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,