HesapHanem

Whole Life Net Premium Calculator

Enter face amount, issue age, interest and mortality to estimate the net premium.

How it is calculated

This is a teaching model with one constant annual death probability q (in percent) and one constant interest rate i (in percent), not a mortality table. With v = 1 ÷ (1 + i), the engine runs year by year from the issue age to age 120. The annuity-due is ä = Σ vᵗ · ₜp (a premium at the start of each year the person is alive). The assurance is A = Σ vᵗ⁺¹ · ₜp · q (the benefit is paid at the end of the year of death). The net single premium is face × A and the level annual premium is face × A ÷ ä. Age is rounded to a whole number and must be 0 to 110; i and q must be above 0, and q below 100. Because q is constant, the annual premium works out to face × q × v whatever the age, while age does change the single premium and the annuity.

Worked example

Face amount $100,000, issue age 35, interest 4% and mortality 1% per year. The engine sums the survival-weighted discounted premiums to get an annuity-due of 20.4843. It sums the discounted death benefits to get A = 0.196965, so the net single premium is 100,000 × 0.196965 = $19,696.48. The level annual premium is 19,696.48 ÷ 20.4843 = $961.54. A shortcut confirms it: 100,000 × 0.01 ÷ 1.04 = 961.54. At age 55 the same inputs give the same annual premium.

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Common mistakes

  • Expecting the premium to rise with age. In this model death probability does not change with age, so older ages give the same annual premium; a real insurer uses a table where q increases with age.
  • Entering mortality as a fraction such as 0.01. The field is a percentage, so 1 means 1% per year; 0.01 means 0.01% and gives a very small premium.
  • Treating the result as a price to pay. It is a net premium: it has no expenses, commissions, profit margin, taxes or underwriting loadings, so real quotes are higher.
  • Comparing it to a quote from an insurer. Real quotes use sex, health, smoking status and mortality tables, none of which are inputs here.
  • Confusing the single premium with the annual premium. The single premium is a one-off payment today; the annual premium is the level yearly amount that is equivalent to it.

Sources

About this calculator

Whole life insurance premium calculation rests on the actuarial equivalence principle: the expected present value of future premiums the insurer collects must equal the expected present value of the death benefit it will eventually pay. Using a simplified constant mortality rate and a fixed interest (discount) rate, the net level annual premium is derived so these two expected present values balance over the policyholder's remaining lifetime — the same logic behind full actuarial pricing, just without mortality-table granularity.

This calculator takes the face amount, issue age, an interest rate assumption, and a mortality rate, and returns the estimated net annual premium, the net single premium and the annuity factor. Because the mortality rate is the same at every age, the net annual premium does not change with issue age; age only changes the net single premium and the annuity factor. Actuaries and insurance product designers use models like this in early-stage pricing and teaching to sanity-check more complex mortality-table-based premium calculations, and insurance students and agents use it to understand how sensitive whole life premiums are to changes in interest rate or assumed mortality.

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Comments (1)

  • Editorial team

    This is a classroom model with one constant death probability, so it will not match a quote: real insurers use mortality tables where the risk climbs with age, and add expenses and profit on top of the net figure. It is best for seeing how assumptions move the answer. Dropping interest from 4 to 2 percent raises the annual premium from 961.54 to 980.39. Which assumption are you trying to understand?

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