vault backup: 2026-01-29 22:37:15

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 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,