The foregoing definition of the reserve reflects the prospective concept of the reserve, stemming from the emphasis on the future. Under the prospective method of valuation, no consideration is given to past experience apart from the basic mortality and interest assumptions entering into the formula. This approach works well for fixed-premium contracts. On the other hand, the reserve may be derived entirely by reference to past experience; this reserve is known appropriately as the retrospective reserve (the appropriate method to use to calculate reserves for flexible-premium contracts). The retrospective reserve represents the net premiums collected by the company for a particular class of policies, plus interest at an assumed rate, less the death claims paid out. Both concepts are mathematically sound and with the same set of actuarial assumptions will produce identical reserves at the end of any given period. If the actual experience is more favorable than that assumed in the reserve computations, the savings will go into surplus, to be disposed of in accordance with the company�s judgment; the greater portion is normally distributed to policyowners as dividends.

In theory the reserve can be calculated on the basis of either the gross premium or the net premium. Under gross premium valuation, the loading element is taken into consideration; under net premium valuation, only mortality and interest are taken into account. Viewed prospectively, the gross premium reserve is equal to the excess of the present value of future claims and future expenses over the present value of future gross premiums. Viewed retrospectively (as is done for universal life policies), it is the excess of gross premiums collected in the past over death claims and expenses incurred, with this difference growing at an assumed rate of interest. Gross premium valuation was the accepted practice among American life insurance companies until 1858, when the state of Massachusetts enacted legislation requiring the use of the net premium basis. Other states followed Massachusetts� lead, and today net premium valuation is prescribed in every state. This is a stricter standard of solvency, the implications of which will be discussed later.

Finally, policies may be valued on either the full net level premium basis or according to modified reserve plans, methods that permit all or a portion of the normal first-year reserve to be used in meeting the excess of first-year expenses over first-year premium loading. (Modified reserve plans are described in chapter 18.)

Reserves may be classified as terminal, initial, and mean, according to the time of valuation. As its name implies, the terminal reserve is the reserve at the end of any given policy year. The initial reserve for any particular policy year is the reserve at the beginning of the policy year and it is equal to the terminal reserve for the preceding year increased by the net level annual premium for the current year. The mean reserve is the average of the initial reserve and terminal reserve for any year of valuation. For example, the initial reserve, computed on the basis of the 1980 CSO Male Table and 4.5 percent interest, for the 5th policy year of a $1,000 ordinary life contract issued at age 25 is $33.71. This sum is obtained by adding the net level annual premium of $7.49 to the terminal reserve for the 4th policy year, $26.22. The initial reserve of $33.71 will earn interest of $1.52 during the 5th year, producing a fund of $35.23 at the end of the year, from which the cost of insurance, $1.65, is deducted to yield the 5th-year terminal reserve of $33.58. The mean reserve for the 5th policy year then becomes

In the illustration for this particular policy year, the initial reserve is larger than the terminal reserve because the cost of insurance is greater than the interest on the initial reserve. This is not always true, however. Under many circumstances and policy durations, including policies issued at the younger ages and those with high interest assumptions, the terminal reserve is larger than the initial reserve. This relationship would obviously prevail at all ages of issue and at all durations for policies purchased with a single premium.

The initial reserve is used principally to determine dividends under participating policies. One of the major sources of surplus from which dividends can be paid, as will be shown later, is a rate of investment earnings in excess of that assumed in the calculation of premiums. In allocating excess interest earnings to individual policies, the initial reserve is generally selected as the base to which the excess interest factor is applied on the theory that it represents the amount of money invested throughout the year on behalf of a particular policy and hence is the measure of that policy�s contribution to the pool of excess interest earnings.

The terminal reserve is also used in connection with dividend distributions. Insurers allocate mortality savings on the basis of the net amount at risk, and the terminal reserve must be computed to determine the net amount at risk. On policies issued prior to 1948 the terminal reserve also serves as a basis for surrender values (nonforfeiture values); the predeath benefits are equal to the terminal reserve less a surrender charge. (The surrender charge exists during the early years only.) For policies issued since 1948 surrender values are calculated in accordance with the terminal reserve concept but with a so-called adjusted premium rather than with the net annual level premium.

The chief significance of the mean reserve is its use in insurers� annual statements. One of the most important items that must be reported to regulators is the aggregate amount of reserves. Since policies are written throughout the year, on any given reporting date some policies will just be commencing a policy year, some will just be completing a policy year, and some�the overwhelming majority�will be somewhere between one policy anniversary and the next. To calculate the exact reserve on all outstanding policies would be a tremendous�and unnecessary�task. Therefore it is assumed for purposes of the annual statement that on the date of valuation all policies are at exactly the mid-point between two policy anniversaries. This assumes that policies are written at a uniform rate throughout the year, which is not precisely the case, but it is accurate enough for regulatory purposes. Since life insurance companies� annual statements are invariably prepared as of December 31, all policies are valued as if they were written on June 30 by reporting the mean reserve.

The remainder of this chapter is devoted to terminal reserves computed on the full net level premium basis.