Under an individual life insurance policy, a policyholder selects one of several premium payment options. Under a "single premium" policy, the policyholder purchases the policy with a single premium payment at the issue date. It is more common, however, to pay premiums on an annual or more frequent periodic basis, and this discussion will assume that method of payment. The reserve for a fully paid-up premium policy, such as a single premium life insurance policy or a policy for which no further premiums are due, is simply a special case of the reserve for a premium-paying policy.

Under a traditional whole life insurance policy, the insured death benefit (called the face amount of the policy) remains level and guaranteed for the lifetime of the insured person, provided the required premiums are timely paid. The premiums are usually paid in equal annual installments over the lifetime of the insured, or over a fixed number of years. Since the risk of death increases as the insured person ages, the annual cost of insurance under the policy also increases. The annual cost of insurance is called the annual mortality cost, which is simply the expected amount of claim for that year ( "amount at risk" ) based on the insured’s assumed death rate for that year. The assumed annual death rates are obtained from standard actuarial tables, called mortality tables, which the insurance company uses to calculate its premiums and reserves. In order for the insurance company to charge a level annual premium for the policy, when the annual mortality cost is increasing, the premium charge during the early policy years must be greater than the mortality costs for those years. Accordingly, the premium charge for later policy years will be less than the mortality costs for those years. This gives rise to the concept of a policy reserve during the life of the policy because, if the insurance company is to have sufficient funds to pay the claim costs in the later years when those costs exceed the level premiums, it must accumulate the excess level premiums in earlier years. It is this "accumulation" with interest, of past excess level premiums that generates the reserve at each policy duration. Thus, the function served by the reserve is to balance the premiums with the rising mortality costs.

The policy reserves, however, are not actually computed by accumulating, with interest, the actual premiums charged the policyholder and then subtracting the actual past mortality costs. The actual premium charged is called the "gross" premium, which is the total amount that the insurance company determines is required to cover estimated mortality costs, policy expenses and a margin for profit and contingencies. Naturally, the gross premiums must also be competitive with gross premiums charged by other insurance companies if the policy is to be marketable. The setting of gross premium scales for insurance policies is called "pricing," which involves many different actuarial assumptions and complex calculations. Life insurance reserves, on the other hand, are calculated by using an entirely different set of premiums calculated on a "net" basis. These net premiums, sometimes called "valuation net premiums" or "tabular net premiums," are calculated using only mortality and interest assumptions, so as to cover just the mortality costs with no allowance for expenses or profits. The premiums are calculated independently of the gross premiums charged and are used strictly to determine the actuarial reserves. As a margin of safety, the reserve valuation laws of the various states require that life insurance policy reserves for the company’s annual statement must be determined on a net premium basis. The gross premiums charged generally exceed the reserve valuation net premiums. This excess has often been called the "loading." However, since the gross and the valuation net premiums are calculated independently of each other, there are instances where that relationship changes and the valuation net premiums exceed the gross premiums. When that is the case, the state regulatory authorities require that adjustments be made to the reserves otherwise determined so that the annual statement reserves for those policies will not be deficient. Such additional reserves are known as "deficiency reserves."

The first step in the reserve process is to calculate the valuation net premiums using an assumed mortality table and an assumed interest rate, which are the key actuarial assumptions, Under one of several different valuation methods of calculating reserves, known as the Net Level Premium Method, these net premiums are determined as a level amount over the entire premium paying period. Other reserve valuation methods may be used which affect the pattern in which the reserves accumulate, and these will be mentioned later in this section. Once this net premium is determined, policy reserves may be calculated for any policy duration by utilizing either of the two reserve balancing equations—the Retrospective Equation or the Prospective Equation:

After selecting a mortality basis and an assumed interest rate and calculating the net premiums, select one of several acceptable reserve valuation methods. The valuation method defines the pattern or rate at which the reserves accumulate over the life of the policy whichever valuation method is selected. The reserve will become the same at some designated future duration eventually. The reserve must accumulate ultimately to the face amount of the policy when the insured attains the terminal age of the mortality table (i.e., the age by which all insured individuals are assumed to have died). The Net Level Premium Method is one of these valuation methods.

The Net Level Premium (NLP) Method has been the traditional method of calculating life insurance reserves used by life insurance companies. Other valuation methods, called "modified reserve methods," have been developed to compensate for an inherent weakness in the NLP method. Under the NLP method, the net valuation premiums remain level over the entire premium paying period. Consequently, the loading included in the gross premium charge, intended to cover policy expenses, is clearly the same amount for each policy year. A life insurance company’s actual policy expenses, however, are not level and, moreover, are significantly higher in the first policy year than in renewal years. The very high first year expenses are a natural consequence of the process of selling and issuing an individual life insurance policy. Agents’ sales commissions are much higher in the first year than in renewal years. There are also first-year non-recurring expenses to underwrite and approve the insurance application, for medical examinations, and for clerical functions to set up initial records and to issue the policy. The total first year expenses generally exceed the expense loading charged in the first year gross premium, and may even exceed the entire first year gross premium. Under the NLP method, the first year net premium is entirely used to cover the assumed mortality costs of that year and establish the first year policy reserve. As a result, the remaining expense loading from the gross premium becomes insufficient to cover first year actual expenses. The life insurance company is then forced to make up this insufficiency by borrowing from its surplus funds, in effect a "surplus loan," which then gets returned to surplus in renewal years as the gross premium expense loading becomes more than sufficient to cover actual renewal year expenses. Normally, this first year new business surplus strain creates little difficulty for well established companies with ample surplus funds. For small or newly established companies with limited surplus, however, this need to draw on surplus to finance new business ( "surplus strain" ) could impair their financial position and their ability to generate new business.

This situation is alleviated by deploying a modified valuation method that recognizes the decreasing incidence of expenses and provides a greater amount of expense loading in the first policy year than in renewal years. This modification accumulates reserves from a first year net premium that is smaller than the net premiums for renewal years. Under modified reserve methods, the sequence of net level premiums under the NLP method is replaced by a reduced first year net premium followed by a series of increased net level premiums for renewal years over a specified number of years. At the end of the specified modification period, the original net level premiums are restored and full NLP reserves are carried. This modified net premium sequence must be equivalent in actuarial value to the sequence of original unmodified net level premiums, so that the modified reserves will grade up to the NLP reserves. Modified reserve methods produce lower reserves than the NLP method in the first policy year and throughout the entire modification or grading period. The intent of these reserve methods is to reduce the first year net level premium, thereby increasing the amount of the first year expense loading. In effect, the modified method borrows some portion of the first year net premium under the NLP method to partially offset the expense loading insufficiency, and progressively returns the borrowed portion to the reserves in renewal years.

Several of the recognized modified valuation methods that have been in general use for calculating life insurance reserves are the Full Preliminary Term (FPT) Method; Commissioners’ Reserve Valuation (CRVM) Method; Illinois Method; New Jersey Method; and the Canadian Method.

The FPT method provides the greatest additional first year expense allowance because its first year net premium covers only the assumed mortality cost of the first year. As a result, the reserve at the end of the first policy year is zero. Thereafter, the modified renewal net premium is exactly the same amount as the net premium under the NLP method for an exactly similar policy issued one year later at an age one year older, and the reserves accumulate accordingly. The FPT method is not appropriate for all types of policies because of excessive additional first year expense allowances for high premium policies, and its application is restricted by state regulatory authorities.

The other methods listed above are called "modified preliminary term methods," because they all modify in some way the additional first year expense allowance under the FPT method. They differ from each other in the amount of the additional expense allowance and the length of the modification period. The CRVM is significant because it has been adopted by the state regulatory authorities, pursuant to the NAIC Standard Valuation Law, as the prescribed valuation method in defining minimum annual statement reserves for individual life insurance policies. It is also significant for income tax purposes, because it is the prescribed method for calculating life insurance tax reserves for life insurance policies under IRC section 807(d). This is discussed further in text 4.6.3 of this handbook.

In order to closely regulate life insurance companies in certain areas of their activities, state insurance laws and regulations impose minimum reserve requirements on all reserves reported in company annual statements. The states’ concern is with insurance company solvency and the protection of policyholder interests. Policy reserves for all life insurance policies must, in the aggregate, equal or exceed a total reserve level which is determined by using certain prescribed assumptions for mortality and interest and a prescribed valuation method. These prescribed standards for determining minimum statutory reserves generally follow the provisions of the NAIC Standard Valuation Law and its interpretations. CRVM is the value method model as incorporated in state statutes prescribed by both the NAIC and Federal tax law for defining individual life insurance reserves. The prescribed standards for mortality and interest will vary by line of business and policy issue date. Statutory standards are established to produce conservative minimum reserve levels in keeping with the states’ responsibility to regulate financial solvency. It should be noted, however, that companies are permitted to use any actuarial basis for determining statutory reserves, provided the approach results in aggregate reserves that equal or exceed the minimum reserves produced by the statutory standards.

Mortality Tables: The life insurance industry conducts ongoing studies of mortality experience under all types of life insurance policies and annuities. For purposes of calculating premiums and reserves, the industry has constructed and published a number of standard mortality tables. A mortality table tabulates annual death rates for each integral age from age 0 (or the earliest significant age) to an arbitrary terminal age, usually around age 100. For ordinary life insurance policy reserves, the mortality tables are, or have been, in common use the Commissioners 1980 Standard Ordinary Tables (1980 CSO); Commissioners 1958 Standard Ordinary Table (1958 CSO); Commissioners 1941 Standard Ordinary Table (1941 CSO); American Experience (AE) Table; and the American Men (AM) Table.

Interest Rates: The Standard Valuation Law prescribes the maximum interest rates that may be used in calculating the minimum reserve standards for life insurance and annuity contracts. Again, this is to ensure that such policy reserves will be conservatively valued. Since life insurance and annuity contracts generally reflect long-term commitments, the effect of the assumed interest rates on their reserves can be highly dramatic. Generally, the higher the interest rate assumption, the lower the required reserve.

One further component in the calculation of a policy reserve is the timing function. This refers to the assumptions as to the time when claims and premiums will be payable. Normally, it is the practice of life insurance companies to pay death benefits as soon as possible after the death occurs. Premiums, on the other hand, are usually payable at scheduled dates depending on the payment mode elected by the policyholder. However, to facilitate the computation of premiums and reserves, it is customary to make convenient assumptions as to the timing of claims and premiums.

Curtate Function: Under this function, death benefits are assumed to be paid at the end of the policy year of death, and all annual premiums, irrespective of the actual payment mode, are assumed paid at the beginning of the policy year. This claim payment assumption is convenient because annual death rates, as measured to the end of a year, are exactly calculated from mortality tables.

Continuous Function: Under this function, death benefits are assumed to be paid at the moment of death, and all annual premiums, irrespective of the actual payment mode, are assumed to be paid uniformly throughout the policy year. This idealized premium payment assumption is particularly convenient when the actual premium mode is quite frequent, such as the weekly mode (under industrial life insurance) or the monthly mode (when paid through a payroll deduction plan). Special actuarial adjustments are made to convert curtate functions to continuous functions. Reserves calculated by continuous functions will be higher than when calculated by curtate functions. The reason for this is that, since, on average death benefits are assumed to be paid one-half year sooner and premiums are assumed to be received one-half year later, additional reserves are needed to compensate for the loss of interest on the death benefit and for the loss of one-half year’s premium during the policy year of death.

Semi-continuous Functions: Under these functions, either death benefits are assumed to be paid at the moment of death, or annual premiums are assumed to be paid uniformly throughout the policy year.

For any individual policy, actuarial reserves may be exactly calculated for each policy year as of the end of the policy year. A reserve value at the end of a policy year is called a "terminal" reserve. A reserve value at the beginning of a policy year is called an "initial" reserve, which is simply the sum of the terminal reserve for the preceding policy year plus the net premium for the current policy year. For statutory reporting purposes, however, reserves must be established as of the annual statement’s year-end date, December 31, in total for all policies in force as of that date. Life insurance companies issue policies throughout the calendar year and, as a result, policy anniversaries fall on many different dates. For most of the policies in force, the December 31 valuation date will not coincide with a policy year-end date, but will fall at an interim point during the current policy year. When a policy’s reserve must be valued as of a date that falls between its policy year-ends, the valuation is called an "interim" valuation. Life insurance companies often use approximation methods, which deploy terminal reserves, to conveniently estimate interim reserves for annual statement purposes where large numbers of policies are involved. Three such approximation methods in common use are the Mean Reserve, Mid-Terminal Reserve and Interpolated Reserve methods.

Mean Reserves: This method assumes that a large group of policies have issue dates evenly distributed throughout the calendar year (so that the "average" anniversary date is July 1, and an average one-half a policy year has elapsed by December 31), and premiums are paid annually at the beginning of the policy year (so that by December 31 it is assumed that every policy has paid a full year’s premium for the current policy year). The mean reserve (or, mid-year reserve) for each policy equals the average (mean) of the current policy year’s initial and terminal reserves. For a large group of policies which do pay annual premiums, the mean method is a reasonable estimate of their total reserves at December 31; and for those annual premium policies which do have a July 1 anniversary date, the mean reserve is the theoretically correct reserve at December 31. For many of the policies in the group that pay their policy year premiums in installments, the mean reserve method’s annual premium assumption overstates the premiums actually paid by December 31 for the current policy year and, thereby, overstates their December 31 reserves. When premiums are paid on a "fractional" or "modal" basis (e.g., semi-annually, quarterly, or monthly) some portion of the total fractional premiums for the current policy year will fall due after December 31, and that portion is called "deferred fractional premiums." To effectively offset the mean method’s inherent reserve overstatement for policies with deferred fractional premiums, statutory reporting requires certain accounting procedures. The total of all gross deferred premiums is compiled and explicitly reported in the annual statement and included in premium income for the current calendar year, gross loading charges are deducted from that income as expenses, and a special asset account is established on the balance sheet as of December 31 equal to the related net valuation deferred premiums (as if the net deferred premiums were amounts receivable). Net valuation deferred premiums are used because the sole purpose of this asset account is to offset the excess net premiums included in the mean reserves. If any deferred fractional premiums are actually paid prior to December 31, they are not included in the deferred premium asset and, under statutory reporting conventions, they are not treated as advance premiums. Moreover, any gross premiums that were due prior to December 31, but uncollected as of that date, are accounted for in the same manner as deferred premiums, with the net portion included in the same asset account. This asset account is identified in the balance sheet as "life insurance premiums deferred and uncollected." Life insurance companies may determine their net deferred and uncollected premiums either on a seriatim basis (i.e., a policy-by-policy listing of gross and net premiums), or on an aggregate basis (i.e., applying group ratios of net to gross deferred and uncollected premiums from historical experience). In the special case where terminal reserves are based on continuous functions, whereby premiums are assumed to be paid uniformly throughout the policy year, the mean reserve is simply the average of the terminal reserves for the preceding and current policy years. There are no adjustments required to these reserves, since the annual premium payment assumption under the mean method does not apply. There are no deferred fractional premiums to adjust for. The mean reserve method is commonly used for computing annual statement reserves for ordinary life insurance policies.

Mid-Terminal Reserves: Under this method, it is also assumed that the policies in the group have an average anniversary date of July 1 and that one-half a policy year has elapsed by December 31. However, no direct assumption is made as to the amount of current policy year premiums paid in by December 31. Therefore, the mid-terminal reserve is determined as the average (mean) of the terminal reserves for the preceding and current policy years, plus an unearned premium reserve equal to the portion of the modal premium due prior to December 31 which covers the period from December 31 to the next modal premium date. The unearned premium reserve may be based on net valuation premiums or gross premiums, and it may be calculated by using either the exact unearned period or a simplified approximation such as one-half the modal period. Under this method, no deferred fractional premium asset is established. If the policy pays annual premiums, then the mid-terminal method is identical to the mean method when one-half year’s net premium is used as the unearned premium reserve. The mid-terminal reserve method is generally used for computing annual statement reserves for industrial life insurance and for individual health insurance policies.

Interpolated Reserves: This method introduces a refinement to the mid-terminal reserve method. There is no assumption as to an average anniversary date of July 1. Instead, the actual anniversary date of each policy is taken into account by applying a linear interpolation between the terminal reserves for the preceding and current policy years based on the exact fraction of a year elapsed from the actual anniversary date to December 31. The unearned premium reserve, which is added to the interpolated terminal reserves, is then determined as the exact unearned portion of the net modal premium. As in the case of the mid-terminal method, no deferred fractional premium asset is established, since no direct assumption is made as to the amount of current policy year premiums paid in by December 31. If the policy has an anniversary date of July 1 and it pays annual premiums, then the interpolated reserve method is identical to both the mean and mid-terminal methods. Some companies use the interpolated reserve method for computing annual statement reserves for ordinary life insurance policies as a refinement and to eliminate the need to establish a deferred fractional premium asset.