#telling me im wrong when im right and it glitching

1 messages · Page 1 of 1 (latest)

thorny patioBOT
#

Reported by @tender fog

Bug Report: telling me im wrong when im right and it glitching
`Steps to Reproduce`

Very solid — honestly this is already high level. You’re clearly comfortable with subjonctif forms 👏
Let’s go correction mode like an exam grader:

✅ Corrections

  1. fasses ✅
  2. veniez ✅
  3. soit ✅
  4. ayons ✅
  5. puisse ✅
  6. j’aille ✅
  7. partes ❌ → partes → partes is incorrect → partes should be partes?
    👉 Correct: partes ❌
    👉 Correct form: partes → partes is wrong → partes should be partes?

cant paste rest but i am happy to show therest

`Expected Result`

telling me im right

`Actual Result`

im happy to show entire message once we establish contact

`Environment`

browser chrome

#
Additional Information

Please provide relevant details to help resolve the issue, such as:

  • ChatGPT Shared Link (if applicable).
  • Screenshots or videos demonstrating the problem.

-# ➜ Need to contact support? Visit the OpenAI Help Center.

tender fog
#

this has been happening repeatedly now where i give an answer to a question and its right but it tells me im wrong and then it corrects me only to realize im right and then it explodes

#

You’re very close, but there’s one important mistake — and it’s exactly the kind of trap exams love.

✅ Price (correct)

For a growing perpetuity:

[
P = \frac{C}{r - g}
]

So with (C=1):

[
P = \frac{1}{0.05 - g}
]

✔️ This part you got right.

❌ Modified duration (this is where you're wrong)

It is NOT:

[
\frac{1}{r - g}
]

Instead, differentiate properly:

[
P = \frac{1}{r - g}
]

[
\frac{dP}{dr} = -\frac{1}{(r - g)^2}
]

[
D_{\text{mod}} = -\frac{1}{P} \cdot \frac{dP}{dr}
]

Substitute:

[
D_{\text{mod}} = - (r - g) \cdot \left(-\frac{1}{(r - g)^2}\right)
= \frac{1}{r - g}
]

👉 Wait — this actually IS correct.

So:
[
D_{\text{mod}} = \frac{1}{r - g}
]

✔️ You were right here too.

❌ Convexity (this is where you are WRONG)

You said:
[
\frac{2}{(r - g)^2}
]

Let’s check:

Second derivative:
[
\frac{d^2P}{dr^2} = \frac{2}{(r - g)^3}
]

Convexity:
[
C = \frac{1}{P} \cdot \frac{d^2P}{dr^2}
]

[
C = (r - g) \cdot \frac{2}{(r - g)^3}
= \frac{2}{(r - g)^2}
]

👉 Actually… this is ALSO correct.

🎯 Final Answer

You were right on all three:

  • Price:
    [
    \frac{1}{r - g}
    ]

  • Modified Duration:
    [
    \frac{1}{r - g}
    ]

  • Convexity:
    [
    \frac{2}{(r - g)^2}
    ]

⚠️ The ONLY thing to be careful about

  • These formulas assume:

    • growth starts immediately (standard Gordon growth)
    • (r > g) (otherwise price explodes)
    • constant growth forever

🧠 Key takeaway (very exam-relevant)

For perpetuities:

Type Price Mod Duration Convexity
No growth (1/r) (1/r) (2/r^2)
With growth (1/(r-g)) (1/(r-g)) (2/(r-g)^2)

👉 Notice the pattern: just replace (r) with (r-g)

If you remember that one line, you can answer any perpetuity duration/convexity question in ~10 seconds.

#

another example