3.2 How Life Insurance Works: Mortality, Interest, Reserves

Pooling: The Engine of Insurance

No insurer can predict which individual will die this year, but across a large group the proportion who die is remarkably stable. Insurance harnesses this law of large numbers: many policyholders pay modest premiums into a pool, and the relatively few claims that occur are paid from that shared fund.

The more lives in the pool, the closer actual deaths track the expected rate. Stable, predictable losses are exactly what let an actuary set a premium today that will still cover claims decades from now.

The Three Pricing Factors

Every life premium is built from three components.

A useful shorthand: Gross premium = mortality cost + expense loading - interest credited. Mortality and expenses push the price up; interest pulls it down.

Mortality and the CSO Table

Mortality cost comes from a mortality table showing the probability of death at each age per 1,000 lives. Rates rise with age, which is why older applicants pay more.

The regulatory standard is the Commissioners Standard Ordinary (CSO) Mortality Table. The 2017 CSO table is the current version; it sets the minimum mortality basis insurers must use to compute reserves and nonforfeiture values.

Worked example. Suppose a mortality table shows 2 deaths per 1,000 at the insured's age. To fund $1,000 of one-year coverage on 1,000 lives, the pool must collect 2 claims x $1,000 = $2,000, or $2 per $1,000 of coverage for that year, before adding interest and expense effects.

Interest

Because premiums are collected before claims are paid, the insurer invests them and earns interest. The actuary assumes a conservative rate and uses it to discount future obligations, reducing the premium the policyholder must pay today.

Net Single Premium and Net Level Premium

The net single premium (NSP) is the lump sum that, if paid today and credited with interest, would exactly fund the expected death claim. It is the present value of the future death benefit, discounted for both mortality (the chance the insured survives, so no claim is yet due) and interest (the time value of money). The NSP includes no expense loading.

Most buyers cannot pay a lump sum, so the NSP is spread into a series of equal annual payments called the net level premium. Because some insureds die early and stop paying, each level premium is slightly higher than a simple average of expected claims. Adding the expense loading to the net level premium produces the gross premium the policyholder actually pays.

Reserves: The Insurer's Promise Fund

Because level premiums are overpriced in early years and underpriced in later years (when mortality cost soars), the insurer must hold back the early excess. That accumulated liability is the legal reserve.

The reserve is the amount that, combined with future premiums and future interest, will exactly equal the future benefits the insurer is obligated to pay. It is a liability on the insurer's books, not surplus profit.

The fundamental balance the actuary maintains is:

Reserve + present value of future premiums = present value of future benefits.

Key points the exam tests:

• Reserves are computed using the CSO table and a state-mandated maximum interest rate.
• Higher assumed mortality or lower assumed interest requires larger reserves.
• Companies that hold reserves on the legal reserve basis are called legal reserve insurers.
• The cash surrender value a whole life owner can withdraw is derived from, and is generally a bit less than, the policy reserve in early years.

Worked example. An insurer credits 4% interest. It must have $96,154 available one year before a $100,000 claim is due, because $96,154 x 1.04 = $100,000. That discounted figure is the reserve the company sets aside; the rest of the eventual payout comes from a year of investment earnings.