FA-63459 / Actuarial life tables / Member archive

Commutation-function life annuities: N_x excludes D_x · case 04

Annuity values are shifted by one payment.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Input l by age from 0, i (per mille), age, n (None = whole life). v=1/(1+i); D_k = v^k l_k (zero beyond the table); N_k = sum of D from k. end = table length for whole life else min(length, age+n). Annuity-due = (N_age - N_end)/D_age; immediate = (N_{age+1} - N_{end+1})/D_age. Missing or extinct age -> 'invalid age'. Return both rounded to 6.

Why this case matters

Life-table arithmetic compounds across ages, so one misplaced index or assumption shifts every downstream value.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
temporary annuity 0	`[1.897581, 1.830347]`	`[1.965733, 1.897581]`	Failed

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