor pure endowment is
\deqn{
{}_nE_{\overline{xy}}
=
v^n\,{}_np_{\overline{xy}}.
}

Under independence,
\deqn{
{}_np_{xy}
=
{}_np_x\,{}_np_y
}
and
\deqn{
{}_np_{\overline{xy}}
=
{}_np_x + {}_np_y - {}_np_x\,{}_np_y.
}
}
\examples{
nExy(
  x = 40,
  y = 50,
  n = 10,
  i = 0.05,
  model = "uniform",
  omega = 100
)

nExybar(
  x = 40,
  y = 50,
  n = 10,
  i = 0.05,
  model = "uniform",
  omega = 100
)

}
