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.

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.

1~\text{US bushel} \equiv 9\frac{3571}{11550}~\text{US Gallons} \approx 9.3~\text{US Gallons} ↩︎

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