Claude Opus 5.5 (effort default (no --effort flag) · thinking on) on Pension claiming-age comparison: lifetime totals, present values and break-even ages

AClaude Opus 5.5default · thinking on · Claude Code 2.1.299 (headless -p) · cloud · 2026-10-20 · by @bobsiopener

Trust 80%Fully autonomoussuccess · first tryCompare

Estimated cost: $0.12
Wall time: 24s
Human step-ins: 0
Outcome: Pass

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Exact prompt

# Pension claiming age: lifetime totals, present values and break-even ages `input.json` describes a worker's monthly benefit at full retirement age and the (synthetic, given) rules for claiming early or late. Write `solve.py` (Python 3 standard library only) so that `python solve.py input.json answer.json` compares claiming ages. We re-run it on fresh inputs, so do not hard-code anything. Use only the rules below and the numbers in the input. ## Input `pia_monthly` (monthly benefit if claimed exactly at full retirement age, before cost-of-living raises), `fra_months` (full retirement age in months, e.g. 800 = 66 years 8 months), `reduction_first_36_per_month`, `reduction_beyond_36_per_month`, `delayed_credit_per_month` (fractions), `cola` (yearly raise), `discount_rate`, `claim_ages`, `death_ages`, `max_age` (integers, whole years), `pairs` (list of [earlier, later] claim ages). ## Rules 1. Claiming at whole age A means the first payment is for the month the person turns A. Let m = A*12 - `fra_months`. 2. If m < 0, with k = -m: factor = 1 - (min(k, 36) * `reduction_first_36_per_month` + max(k - 36, 0) * `reduction_beyond_36_per_month`). If m >= 0: factor = 1 + m * `delayed_credit_per_month`. 3. The monthly payment during age-year t (the 12 months from birthday t to the day before birthday t+1) is `pia_monthly * factor * (1 + cola) ** (t - 62)`, for t >= A. Raises apply from age 62 whether or not the person has claimed yet. No rounding of payments. 4. `monthly_at_claim` = the monthly payment for age-year A. 5. `lifetime[D]` = sum of all monthly payments for age-years A .. D-1 (death at birthday D, nothing paid from then on). 6. `pv[D]` = sum over age-years t = A .. D-1 of (12 * monthly payment for t) / (1 + discount_rate) ** (t - 62). 7. Break-even for a pair [a, b]: go month by month from the month of birthday a up to (not including) the month of birthday `max_age`, keeping cumulative totals for both claim ages (the later one starts at birthday b). The break-even is the first month index M (months since birth, counting the birthday-a month as a*12) with M >= b*12 and cumulative(b) >= cumulative(a), reported as M / 12 rounded to 4 decimals; `null` if it never happens. 8. `best_by_pv[D]` = the claim age with the highest `pv[D]` (lower age on ties). 9. Round money to 2 decimals and `factor` to 6 decimals only when writing. ## Output `answer.json`: ``` {"claims": {"62": {"factor": ..., "monthly_at_claim": ..., "lifetime": {"72": ..., ...}, "pv": {"72": ..., ...}}, ... one entry per claim age}, "breakeven": {"62-67": ..., ...one key per pair "a-b"}, "best_by_pv": {"72": 70, ...one key per death age}} ``` Keys are strings of the integer ages. ## Scoring Hidden checks (partial credit = fraction passed; all must pass): `factors_and_monthly` (factor within 0.000001, money within 0.011), `lifetime_totals`, `present_values` (within 0.011), `breakeven_ages` (within 0.0001), `best_by_pv` (exact) on the given input; `fresh_run_1`, `fresh_run_2`: the whole answer on fresh inputs (tolerance 0.011; integers exact). Each run has a 60-second limit.

Two-tier early-claim reduction, delayed credits, raises from age 62 regardless of claiming, a month-by-month break-even search, and present values with a tie rule. Original benchmark task written for usecaserank.com (not based on a specific public post). Headless, offline run on a reproducible fixture. Each run's notes say how its cost was measured (estimates are marked).

These are synthetic test cases for comparing AI models, not financial advice.

Success criteria: 1. factors_and_monthly 2. lifetime_totals 3. present_values 4. breakeven_ages 5. best_by_pv 6. fresh_run_1 7. fresh_run_2

Setup notes: Use Case Scout batch 9 case j03-claiming-age-breakeven (offline fixture). Prepared with batch9/prepare.sh; hidden key/tests kept outside the agent's work dir. Prompt = TASK.md verbatim. Scored with the scout's scorer: `python score.py WORKDIR KEYDIR`. Tools: Read/Write/Edit/Glob/Grep/Bash, web disabled. Single run, no retries. Claude Code's own reported cost for claude-opus-5.5: $0.124922. Score: 7/7. Cost is an ESTIMATE: measured tokens x pricing.json list price (Claude Pro subscription, nothing billed); input_tokens include cache reads and writes. Single run.

Estimated cost List-price estimate; not actually billed.

Metrics

Estimated cost: $0.12
Wall time: 24s
Human step-ins: 0
Turns: 4

Model usage
Model	Input tok	Output tok	Cost
AClaude Opus 5.5anthropic/claude-opus-5.5effort default (no --effort flag) · thinking on	79,169	2,047	$0.12

Reproduce this run

Use the use case prompt on the use case page.
Same setup: Claude Opus 5.5 (anthropic/claude-opus-5.5, effort default (no --effort flag) · thinking on) via Claude Code 2.1.299 (headless -p), cloud.
It counts as a success only if it meets every success criterion: 1. factors_and_monthly 2. lifetime_totals 3. present_values 4. breakeven_ages 5. best_by_pv 6. fresh_run_1 7. fresh_run_2
Log model, tokens, wall time, human step-ins and the evidence log, then submit it as a reproduction. A different model? Submit a head-to-head rerun.

How runs are scored: Methodology.

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Automated checks

Trust 80% comes from these checks (how Trust % works).

Run date is not in the future : passed
Model is in the dated pricing table : passed
Cost recomputed from tokens matches : passed
Cached tokens are consistent : passed
Output throughput is plausible : passed
Autonomy matches step-ins : passed
Step-ins do not exceed turns : passed
Retries agree with first-try result : passed
Evidence log SHA-256 matches : passed
Evidence log is substantial : passed

Evidence log

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  "result": "I wrote `solve.py` and ran it on the given input. It finished cleanly and produced `answer.json`, but I have no expected answers to check it against. The only checks I did were working out the age-62 factor by hand (it matches) and confirming the other results look sensible.\n\nResults on the given input:\n- **Factors:** 0.733333 at age 62, rising to 1.293333 at age 70. Full retirement age here is 66y4m, so claiming at 62 is 52 months early.\n- **Monthly payment at claim:** $2,304.87 at 62, up to $4,626.26 at 70.\n- **Break-even ages:**\n\n| Pair | Break-even age |\n|---|---|\n| 62 vs 67 | 77.0833 |\n| 62 vs 70 | 79.0833 |\n| 67 vs 70 | 81.6667 |\n| 65 vs 68 | 78.9167 |\n\n- **Best claim age by present value:**\n\n| Death age | Best claim age |\n|---|---|\n| 72 | 62 |\n| 78 | 64 |\n| 82 | 68 |\n| 86, 90, 95 | 70 |\n\nHow the script handles a few edge cases:\n- **Lifetime totals:** 12 monthly payments are counted for each year from the claim age up to the year before death. If someone dies at or before their claim age, the total is 0.\n- **Ages outside `claim_ages`:** if a pair uses an age that isn't listed, the script works out its factor from the rules anyway, so it won't break on new inputs.\n- **Rounding:** money is rounded only when the file is written; nothing is rounded during the calculations.\n\nRun it with `python solve.py input.json answer.json`. It uses only the standard library.",
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