Life Insurance Calculator — Level Term (Educational)
Inputs
Estimated premiums & key metrics
Present value check (education)
| Item | Value |
|---|
Year-by-year table (preview)
| Year | Age | qx+k | pcum | vk+1 | PV of benefit chunk |
|---|
Net premium uses the equivalence principle: PV(benefit) = PV(premiums) for level annual premiums paid in advance (annuity-due). Gross premium here adds a simple policy fee and % loading for illustration.
How this life calculator works (plain English)
Life insurance premiums depend on the probability of surviving (or dying) each year of the term. This tool uses a widely taught model (Gompertz–Makeham) to build yearly death probabilities from age, then discounts the promised benefit back to today. The net level premium is the amount that makes the present value of premiums equal the present value of benefits. Loads can be added to display an illustrative gross premium. Results are educational, not quotes.
- Net premium: P = S·A / ä, where S is the sum assured, A is the PV of a £1 benefit paid at end of year of death, and ä is the PV of a £1 annuity-due paid annually while the policy is in force.
- Mortality model: You can adjust the model’s constants and select smoker/sex/risk class, which scale the hazard for simple sensitivity testing.
- Monthly display: Shown as annual ÷ 12 for convenience (real instalment plans may include financing/fees).
Life Insurance Basics — How Premiums Are Calculated (Educational Guide)
This Life Insurance Calculator shows the core ideas actuaries use to price a level term life policy. It is an educational tool to help you understand why a premium is higher or lower as you change inputs like age, term, sum assured, and risk class. It is not a quote, not advice, and does not arrange insurance—real insurers apply detailed underwriting and eligibility rules that vary by country and provider.
What drives a life insurance premium?
- Age at entry: The most powerful driver. Older ages have higher annual probabilities of death, so premiums rise quickly with age.
- Term length: Longer terms expose the insurer to more years of risk; premiums increase with term.
- Sum assured (face amount): Premiums scale roughly in proportion to the benefit (£/$/€100k vs £/$/€500k).
- Risk class & health: Smoker status, preferred/standard/rated classes, and (in real pricing) medical underwriting can change rates substantially.
- Discount/interest rate: Future cash flows are discounted to today. A higher discount rate reduces the present value of future benefits and can lower the net premium.
- Sex (where allowed): Some markets use sex-distinct mortality; others require unisex rates. This tool offers a simple sensitivity toggle.
How the math works (plain English)
Each year of the term has a survival probability and a death probability taken from a mortality
model (we use a standard educational model). The calculator discounts the death benefit back to today and adds up
the expected present value (EPV) across years. It also discounts the stream of level premiums paid in advance
(an annuity-due). The net premium is set so:
PV(benefits) = PV(premiums).
In formula terms, for a level term with sum assured S, term n, and discount factor v = 1/(1+i): the benefit EPV equals S × Ax:n (the present value of a £1 benefit payable at the end of the year of death), and the premium EPV equals P × äx:n (the present value of a £1 annuity-due paid while in force). The net annual premium is P = S·A / ä. We display a monthly figure as annual ÷ 12 for convenience.
Net vs. gross (illustrative) premium
Real premiums include expenses and margins (policy fees, acquisition/admin costs, risk/profit loads, and sometimes reinsurance cost). To keep things transparent, this tool shows:
- Net premium: pure risk cost from the equivalence principle (no expenses).
- Gross premium (illustrative): net premium adjusted by a user-set annual fee and a percentage loading. This is not insurer-grade rating, just a teaching aid.
Why this estimate will differ from a real quote
Insurers use detailed mortality tables by age and duration, medical and lifestyle underwriting, disclosures (e.g., medications, family history), reinsurance, distribution costs, and jurisdiction-specific rules. Some regions permit smoker/sex-distinct pricing; others require unisex or community-rated structures. Taxes, levies and the tax treatment of premiums/benefits can also vary by country (UK, US, EU, etc.). Because this calculator uses simplified assumptions, treat the output as directional rather than definitive.
How to use the calculator
- Choose your sum assured, age, term, and risk class (smoker/preferred/standard/rated).
- Adjust the interest rate to test sensitivity to discounting.
- Optionally tweak loads (policy fee and % loading) to see an illustrative gross premium.
- Review the death probability in term and the PV balance table to understand what’s driving the price.
Important: Educational use only. Not financial advice, not a quote, and not an offer to arrange insurance. For actual cover, obtain quotes from licensed insurers or brokers in your jurisdiction and read the policy documents (benefit triggers, exclusions, waiting periods, and surrender options).