vault backup: 2026-02-20 14:53:32

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 # 2026-01-25
-
-# 2026-01-25 18:46:??
-
-#topic/finance
-
-### Calculating Monthly Principal & Interest Payment
-
-For a **fixed-rate, fully-amortizing mortgage**,
-the monthly payment is computed using the **standard amortization formula**:
-
-#### Standard Amortization Formula
-
-$$
-A = P \cdot \frac{i(1+i)^n}{(1+i)^n-1}
-$$
-
-Where:
-
-* $A$ = periodic payment amount
-* $P$ = amount of principal, net of initial payments
-* $i$ = periodic interest rate
-* $n$ = total number of payments
-
-> [!info]
-> $A$ is constant over the term,
-> the interest portion decreases while the principal portion increases.
-
-#### Example
-
-For a 30-year mortgage of $268,000 at 5.75% annual interest:
-
-$$
-\begin{align*}
-P &= 268000
-i &= \frac{0.0575}{12} = 0.004791\bar{6} \\
-n &= 30 \cdot 12 = 360
-\end{align*}
-$$
-
-The monthly payment amount $A$ is given by:
-
-$$
-\begin{align*}
-A &= 268000 \cdot \frac{0.004791\bar{6} \cdot (1+ 0.004791\bar{6})^{360}}{(1+ 0.004791\bar{6})^{360} - 1} \\
-A &\approx 1563.98
-\end{align*}
-$$
-
-### Calculating Annual Percentage Rate (APR)
-
-$$
-\text{APR} = \frac{\frac{\text{Interest} + \text{Fees}}{\text{Principle}}}{\text{Term Years}}
-$$
-
-# 2026-01-25 21:02:??
-
-[[the-failure-of-risk-management]]
-
-If I have a general complaint about [[hubbard_2020_failure]] it's this:
-Hubbard fails to recognize logical parallels between his different arguments,
-so to a critical reader they appear contradictory:
-
-In [[hubbard_2020_failure#Break It Down, Then Do the Math]]
-Hubbard introduces **decomposition** as a method for reducing error in estimates,
-Providing Fermi's "piano tuners in Chicago" problem as an example,
-without acknowledging that _Fermi_ supplied the decomposition.
-Hubbard also references [[macgregor_1994_judgemental-decomposition]]
-which is a similar case.
-Neither of these examples suggest that decomposition is a magic bullet,
-or even that a layman's decomposition wouldn't be worse than nothing.
-Despite this, Hubbard ends the section without qualifier:
-"Clearly, decomposition helps estimates."
-
-This section comes only pages after
-[[hubbard_2020_failure#The Measurement Inversion]]
-in which Hubbard warns against seeking detail for the sake of it.
-
-See also [[the-failure-of-risk-management#_Exsupero Ursus_]].
-
-# 2026-01-25 22:59:??
-
-[[macgregor_1994_judgemental-decomposition]]
-
-I really hate this study.
-
-I may be out of my league,
-but it seems wrong to draw conclusions about decomposition as a method
-when the work was done by the researchers,
-especially when some of their decompositions really suck.
-
-> ##### Circumference of 50¢ coin
-> 
-> * Diameter in inches of a 50¢ coin
-> * Number of pieces of string the length of the diameter needed to wrap around circumference
-
-That's not a decomposition.
-If you don't remember $\pi$
-that's a harder problem than it was before.
-
-> ##### Bushels of wheat
->
-> * Population of the world
-> * Number of bushels of wheat consumed per person per year
-> * Proportion of wheat wasted per year
-
-I might have included how much a bushel is,[^1]
-there's an order of magnitude right there.
-
-[^1]: $1~\text{US bushel} \equiv 9\frac{3571}{11550}~\text{US Gallons} \approx 9.3~\text{US Gallons}$
-
-The study suggests decomposition has no effect on estimate _confidence_
---which I'm tempted to believe because its funny
-and it tracks with my anecdotal experience---
-but I wonder if subjects using their own decompositions would present similarly.