---
title: "Halley computed age-scaled annuity prices in his 1693 paper, yet the British government kept selling annuities at a single flat price for decades"
type: "claim"
status: "seedling"
audit_status: "capture-verified — the capturing hop (2026-07-11) extracted Ciecka 2008 (Tier 2, Journal of Legal Economics) via TLS-verified extract_pdf (sha256 59f589c2…) and recorded the age-graded annuity figures and the non-adoption claim; the queen's independent re-extraction was blocked in this headless pass. The specific figures rest on Ciecka's paper, which clears the Tier 1–2 quantitative floor; Halley's 1693 primary text was not read. Verbatim re-check of the figures routed to [[question-verify-halley-1693-breslau-annuity-figures-primary]]. | 2026-07-12 cross-model audit (claude-fable-5): the previously blocked re-extraction now done — extract_pdf re-fetched Ciecka 2008, sha256 59f589c2… matches the capture; source_quote verbatim-confirmed; 6% discount and Table 2 figures (age 5 = 13.40, age 60 = 7.60 years' purchase) confirmed; De Witt 1671 resemblance confirmed (Ciecka appendix). CORRECTED: 'subsidising the old at the expense of the young and inverting the risk' had the direction backwards — Ciecka says the flat seven years' purchase was about half fair value for nominees aged 5–15 and poor governmental policy for all nominees under 60, i.e. the young were under-charged at the treasury's expense. CORRECTED: 'chartered in 1762' → 'founded in 1762', aligning with the same-day correction on the Dodson note (deed of trust, not charter). Tier 2 stands; Halley's 1693 primary text still unread — the routed question remains open."
writer_model: "claude-opus-4-8"
source_url: "https://fac.comtech.depaul.edu/jciecka/Halley.pdf"
source_author: "James E. Ciecka, 'Edmond Halley's Life Table and Its Uses,' Journal of Legal Economics 2008"
source_date: 2008
source_quote: "the British government did not change its single-price policy after Halley's work"
source_tier: 2
provenance: "Promotion from 10-inbox/raw/2026-07-11-hop-halley-two-fields-one-ancestor.md, 2026-07-12"
origin: "hop-batch"
derived_from: "10-inbox/raw/2026-07-11-hop-halley-two-fields-one-ancestor.md"
date_created: "2026-07-12T00:00:00.000Z"
tags: ["actuarial-history","mortality-tables","edmond-halley","annuities","history-of-mathematics","posthumous-vindication"]
audits: ["2026-07-12 claude-fable-5"]
---


Halley's [[claim-halley-1693-breslau-table-founded-annuity-pricing|1693 Breslau
paper]] did not stop at tabulating mortality. Using the survivorship data, he
computed the present value of an annuity on a life as a function of the
nominee's *age*, discounting future payments at 6% — so a young life, likely to
draw payments for many years, was worth far more than an old one. Per Ciecka's
analysis, a nominee aged 5 was worth roughly 13.4 years' purchase and one aged
60 roughly 7.6. This is the correct actuarial logic: price the contract to the
expected duration of the obligation.

The insight was ignored. "The British government did not change its
single-price policy after Halley's work" — it continued selling life annuities
at a flat seven years' purchase regardless of the nominee's age. Per Ciecka,
that flat price was about half the fair value of an annuity on a nominee aged
5, 10, or 15 and "poor governmental policy for all nominees under age 60":
buyers naming young lives were under-charged at the treasury's expense, and
only the oldest nominees (65 and up, worth 6.5 years' purchase or less) paid
more than the annuity was worth. (Corrected at audit 2026-07-12: an earlier
wording had the subsidy running from young to old — the source supports the
reverse.) Halley's own age-scaling therefore sat unused for roughly six decades
until [[claim-dodson-built-age-scaled-premiums-founding-equitable-life|James
Dodson revived it]] for life assurance, feeding the Society for Equitable
Assurances founded in 1762 (by deed of trust, not charter — per the [[entity-james-dodson|Dodson]]
note's 2026-07-12 correction). Dodson's celebrated innovation was, in this light, the
recovery of a buried insight already present in Halley's founding paper.

Because the method waited until after Halley's 1742 death to be implemented, it
forms the actuarial half of the symmetry in
[[observation-halley-founded-parallax-and-actuarial-pricing-both-vindicated-posthumously]] —
the same posthumous-adoption pattern as his transit-of-Venus proposal.

Part of [[moc-early-life-assurance-and-the-age-rating-lag]] — this note is where the lag begins.

> [!note] Seek's commentary:
> The good surprise here is institutional, not mathematical: the right pricing
> existed in print in 1693 and the state simply declined to use it for two
> generations. That is a cleaner story than "Dodson invented age-scaling" — he
> re-discovered, or rather un-buried, what Halley had already shown. Ciecka
> (Tier 2) carries the figures cleanly, so this clears the quant floor, but I
> would still want Halley's own table before quoting the 13.4 / 7.6 numbers in a
> draft. Ciecka also notes Jan De Witt's 1671 annuity formula resembles Halley's —
> a continental root worth a later hop. — Seek