In some States laws have been passed to regulate the extravagant race for new business in which some companies would otherwise be impelled to engage, entailing excessive commissions and expensive advertising. In New York, for example, this regulation was attempted by a law providing that increased amounts of insurance must be acquired at a decreasing rate of expense and new business became more and more difficult to

secure.

CHAPTER VII

RESERVES, SURRENDER VALUES AND LOANS

Reserves, surrender values and policy loans. These may well be considered in the same chapter because of their common origin and interrelations. The reserve is a fund that grows out of the premiums paid. The amount of this fund at any time depends on (1) the kind of policy, (2) the face of the policy, (3) the age of the insured at issuance, (4) the length of time the policy has been in force, and (5) the rate of interest assumed by the company. The amount of the surrender value differs from the reserve only to the extent of a small surrender charge, made to meet the expenses incidental to the surrendering of the policy. The policy loan value is usually the same as the cash surrender value except that in place of a surrender charge the loan bears a stipulated rate of interest.

Effect of different kinds of premiums on the reserve.In order that the reserve may be clearly understood, a review of the different kinds of premiums is necessary. Life insurance may be purchased by natural, single, level or decreasing premiums. The natural premium is based on the mortality cost for one year at the age concerned and, with interest, is just sufficient to meet all death claims at the end of the year if the actual experience is the same as the expected experience. With increasing age the probability of dying becomes greater and the natural premiums must be increased to meet the larger number of death claims that will have to be paid, as shown on page 78. The increase is not uniform each year but is constantly accelerated until in the older ages it results in a premium that is prohibitive and impractical. This way of charging premiums is most frequently used in connection with the one-year renewable-term plan, which has an increasing step-rate premium. Since the sum on hand at the end of each year is sufficient to meet only the maturing policies there is no fund placed in reserve.

The single premium is exactly what its name implies, one premium of an amount which, when compounded at the assumed rate of interest, will be sufficient to meet all the losses. and expenses that will ever be charged against the policy. One

lump sum thus paid has to be so large that it is even more impractical than the former method and, therefore, is rarely used. (See page 54)

When the same amount is deposited with the company each year during the premium-paying period of the policy we have what is called a level premium. This method is superior to either of the former because the premium is moderate and is never increased. The policy-holder, it will be noted, pays to the company a larger sum in the earlier years than is necessary to pay mortality costs. This difference, with compound interest, goes into a fund known as the reserve and takes care of the later years when the mortality cost has risen to exceed the amount of the level premium but at an age when a natural premium, as we have seen, would be so high as to be unattractive and almost impossible to collect. It is this level-premium idea, variously applied, which makes possible the many types of policies that are written. Under the decreasing-premium plan, which has never attained great popularity, the premium paid decreases with advancing age and the anticipated decline of the policy-holder's earning power.

It can be seen from this that a reserve will accumulate only under the single, level and decreasing premium plans, because under the natural-premium plan, while some infinitesimal reserve may exist during the year, at the end of the year it is exhausted by the death claims. In the case of a single premium the sum is increased each year by the interest, and then from this total the current mortality cost is deducted. The remainder is the reserve. This process is repeated year after year, the factor of interest making the reserve per policy grow larger and more rapidly, as shown in Table II.

The reserve per policy under the level premium plan is not so large at first, in actual amount, as under the single-premium plan, but grows with greater speed than the single-premium reserve, because it is increased each year, not only by the interest but also by the amount of the level premium, although reduced each year by its share of the matured policy claims.

The reserve on a group of policies and also on the individual policy on the ordinary-life plan, where premiums are paid for the whole of life, taken at age 21, is illustrated in Table I, where its operation may be traced.

It was assumed in this case that there were 91,914 persons insured on the ordinary-life plan at age 21, for $1,000 each,

TABLE 1.-AGGREGATE AND INDIVIDUAL TERMINAL RESERVES

American Experience 34 Per Cent. Reserves. Ordinary Life. Age: 21

$1,000 Insurance. Net Annual Level Premium, $13.77

91,914

1,265,885.565

1,265,885.565

44,305.994

1,310,191.559

722,000

588,191.559

91,192

6.45

91,192

90,471

the net annual level premium at that age being $13.7725, according to the American Experience Table, and 31⁄2 per cent. Since the assumption is that all premiums are paid at the beginning of the year, we have total premiums collected: 91,914X $13.7725, or $1,265,885.565. At 31⁄2 per cent interest this amounts to $1,310,191.559 at the end of the year. However, 722 persons have died, and for calculation purposes it is assumed that all claims are paid at the end of the year. Therefore, $722,000 is deducted from the above total and we have $588,191.559 remaining. Since we began with 91,914 persons and 722 died during the year there are only 91,192 survivors. The sum now on hand belongs to these individuals, or approximately $6.45 per policy-holder.

The second year of the business 91,192 persons paid $13.7725 each, or $1,255,941.82. There was a reserve of $588,191.559 from the previous year, therefore the total on hand to start the new year is $1,844,133.38, and 31⁄2 per cent interest is earned on this amount. Since 721 die this year, only $721,000 will be deducted at the end of the year, the remainder belonging to the surviving policy-holders. This operation is repeated year after year in the same manner until age 96 is reached, always keeping in mind the changing yearly mortality rate. While Table I shows the process by which the individual reserve grows, Table II shows the reserve increasing on individual policies of different types, the principle of obtaining them being the same as in Table I.

TABLE II-INDIVIDUAL TERMINAL RESERVES ON DIFFERENT KINDS OF POLICIES

Amount of Insurance $1,000. Age 21. American Experience Table of