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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts

Which combination of benefits is equivalent to a 25-year endowment assurance with sum assured S, with the death benefit paid at the end of the year of death?

An endowment assurance equals a term assurance plus a pure endowment, both with the same sum assured and term. The term assurance covers death within 25 years and the pure endowment covers survival to year 25, so S is paid exactly once in either case.

  1. AA 25-year term assurance with sum assured S plus a 25-year pure endowment with sum assured SCorrect
  2. BA 25-year term assurance with sum assured S plus a whole life assurance with sum assured S
  3. CA 25-year pure endowment with sum assured S plus a deferred whole life annuity
  4. DA 25-year term assurance with sum assured S minus a 25-year pure endowment with sum assured S
  5. A whole life assurance with sum assured S deferred 25 years plus a 25-year pure endowment with sum assured S

Explanation

Endowment assurance pays S on death within the term and S on survival to the end of the term. This is the sum of a term assurance and a pure endowment, each for S, so A(x:n) = A¹(x:n) + A(x:n)¹ in the usual notation. The other options add or subtract benefits that are not in an endowment.

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