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