For example, a $100k 4% 30-year fixed mortgage has a payment of ~$500/mo resulting in ~$72k total interest paid over 30 years.

[A] Putting a $10k windfall towards the mortgage 1 year later results in ~$19k less total interest paid.

**If instead the $10k windfall came at year 7, only ~$13k interest would be saved.**

Alternatively, if one could pay an extra $500/mo, the total interest paid over ~11 years would be $23k saving $49k in interest.

[C] Similarly a $10k windfall after 1 year in addition to the extra payments now only saves an additional $5k in interest.

[D] And if that $10k windfall came at year 7 with the additional payments, it saves just $1k as the loan is already almost paid off.

If instead of a windfall, one had $10k of taxable investments that could be sold with $1k of capital gains tax, all of the above comparisons could effectively combine the interest costs with the capital gains tax costs. So instead of saving $19k in interest with the "windfall" in situation [A], one would be saving $18k instead. Similarly it might not make sense to realize the gains in situation [D] as the "windfall" would result in about the same amount of taxes being paid as interest being saved.

Is something missing by looking at dollar costs instead of rates?

Alternatively, if one could pay an extra $500/mo, the total interest paid over ~11 years would be $23k saving $49k in interest.

[C] Similarly a $10k windfall after 1 year in addition to the extra payments now only saves an additional $5k in interest.

[D] And if that $10k windfall came at year 7 with the additional payments, it saves just $1k as the loan is already almost paid off.

If instead of a windfall, one had $10k of taxable investments that could be sold with $1k of capital gains tax, all of the above comparisons could effectively combine the interest costs with the capital gains tax costs. So instead of saving $19k in interest with the "windfall" in situation [A], one would be saving $18k instead. Similarly it might not make sense to realize the gains in situation [D] as the "windfall" would result in about the same amount of taxes being paid as interest being saved.

Is something missing by looking at dollar costs instead of rates?