So OP's decision here is about $200-600k, not $20-40K. And that's if the loan in question is $100K - if the loan is $400k, you're talking about possibly $2 million with the pay cash vs. keep the 2.5% rate to the bitter end. If this is in a truly HCOL area, the cost of paying off the house just gets higher and higher. Even a very small mortgage of $50K we're likely talking about a six figure consequence to the decision at the end of 30 years.
So I ask this - is that good feeling (and a paid off house does feel great - I do not dispute that at all having twice been there myself when I was younger and dumber) worth $500K or more? Because when you're talking about someone with a sub 3% 30 year mortgage with almost all of that 30 years left, that's the scale of number you should have in mind as to the cost of the decision. Minimum hundreds of thousands of dollars, possibly into the millions.
OP here, maybe you can help me with the math based on what I'm actually doing.
BTW, as a result of this thread, I stopped my overpayment beginning with my next mortgage payment on 1/1/23.
The loan was ~$550k @ 2.49%. I was overpaying by $640/mo. I owe approx $520k on it now.
Assuming the $640/mo goes into the S&P instead of the house, what does that look like 12 years from now when my youngest is ready to go off to college? What about 28 years from now when the loan matures?
I get about $47,000 difference at 12 years for the 640 payment with that 9% return from the S&P, which is lower than a lot of starting points. For simplicity I assumed you started with 2 years of no extra payment - I get balance of $524K today. Then if you don't pay extra on mortgage your mortgage balance is down to $343K in another 12 years, and the investment has grown to $154K. If you put extra towards mortgage, the balance in 12 years is about $236k.
At end of mortgage 28 years, the difference is starker - 640 / month with that same return grows to $867,000 in 28 years. If you apply that $640 to the mortgage, the mortgage pays off in a little under 20 years, so you have a larger payment of $2810 that has just over 8 years to grow (I got your P&I to be $2170). FV says $391,000. Either way in 28 years you've got a paid off house, but you have $476,000 more in your investment account at the end if you invest the $640 each month vs. putting it towards mortgage.
So if the plan is forever home, and that's how it goes, then you've got a lot more money by keeping the mortgage vs. applying $640 extra per month.
Attaching sheet in case I made a large error here that I've missed, but seems to be in ballpark to me given past reading & exercising these numbers. One slight nod towards conservative is I assume the whole payment each year would be made once at the end of year vs. true monthly.
And keep in mind that while the mortgage paydown at any point can be determined with certainty, there's a range on investments - if you enter a lower number then things tighten up between the "extra" or "no extra" options, if you enter a higher number, then the difference gets larger. Thing is with a rate as low as yours, the odds are heavily in the "no extra" options favor. And final note - really need to be estimating nominal investment returns for this. Because the mortgage payment itself is fixed and doesn't grow with inflation, so you don't need to factor inflation into the analysis. For a lot of stuff it is appropriate to use real returns since most spending we do probably inflates over time, but the mortgage is an exception.
Anyway, I should actually go to my day job today - good luck with it.
