(See No. 144, pp. 1253-1273.)
Naval Constructor D. W. Taylor, U. S. Navy.—I think the Naval Institute is to be congratulated upon the appearance of Commander Nulton’s article upon life insurance. This is not only a subject of great general interest which is little understood, but is one as to which naval officers are particularly concerned, and in need of information.
The American Experience Table of mortality given by Commander Nulton has been the accepted table in this country for many years and one wonders if it is not time to revise it in view of the progress in sanitary matters since it was derived. I believe the Combined Experience Table, sometimes called the British Experience Table antedates even the American Experience Table. The question of mortality in the navy has never been investigated by a skilled actuary so it is impossible to say how a naval table would compare with the American or British Experience.
In 1894-1895 a skilled actuary, Mr. L. G. Fouse, of Philadelphia, employed by the Army Mutual Aid Association, made an investigation of the statistics for army officers and produced a table which he considered applicable to the army, excluding war casualties. There is given below a table giving deaths per thousand at various ages from the American Experience Table, the British Experience Table, and the Fouse Army Table:
Death Rate Per Thousand.
Age. | American Experience. | British Experience. | Fouse Table. | Expectation of Lite Am. Experience. |
21 | 7.85 | 7.38 | 7.16 | 41-53 years. |
30 | 8-43 | 8.42 | 8.45 | 35-33 |
40 | 979 | 10.36 | II.II | 28.18 |
So | 1378 | 15-94 | l6.45 | 20.91 |
60 | 26.69 | 30.34 | 28.17 | 14.10 |
70 | 61.99 | 64-93 | 61.14 | 8.48 |
The Fouse Table seems to indicate a death rate of army officers below the American Experience for ages under 30 and over 70, but above the American Experience from 30 to 70. Whether this would apply closely to naval officers it is impossible to say. The majority of the large insurance companies have recently combined to treat army and navy alike in requiring officers in both services to pay premiums as if they were 6 years older than their actual ages. This is certainly not warranted by comparison of the Fouse Table and the American Experience Table and it is believed that naval officers would show up as well as army officers so we must conclude
that the current experiences of the companies is materially better than the American Experience Table, or their experience with the army and navy officers materially worse than the Fouse Army 1 able. It should be said, however, that Mr. Fouse arrived at his table by averaging the experience of the Army Mutual Aid Association and the army at large and his investigations developed the curious fact that for the earlier ages the Army Mutual Aid mortality has been markedly less than that of the army at large ; the latter being materially above the American Experience. This discrepancy became steadily less as the age increased and above so there was little or no difference between the two.
It would seem that the experience of the insurance companies has been in line with the results found by Fouse for the army at large. Generally speaking it would seem that the vocational risk in time of peace must be greater for young officers. The war risk is, of course, confined to officers on the active list and is moreover greater for the younger officers. Fouse concluded that for the army the war risk or liability to death in battle or from wounds there received represented a yearly cost for that particular risk of $2.18 per $1000 of insurance at age 25 and diminished to o with age 57.
No one can make any real investigation of life insurance without coming absolutely to Commander Nulton’s conclusion that “Life insurance in its real sense is protection and not investment.” Unfortunately human nature is so constituted that the average person will get into life insurance much more readily if he believes there is something in it for him. Hence the companies are driven to devise all sorts of arrangements combining straight life insurance and investment or saving. This works for good in a way since many people arc only induced to take insurance which they should have by the bait of the investment features. As a matter of fact anyone who will carefully figure the returns he may expect from the investment features of any policy will find that his investments are returning him a very low interest. It is not difficult to make such calculations. The table above gives approximately the expectation of life which may be taken as representing what would happen to the average man.
The expression for the amount of $1.00 at compound interest i at the end of n years, the interest being compounded yearly is (I +*’)“• In this 1 should be expressed in absolute terms. Thus for 4%, i = .04. The expression for the amount at the end of n years of $1.00 paid in advance each year, interest being compounded annually, is also comparatively simple. This amount is
(1 •+- »)n+* — 1
------------------------------------------- _ j
I
It is generally known that compound interest is a wonderful accumulator and one is at first sight disposed to think that life insurance companies derive the full benefit of it; that is that the payments made by the insured accumulate at compound interest during their lives. This, however, is very far from being the case.
Using the American Experience Table given by Commander Nulton on page 1255, suppose the 85.441 persons of age 30 combine and each puts in
$1.00 annually in advance until his death, the amounts in hand being compounded annually at 4% interest. The total fund thus provided would be $8,197,444, or $95.96 for each of the 85,441 persons. Hence if each person put in $10.42 annually the total accumulation figured as above would amount to $1,000.00 apiece. Now $10.42 per thousand is very different from the $19.00 per thousand given by Commander Nulton as a standard premium for age 30. This is largely because, as already stated, the insurance fund does not get the full benefit of the compound interest for the lives of the contributors. Some of the money put in by the long-lived contributor does not accumulate until his death but must be used at comparatively early stages to help pay the benefits of those who die and the real net amount which each of the 85,441 persons aged 30 should pay in annually to enable each one to have $1000 at death would be not $10.42, but $16.21 for a 4% interest rate. If this $16.21 could get the full benefit of compound interest the rate need be only 2j/j% instead of 4°/o to cause the fund to amount to $1000.00 per subscriber.
We may adopt an engineering term and call this the effective compound interest rate, the difference between 2^/3% and the 4% being a loss of efficiency, as it were, unavoidable with the level premium life insurance. For the $19.00 premium required, which is $2.79 more than the net 4% premium, the effective compound interest rate need be only 1.7%.
We may look at the matter in another way. Suppose we take the net annual premiums per $1000 for 4% interest and compare them with the net annual premiums required if we could get the full benefit of compound interest. We have seen that for age 30 the net annual premium is $16.21 afld the full interest premium $10.42, the former being 56% greater than the latter.
At 20 years of age the net annual premium is 81% greater than the full compound interest premium; at 40 years 39% greater; and at 50 years 29% greater. These figures apply only to the net premium, not to the actual charge with loading, which as you have seen for 30 years age is $19.00 instead of $16.21.
I hope that the preceding will help to make plain the fact that life insurance is a poor investment. The investor may expect to have returned to him on the average materially less than 2% on his money; whereas depositors in postal savings banks can get 2J/2%; ordinary savings banks usually pay 3%; and a number of mutual savings banks in New England returned very nearly 4% to their depositors in 1911.
I do not wish to be understood as blaming the companies for the small effective interest to holders of insurance policies on the level premium plan. This is mainly due to the fact explained above that from the nature of the case the amounts paid in by a policyholder do not accumulate until his death in the case of the long-lived policyholder.
In the preceding I have used the non-participating payment rate of $19.00 instead of the participating rate which is materially higher for the first payment. When policies are on the participating basis the first payment is materially higher than necessary from the experience of the company. Later payments are made smaller to correspond to the current experience of the company, the amount of reduction being often represented as a dividend. Of course, it is not really a dividend. If it were it would be easy to make it 100% annually by making the first payment double what it should be.
As regards participating policyholders, even if we accept the roseate prophecies of agents as to the “ dividends ” to be expected it will be found that the effective interest rates corresponding to the amounts to be paid are substantially the same as for non-participating policies.
Supplementing Commander Nulton’s remarks upon the Navy Mutual Aid I would like to point out that in a comparatively small association the deaths in any one year are liable to vary quite widely from the normal.
It happened that in 1911 the deaths were above the normal and as the annual cost of the Navy Mutual Aid insurance depends absolutely upon the deaths during the year, the cost as found by Commander Nulton was but little, if any, below that of outside companies for similar insurance.
There was a great difference in 1912, however, the deaths being not nearly so many and probably below the normal so that the 1911 cost to which Commander Nulton refers was more than 40% higher than the cost for last year, 1912.
I give below the actual average cost per thousand dollars per annum of insurance to all members of the Navy Mutual Aid who have died since the beginning. This is given for 5-year periods except for the first period which is longer.
Period. | Cost per $1,000 of insurance. | ||
1879 | to | 1887 inclusive ..... | ............. $8.83 |
1888 | to | 1892 “ ................. | ............. 10.36 |
1893 | to | 1897 “ ................. | ............. 12.50 |
1898 | to | 1902 “ '................ | ............. 16.84 |
1903 | to | 1907 “ ................. | ............. 16.88 |
1908 | to | 1912 “ ................. | ............. 15-39 |
It will be observed that after the gradual increase in early stages the average cost to beneficiaries has remained nearly constant for the past 15 years, the last 5-year period indeed showed a slight reduction.
• These are average costs for all deaths. The cost to many decedents, particularly to those who entered young and died early, was much below the above averages. While this is not a place to set forth the many arguments in favor of the Navy Mutual Aid, I would like to give a few facts with reference to one allegation which seems to be widely current in the service though its source I have been unable to discover.
This is that the Navy Mutual Aid has an abnormal number of members 62 years of age and over and is liable to be swamped by them. It is a fact that the number of the 62-year and over class has largely increased during the last to years. This is simply because the association being founded some 33 years ago and the majority of members having joined at a comparatively early age it is only recently that it has been possible to have any material proportion of the membership in the 62-year class.
The distribution of the ages of members is such that there has been something of a hump passing into the 62-year class during the last 10 years,
but this has reached its maximum and the number of the 62-year class is again on the down grade. There were 267 January 1, 1911, 269 January i, 1912, and 266 January 1, 1913.
These people seem very persistent livers and it will be 30 years or more before the last survivors of the present 62-year class disappear, but the actual number in the 62-year class must diminish steadily for a number of years to come—at least ten— and so far as can be humanly foreseen there is no prospect that the percentage of such people will ever again reach the present value.
Now, how can we tell if this percentage is dangerously great? There is a very simple method which will give us a criterion for judgment. Suppose, starting with age 30, we form an ideal association composed of the members of each age in the American Experience Table given by Commander Nulton on page 1255. We would have 83,441 people aged 30, 84,771 aged 31, and so on until we reach the 21 aged 94 and the 3 aged 95. At the end of the year we would have 84,721 survivors of the 30-year class who have now become 31 years old and so on. There would be during the year 85,441 deaths and if we added 85,441 people aged 30 we would have again exactly what we started with a year before. So we may call such an association a normal permanent association for entrance at 30. The total membership would be 3,061,558 of whom 721,283, or 23.88% would be of the age of 62 and over; the average age would be 50.60 years. Similarly for a normal permanent association for entrance at age 25 we would have 20.90% of the age of 62 and over and the average age would be 47.65 years.
In view of the fact that the Navy Mutual Aid 62-year class has a hump which has passed its maximum and must decrease for a number of years to come, there would be no ground for alarm if at the moment the percentage were appreciably above the 30-year figure since the average age at entrance to the Navy Mutual Aid is not far from 30. As a matter of fact, the Navy Mutual Aid report for January 1, 1913, shows 266 members in the 62-year class of a total of 1322, or a percentage of 20.13. This is even below the percentage for a normal permanent association of entering age of 25 and cannot truthfully be represented as excessive or dangerous.
Commander Nulton rather disparages term insurance on the ground that few men desire to carry an increasing burden. Life insurance companies oppose term insurance, or rather prefer other kinds. Perhaps they are not altogether unselfish in this because in term insurance they pay out the money about as fast as it comes in, and there is no chance for that beautiful compound interest which gives sustenance to those engaged in the business of life insurance. If one must be restricted to one kind of insurance the balance of the argument is perhaps in favor of ordinary life, or limited payment life, but the argument is not all on one side and for naval officers a judicious combination is, I believe, the best.
With term insurance one pays according to his current risk, hence it is cheaper for the lower ages, and more expensive for the higher, than ordinary or level premium life, but when we look at insurance as it should be looked at, namely, as a provision against the contingency of the death of the bread winner, and consider that very few men are so situated that they should make the same provision against death at ripe old age as against
death in early manhood and middle life, we begin to see a field for term insurance. No matter what the form, the man who carries insurance to a ripe old age pays for the benefit of those who die young and is a financial loser.
Life insurance is a lottery in which you must die young to win financially. The long lived pay for the prizes. If any one needing insurance could fix the amount which he should have, no matter what his age at death, and also the additional amount or amounts which he should have in case of death in earlv manhood or middle life, and carry the additional as term insurance until the necessity for it has passed, his cost for insurance during his life would nearly always be less than if he took ordinary life, or a limited payment life. It would certainly be cheaper for those who live materially beyond middle age.
I think the prejudice many people have against term insurance is largely due to the idea fostered by insurance companies that life insurance is a form of investment and that life, or limited payment, policies, owing to the compound interest, pay the highest return.
Commander Nulton quotes an average standard life premium per thousand for the age 30 as $19.00. Suppose we see what could be done if instead of paying $19.00 per annum for life we invest $10.00 per annum at 454% compound interest and allow it to accumulate and also a sufficient amount in term insurance at net cost to make the total accumulation from the $10.00 per annum at the end of each year plus the insurance equal to $1000.00. The results would be as indicated below :
Age. | Accumulation. | Insurance needed. | Cost insurance | Total payment for year. |
35 | $70.19 | $929.81 | $8.32 | $18.32 |
40 | 144.64 | 855-36 | 8.37 | 18.37 |
45 | 237.42 | 762.58 | 8.51 | 18.51 |
50 | 35303 | 646.97 | 8.92 | 18.92 |
55 | 497-11 | 502.89 | 9-34 | 19-34 |
60 | 676.66 | 323-34 | 8.63 | 18.63 |
65 | 900.41 | 99-59 | 4.00 | 14.00 |
70 | 1179-25 |
The accumulation would pass the thousand dollar mark at age 67 when the expectation of life is still about to years.
Now, suppose we apply the same method to the 20-payment life, standard, non-participating premium of $27.00 for the age of 30 years accumulating $20.00 per annum at 4*4% compound interest for 20 years and then apply compound interest to the accumulation. The results are below:
Age. |
Accumulation. |
Insurance needed. |
Cost insurance |
Total payment for year. |
35 |
$140.38 |
$859.62 |
$7.69 |
$27.69 |
40 |
289.28 |
71072 |
6.96 |
26.96 |
45 |
474-84 |
525-16 |
5.86 |
25.86 |
50 |
706.06 |
293-94 |
405 |
24.05 |
55' |
87989 |
120.11 |
2.23 |
2.23 |
60 |
1096.51 |
|
|
|
The accumulation would amount to $1000.00 at age 58 when the expectation of life is IS years. If this $1000.00 were allowed to accumulate at compound interest for 15 years more it would become $1935-
It would appear from the above that if one is prepared to save systematically even small amounts, a combination of term insurance and invested savings would give, for a given annual expenditure, the same or more insurance protection for those who do not reach old age and a very much greater financial return for those who do reach it than ordinary life insurance. The interest rate assumed, while perhaps a little above the average for absolutely safe investment, is certainly not unreasonable.
If the American Experience Table is correct the results are substantially correct, mathematically, and the only fallacy is in the assumption that term insurance can be had at net cost, in annually reducing amounts.
This is not the case now, but with the increasing tendency observable, particularly abroad, for the government to go into the insurance business, it may not be many years before term insurance can be had at practically net cost. .
Even as things stand, the average officer could probably do better by a combination of term insurance and determined saving than by an endowment policy involving the same expense, and the younger he starts the better he can do.
Commander Nulton’s figures seem to be in strong accord with this con elusion. So far as I know, the companies do not write policies for term insurance where the premiums remain approximately constant and the amount of insurance reduced with advancing age. It is very easy to accomplish this result, however, by taking out a number of small policies and dropping them in succession. I have been unable to lay my hands upon non-participating term rates but deducting 15% from the participating rates of a large company for “dividends” I find that by a combination of term insurance and accumulation of savings at 41/2% a man of 30 can in 20 years accumulate $1000 and keep the total of accumulation and insurance at $1000 during the whole period for less than $38.00 per annum. For 4% interest this cost will be less than $40.00 per annum. These figures compare with the $43.00 per annum endowment rates given by Commander Nulton for non-participating endowment policies.
Dispersion and Accuracy of Fire.
(See No. 144.)
Lieut.-Commander D. W. Knox, U. S. Navy.—Lieutenant Long’s article is interesting from an academic standpoint, and no analysis of or investigation relating to gunnery is out of place. It is only by complete knowledge and understanding of every aspect that we can reach truly sound conclusions.
Previous discussion of the article has measurably added to. its value, but it is the writer’s belief that both the article itself and the discussion accompanying it have failed to properly recognize and consider a very essential point, and that the possibility of not having the same duly appreciated throughout the service constitutes a real danger.