S2010 Q4 First Principles

[MoleMan]

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

 

[Mohit Gulati]

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

 

[MoleMan]

Thanks Mohit,

Still worried about losing marks for answering differently than the examiner intends.

 

[Mohit Gulati]

no i donot think, they will disregard this approach, as long as final answer is correct,