Decreasing Term Insurance EPV Calculator

Calculate the expected present value of an n-year decreasing term insurance whose benefit steps down by one each year of the term.

Description

Calculate the expected present value of a linearly decreasing term-insurance death benefit under constant annual mortality and interest assumptions.

Decreasing Term Insurance EPV helps you calculate the expected present value of a linearly decreasing term-insurance death benefit under constant annual mortality and interest assumptions.

Use this calculator for a compact valuation of cover whose insured amount falls by one benefit unit each year, such as a simplified mortgage-protection pattern. It is most useful for teaching, independent checks, and early product sketches where constant annual mortality is an intentional assumption.

When to use Decreasing Term Insurance EPV

How the calculation works

The first policy year pays the term length multiplied by the benefit unit, the second pays one unit less, and the final covered year pays one unit. Each possible end-of-year payment is multiplied by the probability of surviving to that year, dying during it, and the applicable discount factor.

EPV = U × Σ[k=0 to n−1] (n−k) × q × v^(k+1) × p^k ^[1]

Inputs and interpretation

Enter q and interest as decimal annual rates, n as a whole number of covered years, and U as the value of one benefit step. The calculation uses p = 1 − q and v = 1 / (1 + i).

Assumptions and limitations

The result is not a premium quote or a reserve. It excludes expenses, lapses, selection, changing mortality, monthly timing, taxes, profit margins, and underwriting. A real decrement table should replace the constant-q model when timing and age materially affect value.

References

Supplementary Notes for Actuarial Mathematics for Life Contingent Risks — Society of Actuaries