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RETURN FOR THE NEW ZEALAND GOVERNMENT, RENDERED BY THE AUSTRALIAN MUTUAL PROVIDENT SOCIETY. Fifth Schedule. —Statement respecting- the Valuation of the Liabilities under Life Policies and Annuities of the Australian Mutual Provident Society. Question 1, —The date up to which the valuation is made. Answer.- —The 31st December, 1878. Question 2. —The principles upon which the valuation and distribution of profits among the policy-holders are made, and whether these principles were determined by the instrument constituting the company, or by its regulations or by-laws, or otherwise. Answer. —The valuation and the division of profits have been made ou the following principles:— (a.) The assurances were valued in classes according to the office ages attained by the lives assured on the 31st December, 1878. The ages attained were taken as the age next birthday at 31st December, 1878, and were in excess of the real ages of the members by about six months. The next payments of premium were held to be due six, three, or one and a half mouths after the date of valuation, according as the premiums were payable, yearly, half-yearly, or quarterly. In the case of impaired lives to which an addition had been made at the date of assurance, the advanced age was in all instances taken as the age next birthday of the member. The liability of the Society is ascertained by taking the difference between the present value of the sums assured and the present value of the future net premiums. The valuation has been what is technically called a " net premium valuation," with this especial characteristic, that in the case of policies in force for five years and upwards tables have been used applicable to assured lives recently selected, formed from the same data as the Institute of Actuaries' Hm Table, but modified by the exclusion from them of the experience of the first five years of assurance. The table is designated by the svmbol Hm( 3), and determines the valuation reserve that should be held when the effect of selection has been exhausted. The net premiums valued were those arising from the " Institute of Actuaries' Hit Table of Mortality" with 4 per cent, interest. For policies of less than five years' duration the Hm Table with Hm net premiums has been used. The assurances, other than ordinary whole term and endowment assurances, the children's endowments, and the annuities, were valued separately. (j.) The profits will be divided among the members entitled to participate as follows : — (1.) The profit arising from the excess of interest realized, over the rate of interest assumed in the last valuation, will be divided among those members whose policies still remain on the books of the Society, in proportion to the reserve made for each policy at the last quinquennial investigation. (2.) The remaining surplus will be divided in proportion to the loading contributed by members in respect of premiums paid during the quinquennium, under deduction of a percentage from the loading of the first vear's premium paid by members whose policies are of less than five years'duration. The twenty-second by-law requires "that prior to each division of profits such a sum as the directors deem fit shall be reserved by way of guarantee ; aud no appropriation of profits shall be made until it shall have been certified by one or more professional actuaries, appointed by the Board for that purpose, that, according to the most correct calculation of which the case will admit, the interests of all the contributors to this Society and of persons having claims thereon, in possession or expectancy, are, by the proposed scheme of division or distribution, fairly dealt with and secured." Question 3.—The table or tables of mortality used in the valuation. Answer. —The tables of mortality used in the valuation were—For the assurance contracts the "Institute of Actuaries' Ilm( 5) Table" with Hm pure premiums, except for policies of less than five years' duration, for which the Hit Table with Hm net premiums has been used; for children's endowments, the peerage table; for annuities, the Government annuitants' tables for males and females (Finlaison's.) Question 4.' —The rate or rates of interest assumed in the calculations. Answer. —The rate of interest assumed in the calculations has been 4 per cent, throughout, except for non-participating children's endowments, which have been valued at 5 per cent. Question 5. —The proportion of the annual premium income, if any, reserved as a provision for future expenses and profits. Answer. —There has been reserved for future expenses and profits the whole of the loading, i.e., the difference between the premiums payable and the computed premiums for the risk according to the " Institute of Actuaries' Hm Table." The loading by that table on the premiums which were in use at 31st December, 1878, averaged—Under Table A, 363 per cent, of the pure premiums payable; under Table B, 28-2 per cent.; under Table J, 245 per cent. Question 6.—The Consolidated Revenue Account since the last valuation. Answer. —See page 5. Question 7. —The liabilities of the company under life policies and annuities at the date of the valuation, showing the number of policies, the amount assured, and the amount of premiums payable annually under each class of policies, both with and without participation in profits; and also the net liabilities and assets of the company, with the amount of surplus or deficiency. Answer. —See pages G and 7.