Actuarial case explained
What premium funds a death benefit during a defined term?
Purpose
Decision informed
Compare cost, protection period, and reserve pattern before choosing term, whole life, or endowment coverage.
Benefits and cash flows
- 1Premiums while the policy remains in force.
- 2Sum assured at the end of the covered year of death.
- 3The term model pays no survival benefit and builds no surrender value.
Assumptions
| Assumption | Value / unit | Source and status |
|---|---|---|
| Mortality | Bundled EMSSA-09 | Synthetic Synthetic laboratory table |
| Technical rate | 5.5% yearly | Illustrative Illustrative, editable assumption |
| Benefit timing | End of year of death | Convention Model convention |
Method
Equivalence principle
The net premium equates the actuarial present value of premiums and benefits; loadings are shown separately.
P · äₓ:ₙ = SA · A¹ₓ:ₙResults and interpretation
Sensitivity separates the exposure effect, meaning amount and term, from the biometric effect of age.
Applied example
Ana buys a 20-year term policy
Ana, age 32, buys a term life policy to cover her mortgage and her daughter's education in case of death. The policy pays the sum assured only if death occurs within the term and builds no surrender value. The cost of the coverage depends on three variables, adjustable here.
Adjust the parameters to observe how the result changes.
Annual gross premium
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Actuarial interpretation
The premium reflects expected mortality at each age: a higher issue age raises it, while the term and the sum assured scale it. The calculation uses the EMSSA-09 table, a 5.5% technical rate, and expense and profit loadings.
Validation and limits
What is checked
- —Commutation and equivalence identities.
- —Fackler recursion for endowment reserves.
What it does not prove
- —The mortality table is synthetic and does not validate a professional tariff.
- —Loadings are illustrative and do not represent observed expenses.