---
id:
aliases: []
title: 2026-01-25
tags:
  - authorship/original
  - destiny/permanent
  - status/draft
  - type/daily
dg-publish: true
---
# 2026-01-25

## 2026-01-25 18:46

### 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.
