Exercise

# Short- and long-term

Let's discover what happens to the present value of the guaranteed payment and the pure endowment of 10,000 EUR when you change the time horizon from 5 to 10 or 30 years. The interest rate is still constant at \(2\%\) and the survival probabilities `px`

have been preloaded.

Instructions

**100 XP**

- Assign the PVs of guaranteed payments of 10,000 EUR in 5, 10 and 30 years from now to
`PV`

. Use vectorization. - Calculate the survival probabilities
`kpx`

of (20) using`cumprod()`

on the subset of`px`

starting from`20 + 1`

until`length(px)`

. - Use
`kpx`

at times`c(5, 10, 30)`

to transform the`PV`

of the guaranteed payments to the EPV of the corresponding pure endowments.