3.2 How Life Insurance Works: Mortality, Interest, Reserves

Insurance works by pooling risk. Many people who face a similar exposure each contribute a premium to a shared fund. Only some will die in a given year, so the fund can pay large benefits to the few while remaining solvent. Two statistical principles make this possible.

Law of Large Numbers and Mortality

The law of large numbers states that the larger the group of similar risks, the more closely actual losses match the predicted average. With enough insureds, an actuary can forecast deaths per thousand quite precisely even though any single death is unpredictable.

The forecasting tool is the mortality table. It shows, for each age and gender, the death rate — the expected number of deaths per 1,000 lives that year.

The CSO Table

The Commissioners Standard Ordinary (CSO) Mortality Table is the table U.S. regulators require insurers to use for computing minimum reserves and the maximum net premium. The current version, the 2017 CSO, reflects longer life expectancy than its predecessors.

Exam tip: The CSO table sets minimum reserves and the legal ceiling on net premiums. Insurers may use more conservative (higher) mortality assumptions internally, but they cannot use rates that produce reserves below the CSO standard.

Mortality cost rises sharply with age. A 25-year-old might have a death rate near 1 per 1,000; a 65-year-old's rate is many times higher. This is why the pure cost of insurance climbs every year as a person ages.

The Three Premium Factors

Every life premium is built from exactly three elements:

1. Mortality — the pure cost of the death benefit, taken from the mortality table. Higher mortality risk increases the premium.
2. Interest — investment earnings the insurer expects on premiums held before claims are paid. Higher assumed interest decreases the premium because expected earnings offset cost.
3. Expenses (loading) — commissions, underwriting, administration, and taxes. Higher expenses increase the premium.

Net vs. Gross Premium

The net premium reflects only mortality and interest. Adding the expense loading produces the gross premium — the amount the policyowner actually pays.

Gross premium = Net premium + Loading. If the net premium is $420 and the loading is $90, the gross premium billed to the client is $510.

Net Single Premium and Level Premiums

The net single premium (NSP) is the lump sum that, paid today and earning interest, exactly funds the expected death benefit using mortality and interest assumptions. Few buyers pay a single premium, so insurers spread the cost.

With a level premium, the policyowner pays the same amount every year for life even though the true cost of insurance rises with age. In early years the level premium is more than the actual mortality cost; in later years it is less. The early overpayments are invested and accumulate to cover the shortfall when the insured is old.

Reserves

The accumulated overpayments are not the insurer's profit. They are held as the legal reserve, a liability on the insurer's books representing money owed to fund future claims. Reserves are the insurer's central solvency guarantee.

• Reserves are calculated using the CSO table and an assumed interest rate.
• They are a liability, not an asset, of the insurer.
• In a whole life policy the reserve grows until, at the policy's maturity age (often 100, 121, or 100 in older policies), it equals the face amount.
• The policy's cash value is closely related to and supported by the reserve, but cash value belongs to the owner, while the reserve is an accounting measure for the insurer.

Participating vs. Nonparticipating

Mortality, interest, and expense assumptions are deliberately conservative, so a participating (par) policy issued by a mutual insurer often charges more than it ultimately needs and refunds the surplus as a policy dividend. A dividend is treated as a return of overpaid premium and is therefore not taxable until cumulative dividends exceed total premiums paid.

A nonparticipating (non-par) policy, typically from a stock insurer, pays no dividends; its guarantees are fixed at issue. The three favorable factors that produce a dividend are summarized as the three sources of surplus:

• Mortality savings — fewer insureds died than the table predicted.
• Excess interest — the insurer earned more than the assumed rate.
• Expense savings — operating costs ran below the loaded amount.

Because dividends are not guaranteed, illustrations must clearly label projected dividends as non-guaranteed — a point examiners test under unfair-trade-practice rules.

Cash value, reserves, and the legal reserve insurer

A legal reserve life insurer must hold policy reserves — a liability representing the present value of future claims less future net premiums — calculated using a standard mortality table and an assumed interest rate. Reserves are the company's promise that funds will exist to pay claims decades from now. The cash value an owner sees is closely related to the reserve but reduced by surrender charges in early years.

Why level premiums create an overpayment early

Because the mortality cost rises every year but the premium stays level, the policyowner overpays relative to true mortality cost in the early years and underpays in later years. The early overpayments, credited with interest, build the reserve and cash value that fund the higher later-year mortality cost. This is the actuarial engine behind permanent insurance and explains why whole life accumulates cash value while annually renewable term does not.