2.1 KiB
id, title, tags, daily
| id | title | tags | daily | |
|---|---|---|---|---|
| 2026-01-29T17:57:00-0500 | 2026-01-29 17:57:?? |
|
2026-01-29 |
2026-01-29 17:57:??
Calculating Utility of Above-Minimum Mortgage Payment
Follow-up to 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 have a budget surplus of E dollars
and are deciding whether to make an elective payment on your mortgage
or to invest in a promising opportunity.
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 ratei. Afternmonths, 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, and 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}