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.

Sec. 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.

Sec. 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