I think your calculations are confusing here. You are adding and subtracting interest from your networth (which isn’t how it should work) and you are also ignoring the additional funds required to make up for the lost compounding time in the market in scenario 2.
The first most important point is that, as others have mentioned, your estimate of 4% is most likely too low.
And, as you asked, for the sake of simplicity we’ll ignore taxes, downpayments and even the fact that your home will most likely appreciate.
But my main question is - are you calculating what you will gain over 25 years, or are you calculating what your networth will be after 25 years?
Because you seem to be trying to do both simultaneously - and they are two different things.
Scenario 1:
I currently have more than this in stocks but the sake of argument, lets say I only had 212k in stocks and didn't add anything for 25 years and just let it compound:
-212k invested with a 4% rate of return + compound interest = 565k after 25 years (I used networthify calculator)
-this means after 25 years, I have a mortgage paid off, plus the compounded investments, minus a very conservative 50k in mortgage interest that would likely be much higher since my current term is locked in for 5 years but will likely go up after 5 years.
-So 212k paid off house + 565k investments - 50k interest = 727k networth after 25 years
This doesn’t make sense.
Your networth after 25 years would not be 727K.
Instead I would suggest you look at it as gains over 25 years versus estimated networth in 25 years.
Keep in mind we know that your current networth is 212K.
So in this first scenario you would have spent 272K total on the house (212K mortgage +50K interest over 25 years) while ending with a total of 565K in stocks from your original networth of 212k.
So:
565K - 272K = 293K total gains over 25 years.
Whereas your networth in 25 years would be:
212K home + 565K stocks = 777K
Scenario 2: Pay off mortgage in full lump sum
-212k is withdrawn from stocks (yes I know I'd have to pay tax on interest but ignore this for simplicity) so theoretically let's pretend I now have zero in stocks but mortgage is fully paid off; it will only cost around 1k in fees to pay off mortgage in full
-I now have an extra 867$ monthly (mortgage payment) to invest
-867$ invested monthly at a 4% interest rate, compounded over 25 years = 446k
-So 212k paid off house + 446k investments + 50k that we'd save on interested = 708k
You may save 50K on interest here, but you will spend 48,100 dollars more on stocks all to make a lower return overall.
In this scenario you would have spent 212K total on the house while gaining a total of 446k in stocks, but
also investing 260,100 total over 25 years (867/month over 25 years). In scenario 1 you only had to invest your original 212K, so this case has an additional investment of 48,100 from you over 25 years.
So:
446k - 212K - 48,100 = 185,900 total gains over 25 years.
Meanwhile your networth in 25 years would be:
212K home + 446k stocks = 658K
EDITED TO ADD: Apologies if others already covered this in the time it took me to type.