From 02b428a8c3d39a41432497f57600ceab290eea5a Mon Sep 17 00:00:00 2001
From: Zane Meyers <zanemeyers@gmail.com>
Date: Thu, 29 Jan 2026 22:37:15 -0500
Subject: [PATCH] vault backup: 2026-01-29 22:37:15

---
 2026-01-29.md | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/2026-01-29.md b/2026-01-29.md
index fdc96a2..cd87bd9 100644
--- a/2026-01-29.md
+++ b/2026-01-29.md
@@ -73,6 +73,20 @@ $$
 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,