f f1 f2 fn
P = __________ + _________ + ________ + _________
(l + r) (l + r)^2 (l + r)^3 (l + r)^n
P
p = _________
X
The payment in advance of the single premium for any selected period provides a reserve fund sufficient, on the assumptions made, to carry all the insurance without further payments. Each year there is added to the fund the income earned on investments, and there is subtracted the amount of the losses for the year, until the death of the last member of the insured group. If the deaths in the earlier years are fewer than were expected in the mortality table, this will be offset eventually by more deaths at the advanced years; but in the meantime a reserve larger than was expected is yielding income, thus providing a larger sum than is needed to pay all the policies at maturity. This surplus might be distributed as so-called "dividends" from time to time to those surviving, or be added pro-rata, at intervals, to the amount of the policies as accumulated dividends.
§ 13. #Level annual premiums and reserves.# It is a matter of no very abstruse mathematics (in principle) to find the equivalent of this single premium in any one of many other forms of premium payment. The processes are mainly but variations of present worth and compound interest calculations. Such calculations, however, lead into many complexities of practical detail difficult to explain in brief compass, and are the special task of the actuary (the mathematical expert dealing with such problems in the insurance business). The most useful actuarial equivalent of the single premium is the level annual premium for any period (term or life). Almost all policies now written have the level annual premium as a feature. The amount of the level annual premiums at first is greater than the losses; this causes for a time the steady accumulation of a reserve which yields income. Then, as the losses grow, they overtake and finally surpass the amount of the annual premiums. Therefore, the total reserve for any group of insured increases year by year to a maximum and then declines until it reaches zero with the payment of the last claim. The individual reserve for each policy not yet matured increases steadily the longer it is in force. The total reserve is essential to the solvency of the company and the payment of all the policies as they fall due. The companies which issue policies on the level premium plan or reserve plan are known as "old line" companies, or as "legal reserve" companies, because the state laws require every company of this type to maintain the reserves calculated on the basis of a certain rate of yield. The growth of the legal reserve companies in recent times constitutes one of the financial marvels of the age.
§ 14. #Different features of policies.# The premiums thus far discussed are "net premiums" estimated as just sufficient to meet the actual payments required by the contracts in the policies. To provide for the expenses of management an addition is made to the net premium called the "loading." The entire premium is called the "gross premium."
Reserve insurance is still carried on by a few stock companies, but of late some stock companies have been transformed into mutual companies, which are the prevailing type. The mutual company legally belongs to the policyholders. The gross premiums in reserve insurance are, for the purpose of safety, fixed at a figure larger than the expected cost of the insurance, and normally the earnings from interest are higher, the mortality is lower, and expenses are less than those on which the calculation of rates is based. From the excess of income resulting, the company sets aside a surplus and then divides the rest among the policyholders. These returns, virtually but the refund of excess premiums, are called "dividends" (a somewhat misleading term, not to be confused with dividends on corporate stock). The policies that receive dividends are called "participating" and are said to participate in the earnings. Formerly the majority of policies paid "deferred" dividends after 5, 10, or 20 years, according to various tontine and semi-tontine plans, the survivors to these periods receiving their dividends plus those of the other policyholders who had died or had withdrawn from the company. This form of payment having been found objectionable, it was made illegal in New York and other states, and in most cases dividends are now paid annually. The stock company, organized for profit, frequently charges lower premiums for "non-participating" policies, and then retains such profits as may result from keeping expenses below receipts.
The most popular policies are term policies (usually for 5, 10, 15, or 20 years); ordinary life policies with annual premiums; limited payment life policies (the policy payable at death, with premiums fully paid up after 10, 15, or 20 years); and endowment policies (the face of the policy payable after 10, 15, or 20 years if the insured is still living). An endowment policy must be understood to be a regular term policy of insurance for the specified number of years, plus a plan of regular annual savings, which at compound interest, accumulate to the face of the policy. Many persons are attracted to endowment insurance by the oft expressed thought that "you don't have to die to beat it." But this is a mistaken thought. For the premium in endowment insurance is much higher than that for life insurance alone during the same period, so that the endowment is merely a pretty convenient but somewhat costly plan of saving, hitched on to an insurance policy, with which "actuarially," it has no essential connection. In "scientific" insurance the insured pays its full actuarial cost for each additional feature of the policy that he buys. The various policies issued by a company are approximately equivalent actuarially, on the basis of the assumptions made, but they are of very different degrees of desirability, in view of the circumstances of the insuring individual. The choice of policies deserves a more careful investigation than it usually received. Moreover, carelessness and ignorance in the choice of a company is responsible for widespread loss and suffering.
Policies differ in respect to the mode of payment. The payment usually takes the form of a lump sum payment at death or at the maturity of the endowment. In recent times there has been a growing use of optional forms of payment which give to the beneficiary annual or monthly installments for a definite number of years or for life.
§ 14. #Insurance assets and investments as savings.# The discussion of savings institutions in the last chapter left unmentioned insurance, which probably is destined to be the most important of all. The assets of life insurance companies in the United States have already attained the enormous sum of $5,000,000,000, a sum equal to the reported savings bank deposits. In the last twenty years life insurance assets have more than doubled in each decade, and are now increasing by about a quarter of a billion dollars every year.[7] These great funds, which in equity nearly all belong to the policyholders, form already approximately one thirtieth of all the private capital of the country. They are invested in many ways, in real estate, in loans secured by mortgages on real estate, in bonds—municipal, railroad, and industrial. The problem of wise legislation for these organizations, of their competent and honest management, and of their relation to the social, business, and political life of the nation, is certain to be of ever-increasing importance. We are hardly more than emerging from the experimental stage of life insurance, hardly more than at the beginning of its development.
The premium in personal insurance (life, accident, sickness, invalidity, old age pensions) is in almost all cases paid out of some current income. The premium paid is just so much subtracted from the amount available for present direct use and applied to the purchase of future incomes for one's self or family. The insurance method differs from the method of depositing savings by its contingent nature, the resulting income of any individual being possibly much greater than the amounts actually saved (e.g., when the insured dies or is injured soon after taking insurance), and possibly less or nothing at all. A very desirable kind of insurance which is yet little developed is that for a term ending with the usual retirement age (say 65 years) combined with an old-age pension for life thereafter.