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

A 10-year endowment assurance pays a sum assured S at the end of the year of death if death occurs within 10 years, or S at the end of year 10 if the life survives. Which expression gives its expected present value, using standard notation at a given interest rate?

The endowment assurance value is the term assurance value plus the pure endowment value, S times (A^1_{x:10} + v^10 times 10p_x). Death within the term pays S, and survival to the end also pays S, so both components must be added.

  1. AS times A^1_{x:10} only
  2. BS times (A^1_{x:10} + v^10 times 10p_x)Correct
  3. CS times v^10 times 10p_x only
  4. DS times (A^1_{x:10} - v^10 times 10p_x)
  5. S times (A_x + v^10 times 10p_x)

Explanation

An endowment assurance is a term assurance plus a pure endowment. The term assurance part has value S A^1_{x:10} and the pure endowment part has value S v^10 10p_x. Option A omits the survival benefit, option C omits the death benefit, and option D subtracts rather than adds.

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