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

2026-02-20 14:53:32 -05:00
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 # 2026-01-29
-
-# 2026-01-29 10:07:37
-
-#topic/estimating
-
-A peer's senior, expressing frustration,
-told them that it if they disagree with an instruction,
-they must have a reason,
-implying that the estimator's previous complaints,
-which were based on conflicting direction
-received from other estimators and seniors,
-were made _without_ reason.
-
-See [[realism-vs-instrumentalism]].
-
-The peer's senior is looking for a _realist_ objection to his methods,
-which an estimator without field experience (which the senior has)
-would be unlikely to be able to provide.
-Their dismissal of legitimate _instrumental_ complaints
-(misplaced effort, and deviation from more widely accepted standards)
-speaks to a fundamental misunderstanding of the purpose of estimating.
-
-# 2026-01-29 17:57:??
-
-#topic/finance
-
-### Calculating Utility of Above-Minimum Mortgage Payment
-
-See [[2026-01-25#Calculating Monthly Principal & Interest Payment]].
-
-Homeowners are often advised to make elective mortgage payments
-to reduce the total interest paid on the loan,
-but an unrelated investment with a sufficient return
-could outweigh the reduced loss.
-
-Suppose you have a budget surplus of $E$ dollars
-and are deciding whether to make an elective payment on your mortgage
-or to invest in a promising opportunity.
-
-The return on electing to pay $E$ to the mortgage
-is the
-(i.e., interest that will no longer accrue)
-at the end of the loan is:
-
-$$
-R_{\text{mortgage}} = E(1+i)^{n}
-$$
-
-> [!info]- Explanation
-> This formula may seem suspiciously straightforward,
-> but suppose you did _not_ contribute $E$.
-> That portion of the principle would accrue interest
-> every month at rate $i$.
-> After $n$ months, the interest accrued by that portion is given by:
->
-> $$
-> E(1+i)^{n}
-> $$
-
-If the same $E$ is invested elsewhere at monthly return $j$,
-its future value after $n$ months takes the same form:
-
-$$
-\text{FV}_{\text{investment}} = E(1+j)^{n}
-$$
-
-Therefore, $j$ must exceed $i$
-for the alternative investment to be preferable to elective payment.
-
-Note that $i$ and $j$ are adjusted rates,
-including respect for taxes and utility.
-
-On second thought, in a utility context,
-time preference could make $j$ preferable
-even when slightly lower.
-
-Short-term investments may be favored
-when liquidity is needed during the term,
-and tax deferred investments (IRA)
-are strongly favored over elective payment
-since interest is deductible
-(effective interest < nominal).
-
-### Calculating Effect of Elective Payment on Term Length
-
-The monthly payment and interest rate are fixed,
-so the term length must decrease
-
-$$
-\begin{align}
-A &= P \cdot \frac{i(1+i)^n}{(1+i)^n-1} \\
-P &= A \cdot \frac{(1+i)^n-1}{i(1+i)^n} \\
-n &= \frac{\ln\left(\frac{A}{A-Pi}\right)}{\ln(1+i)} \\
-\end{align}
-$$