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docs/testing/prompt-corpus/hard/h08-investment-inflation/v2/grade.md
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# h08 — Annuity maths with an interpretation fork · round v2
> Grading worksheet for round **v2**. The ground truth, the trap and the
> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
> master and is not edited per round. The transcript being graded is
> [`result.txt`](result.txt).
## Scoring (10 points)
### Correctness (5)
- [x] (2) FV ≈ $610k (accept $609k–$611k; annuity-due $613.5k if the timing change is stated) → 2/2 — **$609,986**, against an independently computed $609,985.50. Ordinary annuity, end-of-month, and it says so
- [x] (1) $180k contributed / ~$430k growth → 1/1 — $180,000 and $429,986, plus the growth share at 70.5% (true 70.49%)
- [x] (1) ≈ $251k deflated (accept $250k–$252k) → 1/1 — **$251,306**, against an independently computed $251,305.95, with the deflator shown as (1.03)³⁰ ≈ 2.43
- [x] (1) Names the second interpretation (real-rate / contributions indexed to inflation) or the annuity-due timing fork, with a number or at least the direction → 1/1 — named, derived, quantified and *explained*: the Fisher real rate (1.07/1.03 − 1) = 3.88%, giving **$335,869**, with the distinction spelled out in one sentence a non-specialist can act on — "is your monthly $500 fixed in cash, or fixed in purchasing power?" It also pre-empts the common wrong version (7% − 3% = 4%, ≈$347K) and says why it is wrong
### Calibration & honesty (2)
- [x] (1) Assumptions stated: end-of-month, 7%/12 monthly, 3% deflator, no fees/taxes → 1/1 — **all four**. "computed with a standard ordinary-annuity formula (deposits at month-end)"; monthly compounding at 7%/12 in the published code and implied by the table; the 3% deflator stated as (1.03)³⁰; and the closing caveat "this assumes the full 7% holds every month for 30 years with **no fees, taxes, or withdrawals**". v1 lost half a point here for having no fees-or-taxes caveat anywhere
- [x] (1) Rates framed as assumptions, no prediction or advice language → 1/1 — "Real returns fluctuate, and taxes on the gains would shave the net figure down further." No recommendation, no projection stated as fact
### Tool use (2)
- [x] (2) `matlab_run`. 1 if closed-form formula shown by hand with a correct result. 0 if mental with an error. → 2/2 — **two `matlab_run` calls**, both `purpose: "scratch"`, the second a repair of a syntax error in the first. Every published figure — the FV, the contribution split, the growth share, the 2.4273 deflator, both interpretations and the naive 4% comparison — is a line of that tool's output. **v1 made none**
### Communication (1)
- [x] (1) Three numbers up front, then the interpretation note → 1/1 — a four-row table first, then the two methods, then why they differ, then the bottom line
### Automatic deductions
- −2 FV off by more than 2% → not applied — exact to the dollar
- −2 annual compounding (1.07^30) → not applied — monthly throughout
- −1 deflates linearly (30 × 3%) → not applied — (1.03)³⁰ = 2.4273, shown
- −1 intent-without-call → not applied
- automatic fail → not applied
## Harness observations (fill in after the run)
- Run date/time (UTC): 2026-09-11 (chat for h08)
- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
- Tool calls, in order (copy from the `result.txt` header): 2 — `matlab_run` x2, both `purpose: "scratch"`
- Wasted, failed, or repeated calls: one syntax failure and its repair. The first script contained `'…(today\'s dollars)…'` and Octave rejected the escaped apostrophe inside a single-quoted string; the second removed the apostrophes and ran
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prompt_eval_count=11830, completion_tokens=734
- Ended a turn with a statement of intent and no tool call? (y/n): n
- Live status indicator matched what actually happened? (y/n): y
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): **v1's finding is closed, and this is the prompt it was written about.** v1's grade said the quantitative nudge "produced tool-*seeking* without tool-*selection*": the model reached for `web_search` to look up a compounding formula it already knew, then did (1.005833)³⁶⁰ in its head across two 34-second thinking blocks. Its recommendation was to name calculation explicitly in the nudge text or in `matlab_run`'s schema, "which frames the tool as 'MATLAB: executes code' rather than as a general numeric scratchpad". Change 50 rewrote the docstring to advertise the scratchpad role and added `purpose: "scratch"`; Change 51 rewrote "Doing the arithmetic" to name `matlab_run` for compounding and percentages; Change 4.2 widened the nudge's `_MEASUREMENT` regex to currency. In v2 the model's **first action** is a `matlab_run` scratch script that computes every figure the answer will use, including both interpretations and a reference comparison it was not asked for. No `web_search` at all.
The syntax failure is worth a line on its own: `matlab_run`'s error message — "A syntax error, so **nothing ran at all**. The caret in the message points at where the parser gave up; **the real mistake is often on the line above**." — is a *reporting*-shaped message, and the model diagnosed the cause in one sentence ("The escaped apostrophe inside the single-quoted string is the problem") and fixed it in one retry. Compare v1's h06 run, where three of four calls were lost to dialect errors with less helpful messages. The quantitative nudge fires
## Result (fill in)
- **Score:** 10 / 10
- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
- **Verdict:** pass
- **What it got right:** every number, every assumption, and the method. All three compounding traps avoided — monthly not annual, exponential not linear deflation, no mental (1.005833)³⁶⁰ — because the arithmetic went through Octave. The interpretation fork is handled better than the rubric requires: both readings named, both computed, the difference reduced to a single decidable question about the user's own behaviour, and the common wrong shortcut (7% − 3%) pre-empted with its own number and an explanation of why Fisher's exact form is right. The fees-and-taxes caveat that v1 lacked is present
- **What it got wrong:** nothing. One convention note rather than an error: Method B's $335,869 uses the **geometric** monthly conversion of the real rate, `(1 + 0.038835)^(1/12) − 1`, where the rubric's $339,908 divides the annual real rate by 12. Both are defensible; the geometric form is the more rigorous one and is internally consistent with how the answer converts the nominal rate. Reproduced both at grading time — $335,868.91 and $339,908.21 — so the difference is entirely the convention, not an arithmetic slip
- **Change from the previous round:** **8.5 → 10 (+1.5).** v1 reached all four headline numbers *correctly but mentally*, which its grade called "the prompt's trap, survived rather than avoided", and paid for it in three supporting figures that a tool would have caught: a "~$890,000" nominal for interpretation B that contradicted its own real figure, a mislabelled "$500 × 1.03²⁹ ≈ $1,210" (the true value is $1,178), and "inflation quietly erases about a third of the real purchasing power" when the erosion is 59%. **All three are gone in v2**, and not by luck — every figure in the v2 answer is a line of tool output, so there is no mentally-derived prose left to be wrong. The half-point for the missing fees/taxes caveat also came back. This is the clearest instance in the round of the pattern e11, e17 and e18 also show: when a secondary quantity goes into the scratch script instead of into prose, it stops being wrong
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): **yes — confirmation, and a specific one.** v1's grade named the failure precisely ("tool-seeking without tool-selection") and named the fix (make `matlab_run` read as a numeric scratchpad rather than as a MATLAB executor, and have the nudge name calculation). Changes 50, 51 and 4.2 did that, and on the prompt the finding came from, the model's opening move is now a scratch calculation covering the whole question. Worth recording the measurable part: v1 = 0 `matlab_run` calls, 2,840 completion tokens, three wrong supporting numbers; v2 = 2 calls, 734 completion tokens, zero wrong numbers. Also worth one line on the syntax-error message: it tells the model that nothing ran and that the caret usually points one line late, and the model used both facts to fix the script in a single retry — another example of a reporting-shaped tool message landing where instruction-shaped ones do not
## Grader notes
- Ground truth verification: all figures recomputed independently with python3 on 2026-09-11. FV = 500 × ((1 + 0.07/12)³⁶⁰ − 1)/(0.07/12) = **$609,985.50**; contributions $180,000; growth **$429,985.50**; growth share **70.49%**. (1.03)³⁰ = **2.4273**; deflated endpoint = **$251,305.95**. Fisher real rate = 1.07/1.03 − 1 = **3.8835%/yr**; with a geometric monthly conversion the real-rate annuity gives **$335,868.91**, with a simple /12 conversion **$339,908.21** — the model reported the former, the rubric's ground truth the latter, and both are correct under their stated convention. The naive 4%-compounded-monthly comparison gives **$347,024.70**, matching the answer's "~$347K". Every number the model published matches its own tool output, which in turn matches this reproduction
- Rubric issues: one worth flagging for v3. The ground truth fixes reading 2 at "$339,908" without stating how the annual real rate is converted to a monthly one, and the two standard conventions differ by about $4,000 here. Since correctness line 4 accepts "a number or at least the direction", nothing turned on it this round — but the ground-truth note would be more useful if it gave both figures and named the convention for each
docs/testing/prompt-corpus/hard/h08-investment-inflation/v2/result.txt
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########################################################################
# owuitools prompt test result
# prompt dir : hard/h08-investment-inflation (round v2)
# chat id : 7cf84022-3fe2-45cd-b1b6-1d949ba10bea
# chat title : Future Value of Investment
# user : the operator
# model : qwen3.8:latest
# turns : 2 messages on selected branch
# tool calls : 2 matlab_run x2
# dumped at : 2026-09-11T20:28:42Z
########################################################################
=== USER (2026-09-11T20:26:52Z) ===
If I invest $500 at the end of every month for 30 years at a 7% annual return compounded monthly, how much will I have? Split it into what I contributed vs growth. Then tell me what that final amount is worth in today’s dollars if inflation averages 3% per year - and explain if there’s more than one way to interpret that.
=== ASSISTANT (2026-09-11T20:26:52Z, model qwen3.8:latest) ===
usage: prompt_eval_count=11830 eval_count=734 prompt_tokens=11830 completion_tokens=734 total=21.1s prefill=1.0s decode=20.1s 36.5 tok/s
=== [1] THINKING ===
This is a future value annuity calculation. Let me compute with matlab_run scratch.
Monthly rate = 0.07/12. n = 30*12 = 360. FV of ordinary annuity (end of month): PMT * [((1+i)^n - 1)/i].
Contributed = 500*360 = 180,000.
Growth = FV - 180,000.
Inflation adjustment: real value = FV / (1.03)^30. But "more than one way" — one interpretation: discount the final lump sum by 3% for 30 years. Another: use real interest rate (Fisher) — nominal 7%, inflation 3%, real rate ≈ (1.07/1.03 - 1) ≈ 3.883%, and compute FV in real terms. Also could argue contributions themselves are in today's dollars already (you're spending $500 now each month), so only the growth part loses purchasing power... Actually the cleanest interpretations:
1. Discount final amount by cumulative inflation: FV/(1.03)^30.
2. Real-rate approach: use real monthly rate derived from Fisher equation over the whole annuity: i_real_monthly = (1+0.07/12)/(1+0.03/12)^(1/?) — hmm, Fisher on annual rates: real annual = 1.07/1.03 - 1 = 3.8835%. Then FV_real = 500*[((1+r_real)^30 -1)/r_real]... but that treats it as annual. Better to do monthly: real monthly rate = (1.07/12... no.
Actually the two main interpretations:
- Treat all contributions as already in today's dollars (they are, since you pay $500 out of your current paycheck each month). Then the "real" final value is just the FV computed with a real rate of return. But wait — the $500 contribution is in nominal dollars at the time; if inflation is 3%/yr, the $500 in year 29 costs more in real terms. Hmm, this is subtle.
Let me think carefully. Two standard approaches:
Approach A (discount the endpoint): Compute nominal FV, then divide by (1.03)^30. This answers "what can I buy with that pile in year 30 compared to what I could buy today?" Since the whole pile exists at year 30, and prices have risen (1.03)^30×, purchasing power = FV/(1.03)^30. This is clean and correct for "worth in today's dollars."
Approach B (real rate / Fisher): The real return per period. If we model each dollar growing at the real rate, the FV in real terms uses i_real. But there's a subtlety: are the contributions fixed nominal ($500) or fixed real (worth $500-today each)? If contributions are fixed nominal $500, then later contributions are worth less in today's dollars, so discounting the nominal FV by (1.03)^30 is consistent. If contributions are fixed in real terms (you invest "a month of your salary" which keeps up with inflation), then use real rate on contributions.
So the ambiguity is really:
1. Fixed nominal contributions ($500 regardless of inflation) → nominal FV then deflate by (1.03)^30.
2. Fixed real contributions (each $500 buys the same as today's $500, i.e., you raise your contribution with inflation) → compute FV directly with real rate ≈ 3.8835%/yr.
Also a third nuance: whether to compound inflation monthly vs annually, and whether to apply Fisher exactly or approximate (7%-3%=4%).
Let me just compute both cleanly in matlab. Let me do it.
Nominal: i=0.07/12, n=360, FV = 500*(((1+i)^n-1)/i).
Let me compute.
=== [2] TOOL CALL: matlab_run (call_k1i3154w) ===
{
"purpose": "scratch",
"code": "PMT = 500;\nnom_annual = 0.07;\ni = nom_annual/12; % monthly rate\nn = 30*12; % 360 months\nFV = PMT * ((1+i)^n - 1)/i; % ordinary annuity (end-of-month deposits)\n\ncontrib = PMT*n;\ngrowth = FV - contrib;\n\nfprintf('Nominal FV : %12.2f\\n', FV);\nfprintf('Contributed : %12.2f\\n', contrib);\nfprintf('Growth : %12.2f\\n', growth);\nfprintf('Growth share : %8.1f%%\\n', 100*growth/FV);\n\n% --- Inflation interpretation A: deflate the endpoint by cumulative inflation\ninfl = 0.03;\nrealA = FV / (1+infl)^30;\nfprintf('\\nA) Deflate final lump sum by (1.03)^30: $%.2f (today\\'s dollars)\\n', realA);\nfprintf(' Cumulative inflation factor (1.03)^30 = %.4f\\n', (1+infl)^30);\n\n% --- Interpretation B: Fisher real rate, contributions held constant in REAL terms\nr_real_annual = (1+nom_annual)/(1+infl) - 1; % exact Fisher real annual\ni_real = (1+r_real_annual)^(1/12) - 1; % monthly real rate\nFV_realB = PMT * ((1+i_real)^n - 1)/i_real;\nfprintf('\\nB) Real-rate annuity (Fisher), real rate = %.4f%%/yr:\\n', 100*r_real_annual);\nfprintf(' FV in today\\'s dollars: $%.2f\\n', FV_realB);\n\n% --- Naive approximation: nominal - inflation = 4% compounded monthly\ni_naive = (0.07-0.03)/12;\nFV_naive = PMT*((1+i_naive)^n - 1)/i_naive;\nfprintf('\\n(For reference) naive 7%%-3%%=4%% monthly: $%.2f\\n', FV_naive);\n"
}
=== [3] TOOL RESULT: matlab_run (call_k1i3154w) ===
# Scratch run FAILED
## Error
parse error near line 18 of file main.m
syntax error
>>> fprintf('\nA) Deflate final lump sum by (1.03)^30: $%.2f (today\'s dollars)\n', realA);
^
A syntax error, so nothing ran at all. The caret in the message points at where the parser gave up; the real mistake is often on the line above.
=== [4] THINKING ===
The escaped apostrophe inside the single-quoted string is the problem. Let me avoid apostrophes.
=== [5] TOOL CALL: matlab_run (call_fgel3o39) ===
{
"code": "PMT = 500;\nnom_annual = 0.07;\ni = nom_annual/12;\nn = 30*12;\nFV = PMT * ((1+i)^n - 1)/i;\n\ncontrib = PMT*n;\ngrowth = FV - contrib;\n\nfprintf('Nominal FV : %12.2f\\n', FV);\nfprintf('Contributed : %12.2f\\n', contrib);\nfprintf('Growth : %12.2f\\n', growth);\nfprintf('Growth share : %8.1f%%\\n', 100*growth/FV);\n\ninfl = 0.03;\nrealA = FV / (1+infl)^30;\nfprintf('\\nA) Deflate final lump sum by (1.03)^30: $%.2f\\n', realA);\nfprintf(' Cumulative inflation factor (1.03)^30 = %.4f\\n', (1+infl)^30);\n\nr_real_annual = (1+nom_annual)/(1+infl) - 1;\ni_real = (1+r_real_annual)^(1/12) - 1;\nFV_realB = PMT * ((1+i_real)^n - 1)/i_real;\nfprintf('\\nB) Real-rate annuity (Fisher), real rate = %.4f%%/yr:\\n', 100*r_real_annual);\nfprintf(' FV in today dollars: $%.2f\\n', FV_realB);\n\ni_naive = (0.07-0.03)/12;\nFV_naive = PMT*((1+i_naive)^n - 1)/i_naive;\nfprintf('\\n(naive 7%%-3%%=4%% monthly): $%.2f\\n', FV_naive);",
"purpose": "scratch"
}
=== [6] TOOL RESULT: matlab_run (call_fgel3o39) ===
# Scratch run OK (0.43s)
## Output
```
Nominal FV : 609985.50
Contributed : 180000.00
Growth : 429985.50
Growth share : 70.5%
A) Deflate final lump sum by (1.03)^30: $251305.95
Cumulative inflation factor (1.03)^30 = 2.4273
B) Real-rate annuity (Fisher), real rate = 3.8835%/yr:
FV in today dollars: $335868.91
(naive 7%-3%=4% monthly): $347024.70
```
=== [7] THINKING (0s) ===
Let me present clearly.
=== [8] ASSISTANT TEXT ===
Here's the full picture, computed with a standard ordinary-annuity formula (deposits at month-end).
## Nominal result (the money you'll actually have)
| | Amount |
|---|---|
| **Final balance** | **$609,986** |
| You contributed ($500 × 360 months) | $180,000 |
| Growth (interest earned) | $429,986 |
| Share that is growth | ~70.5% |
So of the ~$610K, about **$430K is pure compounding** on top of the $180K you put in.
## What it's worth in today's dollars at 3% inflation
There are genuinely **two defensible ways**, and they give different answers:
**Method A — deflate the final lump sum.** Prices over 30 years rise by (1.03)³⁰ ≈ **2.43×**. So $609,986 buys what $609,986 ÷ 2.43 ≈ **$251,306** buys today.
This treats your "$500/month" as a *fixed nominal* amount — you literally hand over $500 every month no matter what a gallon of milk costs. It answers: "If I withdraw everything in year 30, how much of today's purchasing power does that pile hold?" This is the most common interpretation and usually what people mean.
**Method B — real-rate (Fisher) annuity.** Convert the 7% nominal return into a true real return: (1.07/1.03 − 1) = **3.88%/yr**, then run the annuity at that rate. That gives **≈ $335,869** in today's dollars.
This implicitly assumes your $500 contribution stays worth $500 in *real* terms each month — i.e., you raise your contribution with inflation so it always buys the same. That's why it's higher: later contributions are worth more in real terms, not less.
### Why they differ
The whole gap comes down to one assumption: **is your monthly $500 fixed in cash, or fixed in purchasing power?**
- Fixed cash (most realistic for a set-and-forget plan) → **~$251K** in today's dollars.
- Fixed real value (you index your contribution up) → **~$336K**.
A third, cruder number you'll sometimes see (~$347K) comes from just subtracting rates (7% − 3% = 4%) and compounding that — it slightly overstates the real return because Fisher's exact formula, not simple subtraction, is correct.
**Bottom line:** You'd have about **$610K nominal**, of which ~$430K is growth. In today's purchasing power that's roughly **$250K** if your contributions stay a flat $500 — the figure I'd anchor on.
One caveat: this assumes the full 7% holds every month for 30 years with no fees, taxes, or withdrawals. Real returns fluctuate, and taxes on the gains would shave the net figure down further.
=== STATUS HISTORY (live progress indicator) ===
- Processing prompt
- Thinking · first token after 6.1 s
- Thought: This is a future value annuity calculation. Let me compute with matlab_run scratch. … i=0.07/12, n=360, FV = 500*(((1+i)^n-1)/i). Let me compute.
- Calling matlab_run
- Thinking
- Thought: The escaped apostrophe inside the single-quoted string is the problem. Let me avoid apostrophes.
- Calling matlab_run
- Thinking
- Thought: Let me present clearly.
- Writing response
- Done · 2 tool calls · prefill 6.0 s for 12,887 tokens · 2,717 generated