Skip to content

IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross premiums and reserves

A whole life assurance on a life aged x is issued with level annual premiums payable in advance throughout life, and the sum assured is paid at the end of the year of death. For a life now aged x+t, which expression gives the prospective net premium reserve per unit of sum assured, using the same basis as the premium basis?

The prospective net premium reserve is A_{x+t} − P_x ä_{x+t}. It is the expected present value of future benefits at the attained age less the expected present value of the original level net premium P_x payable from that age. Using the new-entrant premium P_{x+t} would wrongly give zero.

  1. AA_{x+t} − P_{x+t} ä_{x+t}
  2. BA_x − P_x ä_{x+t}
  3. CA_{x+t} − P_x ä_{x+t}Correct
  4. DP_x ä_{x+t} − A_{x+t}
  5. A_{x+t} + P_x ä_{x+t}

Explanation

The prospective reserve is the EPV of future benefits minus the EPV of future net premiums. Benefits are valued at the attained age, A_{x+t}. The premium is still the original P_x, paid as an annuity-due from age x+t, so the reserve is A_{x+t} − P_x ä_{x+t}. Using P_{x+t} would reset the policy to a new one and give zero.

Did you get it right without looking?

One question tells you little. A timed set on Gross premiums and reserves shows your real accuracy, how long you take and where you lose marks.

Practise Gross premiums and reservesFree diagnostic mock

More Gross premiums and reserves questions