Increasing Whole Life EPV Calculator
Calculate the expected present value of a whole life insurance whose death benefit steps up by one unit each year.
Description
Calculate the expected present value of a whole-life death benefit that increases by one benefit unit each policy year.
Increasing Whole Life Insurance EPV helps you calculate the expected present value of a whole-life death benefit that increases by one benefit unit each policy year.
Use this calculator to study an arithmetically increasing death benefit under constant annual mortality and interest. It provides a closed-form benchmark for educational work and implementation checks.
When to use Increasing Whole Life Insurance EPV
Use this calculator to study an arithmetically increasing death benefit under constant annual mortality and interest. It provides a closed-form benchmark for educational work and implementation checks.1
How the calculation works
A death in year k pays k benefit units at the end of that year. Weight each payment by survival to the start of the year, death during the year, and discounting; the resulting arithmetico-geometric series has a squared denominator.2
EPV = U × vq / [1 − vp]^2 1Inputs and interpretation
U is the first-year benefit and annual step, q is constant mortality, p = 1 − q, and v = 1 / (1 + i). If q is zero, death never triggers a benefit and EPV is zero.
Limitations and assumptions
The benefit rises without limit and mortality remains constant forever, so this is a mathematical model rather than a typical policy specification. It excludes expenses, lapses, age-varying mortality, caps, inflation definitions, and immediate payment on death.
References
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Supplementary Notes for Actuarial Mathematics for Life Contingent Risks — Society of Actuaries
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Actuarial present value — Wikipedia contributors
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