A and B, both age 55 have been partners in a successful business. B is worried about what will happen to his income if A dies and so is willing to pay 12% of this year’s earnings for some contingent life assurance. A life assurance company offers B two options:

Option 1: A reversionary annuity of £40,000 per annum payable annually in arrears with A as the counter life.

Option 2: A contingent whole life assurance with sum assured of £250,000 payable at the end of the year of death if A dies before B.

(a) If B evaluates these options assuming 4% per annum interest and mortality such that ¨a55 = 14.543 and ¨a55:55 = 12.947, which option should he choose?

(b) What assumptions underlie your calculation in (a) and how realistic are these?

(c) If the life assurance company assumes that the present value of future expenses is 2% of the present value of future benefits, write down a formula for the gross premium reserve 8 years after inception of the policy you selected in (a) above assuming both A and B are still alive.

(d) Explain what will happen to the gross premium reserve immediately after the first death.