Life Insurance Pricing: Expected Value of a $100,000 Policy at $600 Premium

How Insurers Price a $100,000 Life Insurance Policy

A $100,000 life insurance policy costs $600 for one year. If the probability that persons in a given risk pool die within that year is known, the insurance company can calculate the expected value of the policy. This expected value determines whether the premium is profitable, break-even, or a loss for the insurer. Understanding this calculation reveals how life insurance companies balance risk, probability, and pricing to stay in business while paying out claims.

The Expected Value Formula for a Single Policy

The expected value (EV) represents the average outcome the insurer can expect per policy sold over many repetitions. The formula for a one-year term life insurance policy is straightforward:

EV = (Premium Collected) − (Probability of Death × Death Benefit)

If we define the variables:

• Premium (P) = $600
• Death Benefit (D) = $100,000
• Probability of death within the year (q) = a value derived from mortality tables

Then the expected profit per policy is:

EV = P − (q × D) = 600 − (q × 100,000)

For the insurer to expect a profit, the premium must exceed the expected payout. That means:

600 > q × 100,000

q < 0.006

If the probability of death is less than 0.6%, the $600 premium generates a positive expected value. If the probability equals or exceeds 0.6%, the policy breaks even or loses money on average.

Worked Example with a Specific Mortality Rate

Suppose mortality tables indicate that the probability of death for a person in a certain age bracket and health class during one year is 0.004 (or 0.4%). Plugging into the formula:

EV = $600 − (0.004 × $100,000)

EV = $600 − $400

EV = $200

In this scenario, the insurer expects to profit $200 per policy on average. Over 1,000 similar policies, the expected total profit would be $200,000.

Now consider a higher-risk group where q = 0.008:

EV = $600 − (0.008 × $100,000)

EV = $600 − $800

EV = −$200

Here the insurer expects to lose $200 per policy. This is why life insurance companies classify applicants by age, health, occupation, and lifestyle before setting premiums.

What the Probability Threshold Means

The critical probability threshold for a $100,000 policy at $600 premium is 0.006, or 0.6%. This means:

• If fewer than 6 out of every 1,000 insured persons die in the year, the insurer profits.
• If exactly 6 out of 1,000 die, the insurer breaks even.
• If more than 6 out of 1,000 die, the insurer loses money on the portfolio.

This threshold is not arbitrary. It reflects the fundamental law of large numbers. Individual outcomes are unpredictable, but across thousands of policies, the actual death rate converges toward the expected probability. Insurers rely on this statistical principle to price policies with confidence.

How Insurers Use Mortality Tables

Actuaries use life tables that break down the probability of death by age, gender, and other factors. These tables are built from decades of demographic data. For a $100,000 term policy costing $600 annually, the implied mortality assumption can be reverse-engineered:

Implied q = Premium / Death Benefit = 600 / 100,000 = 0.006

This means the insurer is pricing the policy assuming a 0.6% chance of death within the year. In practice, the premium includes additional loadings for:

• Administrative and underwriting costs
• Reinsurance expenses
• Profit margin
• Reserves for claims that may be paid after the policy year ends

A pure expected-value premium based solely on mortality would be lower than $600. The difference between the pure premium and the actual premium charged is called the loading, and it covers all expenses and profit.

Expected Value Across a Portfolio

While a single policy outcome is binary — the insured either survives or dies — the insurer sells millions of policies. The expected value of the entire portfolio is the sum of expected values across all policies. Variance decreases as the portfolio grows, making actual results increasingly predictable.

Consider a simplified portfolio of 10,000 policies, each with a $600 premium and a 0.005 probability of death:

The expected profit of $100 per policy illustrates how insurers generate consistent returns when probability estimates are accurate and the risk pool is sufficiently large.

Factors That Shift the Probability

The probability of death used in pricing is not static. Several factors cause it to vary across populations:

• Age: Older applicants have higher probabilities of death, requiring higher premiums for the same death benefit.
• Health status: Pre-existing conditions, BMI, and family medical history all affect mortality probability.
• Occupation and hobbies: High-risk jobs or activities like skydiving increase q.
• Smoking status: Smokers face significantly higher mortality rates than non-smokers.
• Term length: A 1-year policy uses a different probability than a 20-year term policy, where cumulative risk compounds.

When any of these factors change, the premium adjusts to maintain the desired expected value. A $600 premium on a $100,000 policy is not universal — it reflects the specific probability assigned to that applicant's risk profile.

Why Expected Value Matters to Consumers

Understanding expected value helps consumers evaluate whether a life insurance policy is fairly priced. If the implied probability embedded in the premium seems too high relative to the applicant's actual mortality risk, shopping around may yield better terms. Conversely, if an insurer's pricing reflects a lower probability than the applicant's true risk, the policy may be underpriced and the insurer may later adjust rates or decline renewal.

The $600 premium on a $100,000 policy is a concrete example of how probability drives financial decisions in the insurance industry. It connects abstract statistical concepts — expected value, mortality tables, law of large numbers — to the real-world transaction of buying and selling life insurance protection.