£5000; the loan to be discharged and the interest paid by an equal halfyearly charge upon the rates extending over thirty years. Assuming that the rate of interest at which the loan is obtained is 5 per cent per annum, find what the half-yearly charge should be. Given v60 at 2 per cent to be 2272836.

Draw up a schedule showing what portions of each of the first four payments are applicable for the payment of interest and the discharge of the capital account.

6. Describe the ordinary form of a mortality table; and mention the tables which are generally constructed from it in order to make it available for monetary calculations.

7. Given a table of the values of annuities on two joint lives for every combination of quinquennial ages, explain how to approximate to the value of an annuity for two intermediate ages.

9. State the approximate increase to be made to the value of a life annuity payable yearly when the same is to be paid half-yearly, quarterly or monthly.

10. Given a table of annual premiums for assurances for the whole of life, how would you construct a table of half-yearly premiums?

11. Find a formula for the value of a reversionary annuity so as to return one rate of interest while the annuity is in reversion, and another rate when it is in possession.

12. What addition should be made to the value of a curtate annuity payable yearly (a), to obtain the value of a complete annuity payable half-yearly (å)?

13. A sum of money (s) is to be applied in the purchase of an annuity on three lives, x, y, z, such that the annual payment while all three are alive shall be A, when one has died A, and when only one survives A. Find the value of A.

II.

14. Explain the principles upon which Mr. Woolhouse has constructed his "Improved Theory of Annuities and Assurances”, and state briefly the advantage of the proposed system.

15. Investigate the formula for finding the annual premium for a contingent assurance. If asked to quote a premium, how would you proceed?

16. How would you proceed to form D and N columns; and what checks would you use to secure accuracy?

17. Show how to construct a table of premiums for the assurance of £1 for the term of one year, by a continuous process.

18. Show that Dx-Mx=(1-v)Nx−1·

19. Required the value of a policy for £100, effected at age 40, which has been in force for 5 years and 7 months.

20. Give a form of endorsement to be placed upon a policy in order to substitute a half-yearly for an annual premium.

21. Draw up a form of Policy Register, omitting the consideration of bonus.

22. What does the following formula represent

23. A at the age of x effected an ordinary whole life assurance at a premium Pr; n years having elapsed he wishes to convert it into a contingent assurance, the counter life being aged y; what premium should he pay on the new policy?

24. Investigate an expression for the nth presentation to a living. 25. Find a formula to express the amount to which a life annuitydue will on the average accumulate at the end of the year of death, supposing each payment to be invested and accumulated at compound interest.

JOURNAL

OF THE

INSTITUTE OF ACTUARIES

AND

ASSURANCE MAGAZINE.

On the Rate of Mortality among Adult Government Emigrants on the Voyage to Australia, during the Years 1847-1861 inclusive, as determined from the Reports of the Emigration Commissioners. By J. J. McLAUCHLAN, A.F.A., of the Scottish Equitable Life Assurance Society.

THE object of the following paper is to describe an investigation

recently made, to determine, from observed facts, the risk incurred by persons making voyages to the Australian Colonies. This investigation was carried out under the superintendence of Mr. Sprague, at whose suggestion the following account of it was prepared.

For more than thirty years past, an Annual Report has been presented to Parliament by the Emigration Commissioners; and a set of those Reports, extending from the 1st to the 25th inclusive (with the exception of the 22nd), supplied the required material. Among the other duties of the Commissioners, is that of chartering ships for the conveyance of emigrants, either wholly or partly at the public expense, to certain of the colonies; and in the Appendixes to their 8th and subsequent Reports, they have given returns of the number of ships and emigrants despatched by them annually to each of the colonies. Among

VOL. XVIII.

2 D

other information, the returns contain the number of adult emigrants of each sex (ages not stated) embarking in each vessel, the duration of the voyage, and the number of adult males and females that died before reaching their destination. Those returns for the years 1847-1861 inclusive, as summarized in the 24th Report, pp. 80, 81, were selected to form the basis of the present enquiry.

As but a small proportion of the total number of emigrants proceeded to Western Australia, Queensland, and New Zealand, the investigation was confined to the mortality among those making the voyages to New South Wales, Victoria, and South Australia. From the summary referred to above, the following Table (A) is extracted. It shows the number of ships despatched to New South Wales, Victoria, and South Australia respectively, the total numbers of adult males and females embarked for each voyage, and the total numbers of each sex that died before reaching their destination, during the period over which the observations extend.

The deaths entered in the summary are exclusive of those arising from the wreck of vessels. From the 20th Report, p. 17, and the Appendixes to the succeeding Reports, we learn that the only loss of life by wreck during the period 1847–1861, was in the case of the "Guiding Star", which sailed for Melbourne in 1855, and never reached her destination. By a comparison of the original return for 1855 with the summary, we see that this vessel is included in the number of those despatched; the 328 adult emigrants-118 males and 210 females-who sailed on board of her, being included in the number embarked, but not in the number dying upon the voyage. They are not included in the numbers embarked as given in Table A.

* One ship, in 1853, conveyed emigrants both to Victoria and South Australia.

Table B is similar to Table A, except that it contains the deaths arising from the loss of the "Guiding Star", distributed over the three Australian voyages in proportion to the number of emigrants embarked upon each. For For purposes of comparison, Table B may be considered fairly to represent the mortality experienced.

In order to know whether the rate of mortality shown by Tables A and B is excessive or otherwise, it is necessary to compare it with that which prevails among a similarly constituted body of persons in this country; and with this view it was resolved to calculate the expected deaths according to Dr. Farr's English Life Table, No. III. As a preliminary to doing so, it is necessary to make some assumption as to the ages of the persons embarking, these not being given in the annual returns, or elsewhere in the Reports; and also to determine the average duration of each of the three voyages during the period 1847-1861.

There are contained in the Appendix to the 25th Report (pp. 72–78), tables giving an analysis of the mortality in ships despatched by the Commissioners to each of the Australian Colonies, for a period of years ending 31st December 1864,—the number of years being 10 for New South Wales, Victoria, and South Australia, 9 for Western Australia, and 5 for Queensland. From those tables may be obtained, classified according to age, the total number of adults, without distinction of sex, that died on each of the voyages during the above periods. The numbers dying in each of the following intervals of age are grouped together, 10-19, 20-29, 30-39, 40-49, 50-59, 60 and upwards. This information is contained in the following Table C, which shows the ages of the adult emigrants who died on the voyage to each of the Australian Colonies during certain periods of years ending 31st December 1864.