zmVault/2026-01-29.md

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2026-01-29

2026-01-29 10:07

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

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 had E dollars to

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, 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}