A good deal? Outliving your life expectancy
The previous premium calculations for Miss Cathleen's retirement plan are based on the 1999 Belgian period life table for women. This means that the premiums take into account how long on average a 40-year-old woman has yet to live. Recall that curtate life expectancy of (40) is computed as the sum of \(_kp_{40}\) for \(k = 1, 2, 3, \ldots\)
When will this product turn out to be a favorable deal? How much money will Miss Cathleen receive if she would die at age 75? Or at age 95?
The variables kpx, discount_factors, benefits and single_premium defined earlier are preloaded. Start by inspecting the value of single_premium once more in the console.
This exercise is part of the course
Life Insurance Products Valuation in R
Exercise instructions
- Calculate the curtate life expectancy of Miss Cathleen as the sum of
kpxwithout its first element. - Compute the present value of Miss Cathleen's annuity benefits if she would live until 75. First define
subset1as1:36which corresponds to ages 40 to 75. Compute the PV under this scenario by summingbenefitsmultiplied withdiscount_factors, where both vectors have been subsetted bysubset1. - What would be the result if she would live until age 95?
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Curtate life expectancy of (40)
___(___)
# Present value of annuity benefits when (40) lives until age 75
subset1 <- ___
___(___ * ___)
# Present value of annuity benefits when (40) lives until age 95
subset2 <- ___
___(___ * ___)