E.— BA,

will be more fully apparent in the next and succeeding triennia, but some idea of tlie increased liability may be gained by tlie fact that the average normal pension granted during the triennium under review was £233 per annum, as compared with £189 during the previous valuation period. 11. It is somewhat disturbing to note that the outgo for benefits during the triennium exceeded 90 per cent, of the total contribution income and the Government subsidy, and was more than 70 per cent, of the combined income from contributions, interest, and Government subsidy. This is not what might normally be expected in a young superannuation fund, since the liabilities are essentially of a deferred nature, and consequently the funds should at this stage be increasing very rapidly. Possibly the most convincing method of demonstrating this elementary fact—so often questioned by otherwise well-informed persons —is to take groups of actual contributors and ascertain what sum the fund requires to have in hand to be able, with the assistance of their future contributions and interest-earnings, to pay their retirement pensions and other subsidiary benefits, and, by dividing such sum by the number of members in the group, thence obtain the fund's average net liability per member. 12. I submit hereunder a table showing for specimen age-groups the average net liability per member for teachers actually in the Service at the valuation date : — Average Net Liability . per Member. Age-group. Malea> Females. £ £ 15-19 .. .. .. .. .. 80 56 25-29 .. .. .. .. 209 166 35-39 .. .. .. .. 537 560 45-49 .. .. .. .. .. 1,113 1,148 55-59 .. .. .. .. .. 2,158 1,464 The net liability for each member in a given age-group will not necessarily remain constant from valuation to valuation, since changes are likely to occur in the incidence of average salary, length of service, and other factors, but the amount of variation is found in actual practice to be fairly small under normal circumstances, and the figures may be considered sufficiently close to the future experience to base general conclusions. For example, the table shows that to be solvent the fund required to have in hand at the valuation date a sum of £209 in respect of each male teacher aged 25-29, and during the next ten years should, from the balance of contributions, interest, and subsidy after paying for benefits falling in for death, physical breakdown, &c., accumulate an additional amount of approximately £328 in respect of each such male teacher still in the Service. It will be seen, therefore, that increasing funds do not mean progress unless the amount of such increase keeps pace with the increase in the liabilities. The net liabilities given for the youngest age-group, 15-19, are also interesting in that as each such member has only made an average contribution of about £6 to the fund, the figures give a very good idea of the initial deficiency introduced by each such new teacher—or, to put it another way, of the capitalized liability of the State to the Superannuation Fund in respect of each such new appointment. The table is also of interest in demonstrating that in respect of those who do not withdraw from the Service the female teacher is a greater liability to the Superannuation Fund than the male, in spite of the fact that male teachers receive the higher salaries (on which pensions are based) and are, in addition, covered for widows' and children's benefits. This is clearly shown for the central ages, but it is to some extent masked at both ends of the table, for the following reasons : At ages under 30, due to marriage and other causes, the withdrawal-rate of female teachers far exceeds that in respect of males, and as the return of contributions paid to those who withdraw is considerably less than the value of their accrued pension benefits., and the net liability is an average based on the present value of withdrawal benefits and pension benefits in their expected proportions, it follows that for female teachers at these ages the net liability per member is a much smaller proportion of the pension liability per member who does not withdraw from the Service than in the case of males. By the time age 50 is reached the majority of female teachers have either retired or will do so within the next five years. Those remaining in the Service are in general only those with small salaries or short service, whereas in the case of males the effect of retirements on the average of the accrued pension benefits of members left in the age-group does not become marked until a later age, and moreover is counteracted to a great extent by the higher salaries paid and the greater prospects of future promotion prior to retirement. The greater pension liability in respect of female teachers is due to the early ages at which they retire and the superior vitality of female pensioners generally, combined with the fact that they only pay, as contributions to the fund, the same percentages of salaries as do the males. 13. It would be possible, though very laborious, to ascertain what might be termed the " share " of each individual member in the total funds, and proceed to deduce by how much such amount held in the fund on his behalf was, on the average, insufficient or oversufficient to provide his benefits. The sum total of such an analysis in respect of all members —contributors and pensioners—would give the same results as are achieved by the more direct process of actuarial valuation of the fund. The Valuation. 14. The main object of an actuarial valuation is to ascertain whether the current funds, together with the present value of the*future contributions, are sufficient to meet the future liabilities. Before the valuation can be carried out it is necessary to make a careful estimate of the various factors on

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