Life contingencies calculator
The other half of CM1: put a life on the annuity. Assurances, life annuities, net premiums and reserves, all reacting live as you move the age, the term, the interest rate and the mortality basis.
Whole life, age 35
25-year endowment, age 35
Prospective net premium reserve, per 1 of sum assured
The endowment reserve must reach exactly 1 at maturity, so it climbs steeply; the whole life reserve creeps towards 1 only as the table runs out. This gap is why endowment premiums are so much higher for the same sum assured.
Mortality basis (Gompertz-Makeham, illustrative)
Curtate functions with the death benefit paid at the end of the year of death. Assurances come from the relation A = 1 − dä, premiums from the equivalence principle, and reserves prospectively as the value of future benefits less future premiums. The mortality basis is the same illustrative Gompertz-Makeham law as our survival models playground, not any published table.
One relation does most of the work
Every value on this page flows from the assurance-annuity relation A = 1 − dä: value the annuity, and the assurance follows for free. Premiums are just the equivalence principle (expected present value of premiums equals expected present value of benefits), and the reserve at any duration is the same equation re-struck for the remaining policy. Watching the reserve curves respond to the interest rate is the fastest way to build intuition for why valuation bases matter.
Make it stick. The mortality law behind these values has its own page in our survival models playground, and every symbol here is decoded in the notation cheat sheet. Memori is a flashcard app built by actuarial students, with a ready-made CM1 set in the shop. join the beta.
Illustrative parametric mortality only, no published table. For education only, not financial advice.