INSTITUTE OF ACTUARIES.

Income and Expenditure for the Year ended 31 March 1873.

Hardy Memorial

(£200 Consols)

Brown Prize

(£95. 15s. 5d. 104 per

cent East India Stock) £688. 18s. 2d. Consols

INSTITUTE OF ACTUARIES.-SECOND YEAR'S EXAMINATION,

1872.
I.

1. Find the value of e, the base of the Napierean system of logarithms, correct to 4 places of decimals.

2. Given a series of logarithms in arithmetical progression, find the relation in which the corresponding natural numbers stand to one another. 3. If 5 coins be distributed in some unknown way amongst 5 urns, what is the probability that any selected urn will contain 3 coins and no more?

4. Give expressions for the probabilities of the various contingencies arising out of the occurrences of three independent events. Call the events A, B and C, and denote their probabilities by a, b and c respectively.

5. Given log 2=301030, log 3=477121 and log 7=845098, find in what times a sum of money will double and treble itself at 5 percent compound interest.

6. Find the value of an annuity certain for n years, whose several payments are 1, 2, 3, . n.

7. Give some account of the difference between the materials used in the construction of Davies's and Morgan's "Equitable" Tables. 8. State briefly the basis upon which the Government Annuity Tables (Finlaison, 1860) are founded.

9. Find an expression for the average age at death of lx persons. 10. Distinguish between the average after-lifetime and the most probable after-lifetime.

11. Give a practical method of forming a Table of the values of log (Px ̄1-1)(Py ̄1+1).

12. Explain the construction of the several columns of a single life Commutation Table.

13. Given the annual premium and the rate of interest, show how to find the value of £1 payable at the end of the year of death.

II.

14. Assuming the values of 8 and a to be known, find the value of Ar, the present value of a continuous assurance of £1 payable at the instant of death.

15. Find an expression for the value of a life-annuity, when the decrement of life at each age (x) is equal to x.

16. Investigate a formula by which a table of policy-values (nVx) may be formed successively.

17. Show, under what circumstances, the value of a policy at the end of the (n+1)th year, (n+1Vx), will be greater than the value at the end of the nth year with the premium just paid.

18. Assuming that the lives enter proportionately to the numbers shown in Table of Mortality, find the annual premium that may be charged uniformly to all entrants from age (x) to age (x+n) inclusive for ordinary whole term assurances of £1.

19. Investigate an expression for the value of Ay

20. Determine A3 the present value of £1 payable upon (x) failing either the first or last of three lives (x), (y) and (z).

21. A copyhold estate is held on a single life, subject to a fine for

renewal on the death of each nominee. Find the value of the fines in perpetuity.

22. An assurance office guarantees reversionary bonus additions to the sums assured under its policies, at the rate of 1 per-cent per annum on the sum originally assured for each premium paid: what is the average amount of bonus that lives entering at age (x) will receive?

23. For what amount should a policy, free from future payment of premium, be granted in consideration of the surrender of an existing assurance? Assume all values to be net.

24. Prove the following equation:

nVx-1-(1-Vx) (1-Vx+1).... (1-Vx+n-1).

25. A (who is tenant for life in possession of an estate) agrees to join with B (who is tenant for life in remainder, expectant on the death of A) in exercising their joint power of raising money on the fee simple of the estate. The money so raised is to be applied solely for the benefit of B, who agrees to compensate A for the loss of income he will sustain in having to keep down the interest on the sum so raised. How much, out of every £1 so raised, should be reserved for A?

THIRD YEAR'S EXAMINATION, 1872.

I.

1. Explain briefly how the rate of mortality which has been experienced by a Life Assurance Company is to be deduced from the facts contained in its registers.

2. Give some account of the method of graduation adopted in the construction of the Institute of Actuaries' mortality tables.

3. Point out the difference between and compare the merits of the Seventeen Offices' Experience and the Institute of Actuaries' mortality tables.

4. Describe the method of distribution of profits introduced by Mr. Jellicoe.

What is required to make it work equitably?

5. Describe the method of distribution of profits introduced by Mr. Homans, and called by him his "Contribution Method."

6. Does the maxim "caveat emptor" apply to the contract of Life Assurance ?

7. What is meant by a policy being in the order and disposition of the Bankrupt with the consent of the true owner? And explain whether any alteration in the Law has been proposed or effected within the last 4 years.

8. State the effect of the Life Insurance clauses in the Married Women's Property Act 1870.

9. What is meant by "novation " ?

10. The liability of Shareholders in Life Offices is not usually limited in England either by charter of incorporation or registration as limited companies under the Companies Act 1862; explain the manner in which in such unlimited companies a limitation of the Shareholders' liability is sought, and state the limit of the limitation in a Liquidation.

11. What are the principal subjects on which statistics are annually published in the Statistical Abstract for the United Kingdom?

12. Write a valuation report of a Life Assurance Company framed so as to afford in the shortest compass the information required for understanding its real position.

13. What have been the principles adopted in the changes that have been made since 1842 in the customs duties of the United Kingdom?

II.

14. Admitting that it is expedient to obtain part of the revenue of the country by direct taxation, Do you think that the present income tax best answers this purpose? and if not-What alteration would you suggest?

15. Point out the difference in the contract between the Government and the Fundholder: and between a Railway Company and its Debentureholders.

16. Explain the constitution of the Bank of England.

17. State shortly the opinions entertained by Lord Overstone and the late Mr. Tooke in reference to the separation of the Issue and Banking departments of the Bank of England.

18. Name any classes of Investments that you consider to be specially suited for the investments of a Life Assurance Company, and give your reasons.

19. How and why do the fluctuations in the rate of interest on mortgages and similar securities differ from those in the Bank rate of discount?

be

20. If a Company holds British or Foreign Government Securities as part of its investments, describe the different methods which may followed in valuing them at a periodical valuation of the Company's Assets and Liabilities. Which do you consider the best method, and why? 21. State the principal differences between a cash account" and a revenue account," and point out why the latter is more suitable than the former for the accounts of Life Insurance Companies. Describe the connection between the "revenue account" and the "balance sheet" of the 1st and 2nd schedules of the Life Assurance Companies Act 1870.

66

The Candidate having completed and handed in his answers to the above questions will be allowed the use of any books he may desire in answering the following questions:

22. What is the market value of the reversion to £1000 Consols receivable at the death of a lady age 65 if a gentlemen age 30 shall survive her?

23. A, age 35, is entitled to a reversionary life interest in an estate of ample value, provided his uncle age 70 die without leaving male issue his wife being 65 and in good health. What reversionary annuity should A grant in consideration of a present advance of £1000? How would you provide for the risk of A proceeding to a tropical climate?

24. What, in your opinion, is the value of the next presentation to a living producing £600 a year net, with a good house, the age of the present incumbent being 72 ?

25. A loan is raised by the issue of £5,000,000 5 per cent stock at the price of 85; and the stock is to be paid off at par by annual drawings by means of an accumulative sinking fund of £200,000 per annum. In how many years will the loan be paid off? And what rate of interest is virtually paid by the borrower?