Hi, When attempting to do this question I converted to monthly annuities for the calculation and the result differs slightly. Calculation as follows (from first principles): Number of memberships n = 120 Monthly fee per person f = 240 / 12 = £20 Monthly discount factor v = [1 + 0.06]^[-1 / 12] = 0.995156 Monthly survival probability p = [1 - 0.01]^[1 / 12] = 0.999163 Monthly one-year annuity a = 1 + pv + [pv]^2 + … + [pv]^11 = [1 - (pv)^12] / [1 - pv] = 11.632312 Expected Present Value E = fna(1 + 0.8[pv]^12 + 0.64[pv]^24) = 64,362.03 The question states that premiums are payable monthly in advance and premiums cease immediately on the death of the member i.e. no payments in the month following death. Would my answer receive full credit or is it a requirement to use the one-year-annuity-due-payable-monthly method described in the examiners’ report? Not sure where the factor 11/24 the examiner has used comes from; first principles seem far more intuitive. Best regards, MoleMan
since examiner used the approximate formula and in that formula the factor 11/24 is given . the formula is given in actuarial table on page 36. (a dot dot x:n - (m - 1)/2m (1 - (Dx+n/Dx)) so if m is 12 so (12-1)/12*2 = 11/24
