If you have $100k now, is it better to pay off $100k of mortgage of 4.5% or invest in a S&P index fund returning 7% pre-tax ?
Paying off $100k of mortgage is like putting in an investment with a guaranteed return of 4.5%.
Assuming 20% capital gain tax, 7% becomes 5.6%, still worth it?
Is below formula correct?
An investment is worthwhile so long the return net of tax and expenses exceeds the mortgage interest of your primary?
Is this a hyphothetical question? I think you know the answer. You personally can do better than 7%, just stay away from chinese stocks 
Thats not right. You are assuming selling everything every year, take the tax hit and compound again.
If you sell only at the end of 30 years your “interests on interests” get to compound tax free.
Say stocks grow at 10% compound and tax rate is 20%.
Sell all every year: $1 x 1.08^30 = $10.06
Sell only after 30 years: $1 x 1.1^30 x 0.8 = $13.96
10x vs 14x.
Also there’s state tax.
Move to Seattle.
Also with the stock, you might end up not realizing the tax if you have other income (like… margin loans… if you want).
Also isn’t 7% post inflation, bit 4.5% is including inflation?
Also with stocks, you can get stepped up tax basis
You are clouding the main issue. Which is that “interests on interests” compounds tax free.
Allow me to ask it another way. When would it be worthwhile to pay off the mortgage? Is a pure financial question, ignore non financial issues
Tomato,
Helps in evaluating.
You are better off to pay off your mortgage. That’s the decision I made when I retired. The S&P 500 could indeed go up 7% per year, but you have gotten too used to this long running bull market. It could also have 0% return over the next 5 years. Think about all the things that could send it into a downward spiral starting with a true trade war or a Trump impeachment, either of those are a distinct possibility.
trump impeachment might result in a short term pull back - at mosr couple years.
During and after Clinton impeachment market actually went up.
He did not actually get impeached.
He was impeached by the house. Just not convicted by the Senate. Could happen to Trump. Stocks won’t care.
I have been thinking similar lines today for my 100k outstanding balance in HELOC vs my keeping the investment money invested. I continue to hold my investments as the investment returns for this year is appx 37%.
If it is 7%, I would not mind paying off my mortgage as we have small difference of 5.6%-4% is 1.6% benefit.
Two reasons.
If it is strict 7% return and 100k, I would pay off debt even though financially I am wrong.
Never pay off any mortgage. In fact, pull even more home equity out of your house to invest in stocks.
Pay off your mortgage when you are sick of number crunching and just want to twiddle your thumbs until the very end.
What a sad way to live. 
That is the reverse question 
Jil,
Opportunity cost of primary is irrelevant.
Paying off 4.5% mortgage will never be better financially if you only look at the math. But we are humans, not robots. (Alas, @harriet chased our only robot away… 
)
So you need to look at the whole package. I believe humans only have a limited capacity for taking risks. There’s only so much our brains can handle. So it can be that by paying off the primary house you take away the biggest financial risk in your life, and that in turn allows you to take more risks in stock market.
It’s the same way how people are more rational playing with “house money” or only trading paper accounts. The pain is not as bad as if you are under other stress. Paradoxically you can take on far more risks by derisking in certain key vital areas.
