Pension calculations accounting for mortality
How does the present value change if you take mortality into account? The pension payments are then no longer guaranteed but depend on the survival of the recipient. The one-year survival probabilities px
have been preloaded as well as the variables benefits
, discount_factors
, PV_65
and PV_20
created in the previous exercise.
This exercise is part of the course
Life Insurance Products Valuation in R
Exercise instructions
- Store the survival probabilities of a 65-year-old up to age 100 in the variable
kpx
. Make surekpx
starts with a 1. - Calculate the EPV at age 65 of the pension taking mortality into account. Assign the result to
EPV_65
and compare the value toPV_65
which does not take mortality into account. - Discount the EPV at age 65 to the EPV at age 20 by taking both the interest rate of 3% and the survival of (20) to age 65 into account. Again, compare
EPV_20
toPV_20
.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Survival probabilities of (65) up to age 100
kpx <- c(1, ___(px[(___):(___)]))
# EPV of pension at age 65
EPV_65 <- ___(___ * ___ * ___)
cbind(PV_65, EPV_65)
# EPV of pension at age 20
EPV_20 <- EPV_65 * (1.03 ^ - 45 * ___(px[(___):(___)]))
cbind(PV_20, EPV_20)