A simple life annuity

Life Insurance Products Valuation in R

Roel Verbelen, Ph.D.

Statistician, Finity Consulting

The life annuity

$\qquad$ The EPV is $$_kE_x = 1 \cdot \ v(k) \cdot \ {}_kp_x \, . $$

With an annuity certain, the benefit of 1 euro at time $k$ is guaranteed.

$\quad \,$ PV is $v(k)$.

i <- 0.03
discount_factor <- (1 + i) ^ - 5
1 * discount_factor

0.8626088

With a pure endowment, the benefit of 1 euro at time $k$ is not guaranteed.

$\quad \,$ Expected PV is $v(k) \cdot {}_kp_x$.

qx <- life_table$qx; px <- 1 - qx
kpx <- prod(px[(65 + 1):(69 + 1)])
kpx

0.9144015

1 * discount_factor * kpx

0.7887708

Life Insurance Products Valuation in R