interests of the Institute. I cannot entirely accept the flattering compliment which Mr. Brown has been kind enough to pay me, in saying that I have had much more influence in forwarding the interests of the Institute during the last two years than other members of the Council. When the Council did me the honour to recommend me to your notice as President, and you did me the honour of electing me, I certainly should not have undertaken the duties of the office if I had not felt confident that I should be supported by the very able and experienced gentlemen whom I had the pleasure of meeting at the Council. For the assistance I have invariably received from them, and the support they have on all occasions afforded me in the discharge of my duties as President, I beg leave to tender my thanks to the Council. It is gratifying to me to think that the gentleman who is to succeed me is much more calculated to further the interests of the Institute than I could possibly be. Mr. Tucker is a gentleman who is so well known to you that he needs no praise from me, although some of the younger members may not be aware of the great service he rendered at the early establishment of the Institute, and the valuable assistance he afforded during the long period he held the office of honorary secretary. (Hear, hear.) He was also very active as one of the early examiners of the Institute, in which I had the honour of being associated with him, and I do not think we could have committed the interests of the Institute to a gentleman who is better qualified to uphold them, by scientific knowledge, great experience, high character, and the eminent position which he holds in the profession. (Cheers.) Again, gentlemen, I thank you for your kindness, and for the partial view you have taken of my humble services; and although may not perhaps be able at present to render much assistance to the Institute, I shall at all times, in whatever capacity I may be placed, be anxious for its success, and desirous to forward its interests in every way that may lie in my power. (Cheers.)

I

-“

Mr. W. A. BOWSER-"I have very much pleasure in moving that the best thanks of the meeting be given to the retiring Vice-Presidents, Council, and other officers, for their valuable services during the past year. I am sure that you will all cordially join with me in passing this resolution, which is so thoroughly deserved. As one of the younger members, I can bear testimony to the kind way in which the Council have encouraged the younger members during the past year, and I think it is our duty to acknowledge that kindness on the present occasion. (Hear, hear.) I will, therefore, without further remarks, move the resolution which I have read."

Mr. MOUNTCASTLE seconded the resolution, which was carried unanimously.

Mr. A. H. BAILEY-"On behalf of the other Vice-Presidents and myself, I thank you very much for the kind manner in which you have appreciated the services we have rendered to the Institute. As you have heard such a full exposition of the affairs of the Institute, I do not think it necessary to add anything on this occasion, except that I have no doubt the Council will take up Mr. Sprague's suggestion, and, as we are richer than we were some years ago, will do what in them lies to apply the income of the Institute to the general benefit of the members, and our younger members in particular. (Hear, hear.) I do not think there is any occasion for us to go on accumulating money, and therefore I hope some means will be found for still further extending the usefulness of the Institute." (Hear, hear.)

The PRESIDENT announced that the library would be closed as usual during the month of September.*

*The above report of the proceedings is extracted from the Insurance Record.

Ordinary Meetings

Subscriptions unrecovered

9 16 0

£688. 18s. 2d. Consols

£2,812

JOURNAL

OF THE

INSTITUTE OF ACTUARIES

AND

ASSURANCE MAGAZINE.

On the Means of dispensing with Extra Premiums for Deteriorated Health. By W. M. MAKEHAM, Fellow of the Institute of Actuaries.

THERE are few things so discouraging to an agent, after successfully canvassing for an assurance, as to find that the medical examiner is unable to recommend the case (which has, perhaps, been secured by a serious expenditure of time and trouble), without an addition to the ordinary rate of premium. Knowing the difficulty he has experienced in persuading the proposer to take the decisive step, the agent feels that, in nine cases out of ten, the demand for an extra premium is tantamount to the rejection of the proposal-for, somewhat unreasonably, perhaps, instead of impressing more strongly upon the party concerned the importance of life assurance, the effect is generally to irritate and annoy-or even to create in his mind a suspicion that he is treated unfairly in being required to pay a higher rate than other persons of the same age.

The recently published experience of Assurance Offices shows, beyond dispute, that lives which have been taken at an extra premium are, upon the whole, materially worse than those taken at the ordinary rates—although, perhaps, not to the extent which might have been supposed. Comparing the average duration of life among the healthy and deteriorated lives respectively, I find

VOL. XVII.

L

while from and after the age of 80 the two tables ab indeed, in some instances, the deteriorated lives h advantage-an anomaly due probably to the pauci under observation at these advanced ages.

It is to be regretted that the average amount of charged in the cases from which these results wer not been ascertained. Nevertheless, I think it is while the existence of a higher mortality is indi covered, and probably considerably more than co extra charges usually made. The conclusion, th drawn from the experience in question, seems to perhaps, the imposition of extra premiums may be s sparingly resorted to than formerly, still it would b dicious to dispense with them in cases where the decidedly unfavourable circumstances is evident. Fo a fair general average were obtained, the tabular ra fully adequate to cover the normal proportion of such office known to adopt a practice of this kind would resorted to by an inferior class of lives, in numbers disturb the average, and thus its aggregate mortality means be affected to a serious extent.

When a medical examiner is called upon to form of the amount of deterioration in the value of a life assurance, he generally expresses it in the number of in his opinion, should be added to the real age in fix of premium-thereby implying (whether intentionally the nature of the deterioration is such, that while th risk is somewhat increased, yet that the principal re addition lies in the probability that the future risk will to a much greater extent as the life gets older-by th were, of a premature old age.

it

This, consequently, is the way in which deteri hitherto been exclusively treated by Assurance Offices.

assumed to be of the age for which the rate of premium is assessed, and in any subsequent calculations the age corresponding thereto is taken as the actual age of the life assured.

When this theory of the nature of the deterioration coincides with the fact—that is to say, when the aggregate extra risk is really distributed in a progression increasing with the age-there is, perhaps, no more satisfactory way of dispensing with the necessity of imposing an extra premium than that of substituting an Endowment Assurance (that is, an assurance payable at death, or upon the attainment of a certain stated age) in lieu of an ordinary assurance payable at death only.

For instance, the net single premium required to provide the sum of £100 at the death of a person aged 30 is (by the Carlisle 4 per-cent table) £31. 6s. 9d., while in the case of a person aged 40 it is £38. 3s. 7d. Hence it appears that in an ordinary assurance effected by a single premium, an addition of 21.8, or nearly 22 per-cent, is necessary to cover the increased risk equivalent to an addition of 10 years to the age.

Again, the single premium (age 30) required to provide £100 to be paid on the attainment of the age of 50-that is to say, at the expiration of the term of 20 years,—or at death, if that event shall happen previously, is £50. 6s. 3d.; while for age 40 a similar assurance (for the same term of years) requires a single premium of £51. 12s. 3d. In this case, therefore, an addition of about 2 per-cent (2·6) is sufficient to cover the increased risk equivalent to precisely the same addition (viz. 10 years) to the age.

It is evident, therefore, that if the effects of deterioration are truly represented by an addition of a certain number of years to the age, a damaged life, which could not safely be taken by the ordinary table without a considerable addition to the usual rate, might without any very material increase of liability be accepted for an endowment assurance at the ordinary rate of premium.

The reason for this somewhat paradoxical result will be found to be as follows. An endowment assurance consists of two entirely distinct parts, viz., first, an ordinary life assurance for the given term, and secondly, a sum payable only in the event of the proposer surviving a certain age; and the premium charged 'really consists of the sum of the premiums required for these separate contingencies. Now, by the assumption made as to the distribution of the extra risk, the portion of the premium required to cover the. term assurance, although increased to some extent, is by no means so much increased as it would be under an assurance for the whole