Calculating the Expected Value of a Life Insurance Policy

Define the payoff structure

Start by writing the exact cash‑flow the policy will deliver: the death benefit paid to beneficiaries if the insured dies during the term, and any surrender value or premium refunds if the policy ends otherwise.

Estimate mortality probabilities

Use an actuarial life table or the insurer's mortality table to assign a probability to each possible age of death within the coverage period. For a term policy, sum the probabilities for each year the policy is in force.

Discount future cash flows

Apply a discount rate that reflects the risk‑free rate plus a risk premium appropriate for the insurer's investment horizon. Convert each yearly benefit into present value: PV = Benefit ÷ (1+r)^t, where r is the discount rate and t the number of years until payment.

Calculate the expected value

Multiply each discounted benefit by its corresponding mortality probability and add the results. Include any premium outflows (the policyholder's payments) as negative cash‑flows, discounted to present value as well. The formula is:

EV = Σ[Probability(death at year t) × PV(death benefit at t)] − Σ[PV(premiums paid)]

Adjust for policy features

If the contract has riders (e.g., accelerated death benefit, waiver of premium) or cash‑value accumulation, model those additional cash‑flows separately and add them to the total expected value.

Example table of components