102 lines
2.7 KiB
Markdown
102 lines
2.7 KiB
Markdown
---
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id:
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aliases: []
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title: 2026-01-29
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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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# 2026-01-29
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## 2026-01-29 10:07
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A peer's senior, expressing frustration,
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told them that it if they disagree with an instruction,
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they must have a reason,
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implying that the estimator's previous complaints,
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which were based on conflicting direction
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received from other estimators and seniors,
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were made _without_ reason.
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See [[realism-vs-instrumentalism]].
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The peer's senior is looking for a _realist_ objection to his methods,
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which an estimator without field experience (which the senior has)
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would be unlikely to be able to provide.
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Their dismissal of legitimate _instrumental_ complaints
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(misplaced effort, and deviation from more widely accepted standards)
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speaks to a fundamental misunderstanding of the purpose of estimating.
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## 2026-01-29 17:57
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### Calculating Utility of Above-Minimum Mortgage Payment
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See [[2026-01-25#Calculating Monthly Principal & Interest Payment]].
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Homeowners are often advised to make elective mortgage payments
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to reduce the total interest paid on the loan,
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but an unrelated investment with a sufficient return
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could outweigh the reduced loss.
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Suppose you had $E$ dollars to
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The return on electing to pay $E$ to the mortgage
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is the
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(i.e., interest that will no longer accrue)
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at the end of the loan is:
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$$
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R_{\text{mortgage}} = E(1+i)^{n}
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$$
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> [!info]- Explanation
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> This formula may seem suspiciously straightforward,
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> but suppose you did _not_ contribute $E$.
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> That portion of the principle would accrue interest
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> every month at rate $i$.
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> After $n$ months, the interest accrued by that portion is given by:
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>
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> $$
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> E(1+i)^{n}
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> $$
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If the same $E$ is invested elsewhere at monthly return $j$,
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its future value after $n$ months takes the same form:
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$$
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\text{FV}_{\text{investment}} = E(1+j)^{n}
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$$
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Therefore, $j$ must exceed $i$
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for the alternative investment to be preferable to elective payment.
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Note that $i$ and $j$ are adjusted rates,
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including respect for taxes and utility.
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On second thought, in a utility context,
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time preference could make $j$ preferable
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even when slightly lower.
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Short-term investments may be favored
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when liquidity is needed during the term,
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Tax deferred investments (IRA)
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are strongly favored over elective payment
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since interest is deductible
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(effective interest < nominal).
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### Calculating Effect of Elective Payment on Term Length
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The monthly payment and interest rate are fixed,
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so the term length must decrease
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$$
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\begin{align}
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A &= P \cdot \frac{i(1+i)^n}{(1+i)^n-1} \\
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P &= A \cdot \frac{(1+i)^n-1}{i(1+i)^n} \\
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n &= \frac{\ln\left(\frac{A}{A-Pi}\right)}{\ln(1+i)} \\
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\end{align}
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$$
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