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.