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  3. Life Insurance Products Valuation in R

Exercise

To survive or not to survive

Cynthia is 20 years old and joins the actuarial department of an insurance company for a summer internship. As a first challenge Cynthia’s supervisor asks her to compare the (expected) present values of a pure endowment on the one hand versus a guaranteed payment on the other hand.

In this chapter you will always work with the 1999 period life table for females in Belgium of which the one-year survival probabilities \(p_x\) have been preloaded as px. For this exercise you will consider a single payment of 10,000 EUR and a constant interest rate \(i = 2 \%\).

Instructions

100 XP
  • Compute the PV of a guaranteed payment of 10,000 EUR in 5 years from now at a rate of 2%.
  • Define kpx as the 5-year survival probability \(_5p_{20}\) of (20) by taking the product over the subset of px corresponding to ages 20 to 24.
  • Multiply PV with kpx to obtain the expected present value of a pure endowment of 10,000 EUR in 5 years from now for 20-year-old Cynthia.