The PMI/interest likely won't be tax deductible due to the recent Trump boosting of the standard deduction, but there will be capital gains tax on future stock appreciation from investing elsewhere. This causes the numbers to likely be a wash, or at least very close.

Nope nope nope nope no nope no. The Mortgage deduction for interest is only <EFFECTIVE RATE> x Interest Paid. He would still be paying interest and in the (very unlikely) event that he gets to itemize, there is still some interest to put on there, but it is minimal. The Tax on gains however is only on Taxable Gains (IE DIVIDENDS) at 15%, again a very small amount. With 8000k, As of December 2017, the dividend yield for the S&P 500 was 1.85%, that leads to $22.20 in additional taxes. (8000 x 1.85% x 15% tax rate). **IT IS A TINY AMOUNT.** Giving up compounding on investments for 22$ in 'tax gains' because you chose not to invest is asinine. It is nowhere near a wash, as noted above. @genesismachine please do the math and understand what is given up by pre-paying before giving advice. This is exactly why the DPOYM Club exists, because #fakemath calling things a wash leads people astray.

But the return on this is risk-free, while the return on other investments is not. If you're ever given the choice between a 10% guaranteed return vs a 10% *average* risky return, investment theory says you should always pick the guaranteed return. This is why risk premiums exist. You are not being compensated for your added risk in this case with higher average expected returns.

Again, not a 10% gain. If it were we would all be telling him to pay it off as fast as possible (or better yet re-mortgage for a better rate) because the math doesn't make sense at 10% to keep the mortgage. It does, however, make sense at 3%. Again, saying that paying down the mortgage is a guaranteed 10% is #fakemath and leads people astray.

Further, you will be gaining another $100/month in free cash flow, which will add to your optionality in case you see other investment opportunities (although it is so small it probably won't add much). One thing you could do with the extra $100/month is to put it into a 401k.

If he isn't (and if you aren't) maxing out your 401k BEFORE paying any extra on a long-term low fixed rate loan, you are WASTING MONEY left and right. Tax free depositing and gains in a 401k will ABSOLUTELY DEMOLISH the so-called 'return' on a mortgage. At a bare minimum, fill up your tax-free buckets before paying any extra on a low rate loan.

Beyond that, the extra 100$ obviously doesn't matter if he has extra **thousands** of dollars to get rid of PMI. The little green soldiers need to be used the most effectively we can, not Russia WWII style marching them by the thousands into battle without rifles to get rid of a secure low-rate loan that can't be called while Moscow burns ... (Little green soldiers is money, battle is PMI and loan extra payments, Moscow is tax free accounts ;) )

In all seriousness, this forum is supposed to be about optimizing and reducing consumption. There is nothing optimal about paying down a mortgage early while leaving space (that is lost FOREVER) in a 401k...

Ok, let's do some math.

The standard deduction for 2018 is $24k for married couples. With the numbers provided, it is highly unlikely that any part of the interest/mortgage insurance will be tax deductible for OP.

Rough numbers: $25k @ 3% interest + $100/month avoided = $1950/yr saved, ~7.8% risk free return

Now, that does seem under the long term stock market AVERAGE return. Forget about the tax on dividends because that's a tiny amount like you said. Eventually, you will be withdrawing the amount, right? In my state, I would be dealing with 15% federal tax rate + 10% state tax rate. Not sure about OP.

So to make $1950/yr from a $25k investment AFTER TAX, with a 25% rate, we would actually need to earn a 10.4% return RISK FREE if we were to compare apples to apples against a pure S&P 500 investment.

Now, let's take on the actual S&P 500 with dividend reinvestment over the last 50 years as a baseline:

https://dqydj.com/sp-500-return-calculator/I got 10.02% return with dividend reinvestment from 1968-2018, which I think is a good baseline.

Now, would you rather have a 10.4% risk free return or a 10.02% risky return? It seems you may not understand how investment theory works if you think the second option is better.

But actually, it gets even worse for your point when you take into account that you could take that $1950/yr and invest it in the S&P 500 too. Using this compound interest calculator, and entering the following:

http://moneychimp.com/calculator/compound_interest_calculator.htmInitial principal: $0

Years to grow: 10

Interest Rate (S&P 500 historical 50 year return including dividend reinvestment): 10.02%

Future Value: $34,224 ($59224 when you include the initial $25k)

Calculate the compound return: $(59224/25000)^(1/10) = 9% return

When accounting for tax rates, it gets a little more complicated since some (the stock market gains) is taxable while some (the interest/mortgage insurance avoided) isn't. This takes it to an 'adjusted' after tax return of 8.3%

Comparing apples to apples, that would mean the pure S&P 500 investment would have to return 11.08% RISK FREE. This is significantly above the 10.02% average return. And again, one is RISK FREE while the other is not. There is a concept called risk premium that says that you should be taking a smaller return in exchange for less risk/volatility. So if you believe in basic investment theory, you would need to have a return far in excess of 10.02% to compensate you for that risk, and that is unlikely to happen based on the past 50 years history.

So I would actually say that my math is just fine, and these numbers agree with what I posted earlier.

Now, paying off the remainder of the mortgage is a much more controversial move... I am by no means a proponent of paying off a 3% mortgage.

Disclaimer: Technically you would've eventually paid off the mortgage principal enough to get rid of PMI automatically at some point. I just used 10 years as a rough number for default payoff time. I admit I did simplify some of the math, not accounting for the wide range of possibilities (we could've had much more than 10.02% S&P 500 returns, or much less, thus the volatility). The numbers may change slightly depending on state tax rates and exact personal circumstances, and future tax rates (capital gains tax rates have changed many times throughout US history), but the general point holds in almost all imaginable circumstances.