§ 4. Level annual term 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 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 that 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, within the definite term for which 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, whatever be the term. The total reserve is essential to the solvency of the company and the payment of all the policies as they fall due.

The companies that 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. They had in 1919 more than 58,000,000 policies in force, for a total of nearly $36,000,000,000 of indemnity (insurance in force) ; their total income was nearly $1,600,000,000 (about one fortieth being from investments, the remainder from premiums), and their total assets $6,700,000,000. These figures grow so rapidly that any statistics are soon out of date. The upward curve may be seen in the following data:

Reserve insurance is carried on by both mutual and stock companies; of late some large stock companies, such as the Equitable and the Prudential, have been transformed into mutual companies. The mutual company legally belongs to the policyholders, though its control is actually in the hands of a self-perpetuating group of trustees and officers, more or less supervised by state officials. 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 five, ten, or twenty 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 policy was objectionable in that it involved a lottery element, the survivors winning the "dividends" that should have been paid to the deceased; 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.

§ 5. Term policies and straight life. A person purchasing life insurance, taking out a policy, finds himself facing a choice among a confusing variety of policy forms. Apart, however, from some comparatively minor features such as those just described, as to distribution of dividends, the various forms of policies result from combining in various ways three features. The first of these is the term within which the level premium is calculated. This may be one year, or any number of years, most frequently five or some multiple. Whatever be the term, the rate of premium is calculated with respect to the expected mortality at the ages included, and at the renewal of the insurance for a new term the premium rate "steps up" to that required to meet the expected losses at the higher ages. Evidently, the shorter the term for which a policy is written, the lower the rate of premium, for the early years, because the smaller the reserve needed to keep down payments in the later years of the term. For example, on a twenty-year term policy taken at age 35 the natural premium would be $10.80 a year. Break this term up into two terms of ten years each, and the annual premium for the first ten year would be $9.36; but when the policy is renewed for the second term of ten years (at age 45) the rate would be nearly $15.00. The policy known as "straight life" or "level life" is simply term insurance for the term limit (or highest age) of the mortality table (in the American Experience table that is 96). The net premium for straight life at age 35 is $19.91, and this permits (at the rate of earnings assumed) the accumulation of a reserve of $310.75 at the end of twenty years, whereas the reserve on the twenty-year term ending then is zero. The income of this reserve, added to the annual premium, is enough to meet the expected losses in the later years as they gradually rise. (These amounts are on the assumption of the American mortality and 3 1/2 per cent interest.)