Exercise

# 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.

Instructions

**100 XP**

- Calculate the curtate life expectancy of Miss Cathleen as the sum of
`kpx`

without its first element. - Compute the present value of Miss Cathleen's annuity benefits if she would live until 75. First define
`subset1`

as`1:36`

which corresponds to ages 40 to 75. Compute the PV under this scenario by summing`benefits`

multiplied with`discount_factors`

, where both vectors have been subsetted by`subset1`

. - What would be the result if she would live until age 95?