Social security bridge sizing

For a delaying claimant: the forgone age-62 monthly benefit (PIA × claim factor at 62), the annualized bridge amount, the bridge years, and the quoted TIPS-ladder cost on the embedded real-yield curve.

Field: Social Security bridge sizing Unit: US dollars Basis: today's dollars (real) Computed by: Engine Status: Complete chain

Appears in: ss-page (Bridge panel rows "$X/yr ($Y/mo, real)" and ladder cost); insights (ss-bridge-gap card via insight-ss-bridge-gap-total)

Calculation records

• Social Security bridge: age-62 replacement sized as a TIPS ladder Formula record, justified by derivation

  Purpose: The real-dollar bridge that pays the forgone age-62 benefit from retirement until the chosen claim, quoted as a TIPS ladder bought this year.

  Statement: Monthly age-62 benefit M = PIA × f_62; annual real amount A = 12M. startYear = max(age-62 year, retirementYear, currentYear+1). For a January claim (months = 0), endYear = claimYear − 1; for a mid-year claim, endYear = claimYear. years N = endYear − startYear + 1. ladderCost is the TIPS-ladder price of N annual real payments of A purchased in the current year. On a zero real curve with unit present value, cost = N A. Returns null when the claim is at or before 62 or the window is empty. Units: today's dollars and calendar years. Rounding: none.

  Formula: M = PIA × f_62; A = 12M; N = endYear − startYear + 1; cost = price of N real payments of A

  • PIA: Primary insurance amount, monthly, today's dollars (unit: usd/month) (domain: > 0)
  • f_62: Claim factor at age 62, already resolved for the date of birth (unit: 1) (domain: 0 < f_62 <= 1)
  • startYear: First calendar year the bridge pays (unit: year) (domain: integer)
  • endYear: Last calendar year the bridge pays (unit: year) (domain: integer >= startYear)

  Timing: annual real payments from startYear through endYear inclusive; ladder purchased in currentYear

  Rounding: none

  Limits:

  • The date formula (January claim ends the year before the claim year; start is the later of age 62, retirement, and next year) is the comments' stated convention
  • Synthetic TIPS coupons are floored at 0.125% (ladderMath MIN_TIPS_COUPON_PCT). On the zero real curve the worksheet states, that floor is absorbed into the back-solved face amounts and the ladder cost equals N x A exactly, which the evidence asserts at 1e-9 (a passing check, not an assumption); on a nonzero curve the cost is the discounted ladder and differs from N x A, and the worksheet does not claim otherwise

  Provenance: derived by codex, implemented by grok.

  Independent review: cursor

  Gates (6 of 6 pass): fixture registers a test: pass; pins resolve: pass; families exist: pass; worksheet exists: pass; mutation receipt exists: pass; provenance independent: pass

  Worksheet: ss-bridge-sizing.md Mutation receipt: ss-bridge-sizing.mutation.md

  Evidence tests: bridge.evidence.test.ts

  Implemented in: bridge.ts

  Is the number of: social-security-bridge-sizing

  Feeds: insight-ss-bridge-gap-total

Engine source: engine/src/ladder/bridge.ts (sizeBridge (monthlyAge62Benefit, annualRealAmount, ladderCost))