§ 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."