The inflation rate is critical in the calculation when future value or purchase power declines every year. For now the assumption is 2% annual inflation. Can you imagine it gets larger in the future? An amount of $1M is not likely to last 30 years.

Or worse, 4% of the balance plus an additional 2% of the balance purportedly to "adjust" for inflation.

Thus the return rate must be higher than 0.1% (4.1%- 4.0%) and that may not be easily accomplished every year.

My commentary (middle block of quotes above) was a distraction about the inflation adjustment. The key point I was making was one does not withdraw 4.0% each year.
One withdraws 4% of the original portfolio (here 4% of $1M, or $40K), and then adjusts that fixed amount for inflation. What percentage of the portfolio balance that withdrawal represents each year is not fixed, but depends on the real return of the portfolio.
For example, if the portfolio doubles in the first year, i.e. grows by 104% (100% after adjusting for 2% inflation), then the $40,800 would constitute only 2% ($40,800/$2,040,000) of the year end balance.
As to what return rate is needed assuming a constant rate of return and a constant inflation rate, Rekenthaler wrote:

The break-even point for portfolios with real withdrawals is the sum of 1) the withdrawal rate [4%] and 2) the inflation rate [2%]. In this portfolio’s case, that means 6%. That conclusion seems trite. But it did not strike me as obvious when I first approached the topic.

So a nominal rate of return of 6% or better means that the portfolio will last forever.
A nominal return rate of less than 6%, e.g. 4.1%, would lead to the portfolio ultimately being exhausted. But for this portfolio, that would still take 36 years. Here's a PV calculation illustrating this, where all figures are in terms of real dollars. One starts with $1M and $40K withdrawal (both real), the portfolio grows at a 2.1% real rate of return (4.1% - 2% inflation), and the withdrawal amount is a constant $40K (real).
The assumptions are simplistic. Rates aren't constant. So matters are more complex. Still, Bengen has not found any historical 30 year period, including ones with low inflation and richly priced markets, where a starting withdrawal rate of 4.5% did not survive 30 years.
People can always say "this time is different". Perhaps that is the only thing that isn't different. People are always saying that "this time is different."

The inflation rate is critical in the calculation when future value or purchase power declines every year. For now the assumption is 2% annual inflation. Can you imagine it gets larger in the future? An amount of $1M is not likely to last 30 years.

Or worse, 4% of the balance plus an additional 2% of the balance purportedly to "adjust" for inflation.

Thus the return rate must be higher than 0.1% (4.1%- 4.0%) and that may not be easily accomplished every year.

By happy coincidence, John Rekenthaler had a column a couple of weeks ago in which he provides similar year-by-year calculations for the same reason as I did above, viz. that seeing all the details year by year helps to understand what is going on.
https://www.morningstar.com/articles/1004651/the-retirement-income-puzzle
Here's his table of a million dollar portfolio over five years where the nominal growth rate is 4.1% (I used -10%), and inflation rate of 2% (I used 0%). Note that even though he says that the withdrawal "rate" is 4%, what he is actually doing is what Bengen described: starting with 4% ($40K on $1M), he adjusts this fixed amount for 2% inflation annually. He is not withdrawing 4% of the balance annually. Or worse, 4% of the balance plus an additional 2% of the balance purportedly to "adjust" for inflation.He also cites a recent interview with Bengen that answers @davidrmoran's question:

Michael [Kitces]: And so, what do you think about as the number in the environment today?
Bill [Bengen]: I think somewhere in 4.75%, 5% is probably going to be okay. We won’t know for 30 years, so I can safely say that in an interview.

Worldwide/Global "Leaders." Harbor. HGGIX. Does anyone care to offer a quick and dirty evaluation of this fund for me? I earlier asked about Seven Canyons because it was featured... I'm not picky about the category, but the money will be for a medium-term goal: 3-4-5 years. Only 138M AUM in HGGIX, but its performance vs. peers looks good to me. Thank you.

If I understand it correctly, when the mortgage is new, then the mortgage payments are mostly interest. But if this is a fixed rate 30 years old mortgage, and only few years left to pay it out, then most of the monthly payment are for the principal. In other words, the effective interest you pay is maximal at the beginning and it is getting smaller and smaller at the end. Therefore it may be less advantageous to refinance during the last few years. A more detailed calculations is required, what I said is just a guess.

You're paying the same rate, say 3%, on the amount of the loan outstanding each month. What is happening is that as you make your monthly payment, you're reducing the outstanding balance - part of your monthly payment goes toward paying down the loan. The rest of the payment is the 3% interest on the outstanding balance.
The next month comes along, and your outstanding balance is less than before, because you paid off some of the principal in the previous month. You still pay 3% on the now smaller outstanding balance. So less of your monthly payment than before is interest. You wind up reducing the balance at a faster and faster pace. Each month you pay less and less interest, but it's still 3% interest on the ever shrinking outstanding balance.

One other point. Is interest payments still tax deductible ?

If the interest is deductible, then paying it off is equivalent to putting the money in the bank at that same rate of interest. For example, if your interest rate is 4% and your tax rate is 25%, then you're really paying only 3% (3/4 of 4%) after counting the value of the deduction. That's the same after tax return you get from a 4% bank account, once you subtract the taxes.
OTOH, if the interest is not deductible, you should compare the nominal rate of the mortgage with the after tax rate of a savings investment. For example, if your mortgage rate is 3% but you can't deduct it, and you're in the 25% bracket, then this is equivalent to a 4% rate at a bank. If you put money in a bank at 4%, you net 3% after taxes, which is what you'd save by paying off the mortgage.

glad for all the responses. @BenWP glad for that factoid about shrinking AUM. I would not want to invest, and then a couple of years later, the fund liquidates.... Now, I'll go check-out ARTYX, @AZRph. Thanks, everyone.

Let's say we're having this discussion in 2000. You'd be staring ahead at a lot of pain for 10 years, while your home and those interest payments are secure. Just sayin'.

@Crash: I use M* to determine fund flows. Not sure if you have to be a subscriber, but the “Parent” tab for the fund provides the data. For Seven Canyons, which has only two funds, it’s a simple matter to see that up until the most recent quarter, the funds had been losing a lot of assets for several years. 2019 was a really cruel year for them.

Look like the large gain is limited to this year. The other years are so so versus its benchmark (click on the Expanded view).
performance.morningstar.com/fund/performance-return.action?t=WAGTX&region=usa&culture=en-US

Yeah, great thread. Very informative. And in addition to "green hydrogen", battery storage solutions have been improving at a breakneck pace, mostly due to research and engineering into EVs. Merely 10 years ago a tiny subcompact like the Nissan Leaf had only a 72 mile range. Today 250 to over 300 miles of range is becoming the norm. The 2020 Tesla Model S is rated at over 400 miles. Illustrating how far battery tech has evolved in only a decade.
I must admit, I always thought of solar as a "local" power solution. If this is a feasible option, it seems like a real game changer. Imagine a continent like Africa, with all it's economic hurdles, becoming a vast exporter of energy to far-flung locations.

Thanks to all for your valuable comments. I didn’t know if the subject held interest for the group so I did not provide personal info that could have informed the advice offered.
We are in our late 70’s and have 10 years to go on a 15-year mortgage at 3%. Our situation is hardly typical in that we up-sized to our current home in 2007-8 because our fortunes improved considerably. We were able to get a very desirable property that has increased a lot in value since then. Our large family of 5 daughters, ages 49 to 22, and 3 grandchildren, has required us to have a large place. So far our health is good and we do all our own housework, yard work, and routine maintenance. Many of our friends have moved to condos, but we’re not ready for that yet (knock on wood...).
One development of importance is that when the COVID crisis hit this spring, I purposely raised quite a lot of cash in our taxable account, partly out of a fear that our two youngest daughters (single) might have lost their employment and would have had to be supported. That fear appears to be unfounded now. Even though I stopped my TIAA RMDs, we do not have a cash flow problem because we haven’t traveled since January, nor have we needed a new vehicle or a major home project done. In short, there’s ample cash to pay off the mortgage without altering our current lifestyle. My thinking is to retire the debt because it seems a good way to use the cash that’s sitting idle now. Please comment. Thanks in advance.

My results, which are not accurate as yours came up pretty close after 22 years.
The ending size of your portfolio is $876K nominal, $543K real. The size of the portfolio resulting from Bengen's scheme is $1.366M nominal, $847K real. These two portfolios are not close in value.
You designed a scheme radically different from Bengen's. Bengen assumed that one would withdraw a constant amount of money each year, in real dollars. Your scheme withdraws an amount each year that fluctuates based on the value of the portfolio.
From the way you describe your design, 4.5% + 2% for inflation, it seems that you still think that Bengen's scheme is to withdraw 4.5% of the value at the end of each year after adjusting for inflation. This is the miscommunication.
Bengen wrote (same quote as before): "After the first year, the withdrawal rate is no longer used for computing the amount withdrawn; that will be computed instead from last year's withdrawal, plus an inflation factor." In contrast, each year you use a withdrawal rate (7%) to compute the amount withdrawn.
You direct PV to withdraw 7% of the portfolio each year, leaving 93% to grow (or shrink) over the following year. So the withdrawals can never exhaust the portfolio. However, as the portfolio shrinks in size, so will the size of the withdrawal.
----------
For example, suppose that the portfolio is invested in something that loses 10% of its value, no more, no less, each year. Then under your scheme, a portfolio that started with $1M would progress as follows:
Start: $1,000,000.
Year 1 end: $900,000.
Withdraw $63,000 (7%).
Year 1 after withdrawal: $837,000.
Year 2 end: $753,300.
WIthdraw $52,731 (7%) - notice that the size of the withdrawal is shrinking.
Year 2 after withdrawal: $700,569.
...
Year 22 end: $21,452.46
Year 22 withdrawal $1,501.67
Year22 after withdrawal: $19,950.79
I find it instructive to do calculations by hand, but in case you don't believe me, here's PV's calculation. If you mouse over the graph to year 22, you'll see that the value is $19,951 (before adjusting for inflation).
----------------------
Bengen's scheme (assume 0 inflation for simplicity, higher inflation would merely make the results worse):
Start: $1,000,000
Year 1 end: $900,000
Withdraw: $45,000
Year 1 after withdrawal: $855,000
Year 2 end: $759,500.
Withdraw $45,000 - or more if there is inflation
Year 2 after withdrawal: $724,500.
...
Year 11 end: $50,025.36
Withdraw $45,000
Year 11 after withdrawal: $5,025.36
Year 12 end: $4,522.83
Not enough to withdraw $45,000. Portfolio is exhausted.
Again, I think that the figures above are more instructive than blindly using a calculator. But here's PV's calculation. Mouse over year 11, and you'll find the value $5,025 (before adjusting for inflation). Obviously PV reports that the portfolio is exhausted in year 12.

If I understand it correctly, when the mortgage is new, then the mortgage payments are mostly interest. But if this is a fixed rate 30 years old mortgage, and only few years left to pay it out, then most of the monthly payment are for the principal. In other words, the effective interest you pay is maximal at the beginning and it is getting smaller and smaller at the end. Therefore it may be less advantageous to refinance during the last few years. A more detailed calculations is required, what I said is just a guess.

I think there is a breakdown in communication.
I didn't know 2 things:
1) that PV has Inflation adjusted box under the chart.
2) When you select Withdrawal fix Amount then another window open and you can select Inflation adjusted
So instead, I selected a fix Withdrawal Percentage of 4.5% + added an estimate 2.5% for inflation. There is no need to adjust again for inflation.
My results, which are not accurate as yours came up pretty close after 22 years.

The crucial factor left out is time. How many years are left on the mortgage? Also, liquidity is not to be underestimated. A house is an illiquid asset. If you have an emergency and need cash you can sell your stocks quickly. A house you’re stuck with for a while before you can sell at a fair price.

There is no “right” answer on that one - unless you’re confident you can predict the future.
It’s true some parts of your (or my) diversified portfolio aren’t earning anywhere near 3% today, I choose to look only at the portfolio as a whole. That includes everything: the good, the bad and the ugly portions. That portfolio (100% either tax deferred or exempt) is viewed in my eyes as one singular entity with individual parts working together. Based on the past 25 years in which I’ve kept reliable records it has produced more than 3% annually (averaged out) by a good margin. (Keep in mind that the overall return includes the cash and bond positions.) That’s not braggadocio. Hell, most of the people who visit this board could lay claim to an average return greater than 3% over recent decades.
Now - if one has both the discipline and the psychological make-up to run a portfolio in which his paid off mortgage is included as a “cash” holding (which you’ve converted it to by paying it off), than it’s probably a good decision. The difficulty is one’s more visible “paper” assets (funds, stocks, etc.) will have to be more aggressively invested than that individual may be accustomed to since the portion of the portfolio formerly invested in cash or lower risk bonds is now being occupied by that paid-off mortgage. I’d have a hard time adjusting to that. In addition, I feel I can do a better job of diversifying investments across the asset spectrum with a somewhat larger investable sum. So, while my mortgage (a refi used for adding living space) could easily be paid off with invested money, I’ve chosen to let it run for the time being.
Some other considerations - Currently you control that sum of money that’s owing on the mortgage and invested elsewhere. Once you tender that sum to the mortgage lender they take control of that money. You’ve surrendered control. You’ve also surrendered liquidity. Some of this question relates to how actively and enthusiastically you invest. If you enjoy the game and are very actively engaged, you might like having some “opportunity money” on hand to grab up bargains when they arise - even if carrying that low yielding cash is costing you a couple extra percent a year.
Here’s two respectable truisms that are diametrically opposed, yet both are IMHO accurate and fit your situation.
1) You can’t go wrong by paying off debt. (true)
2) It’s always better to keep your options open. (true)
Mind you, both of the above are true. Yet, the first statement would favor paying off the mortgage while the second would support hanging on to that cash. :)

Back in 2010 when faced with a similar dilemma, CDs coming due and a dearth of good fixed income options I decided to pay off my mortgage. At that time my fixed rate mortgage was 5 3/8%. Refinancing might've gotten me to around 4 1/4% with around $2000 in costs at that time. Instead I used the CD proceeds, my MMF balance and some misc other investments to pay off the mortgage. Saving 5 3/8% with zero additional cost was a good deal I figure.
Now the other side of the coin. Had I taken all that money and invested it in the stock market in 2010, I would be way ahead by comparison. But I was wary of taking too much risk at that time and was already heavily invested in equities. So, peace of mind was my goal and I simply look at that move as a portion of my FI portfolio. Plus, no one can forecast the future. And I suspect that the stock market will not do as well in the next 10 years as it did in the last 10 years. But, that is pure speculation. I think trading a guaranteed 3% savings for money that is earning almost nothing is not a bad idea. Provided you are unwilling to take risk with those funds.
Good luck with your decision.

Both are close...Mine=$876K...yours=$847K.
I ONLY CARE about numbers adjusted for inflation.

If you ONLY CARE about numbers for inflation, you might stop saying that your number is $876K. Adjusted for inflation, it is $543K, which amounts to a 2.64%/year loss in real value over 22.81 years.
Try this: Run a portfolio of pure cash (CASHX), no withdrawals. I've even set it up for you. I hope you'll agree that cash lost value to inflation over the past 22 years. Prove it. What's the inflation adjusted ending value of a $1M starting portfolio? How did you adjust for inflation, and did you do the same thing with your $876K amount?
Alternatively, you could just take your $876K and divide by 1.60, which is roughly the cumulative inflation between 1998 and now. That comes out to $548K. (The difference between this and $543K is likely due to the fact that 1.6 represents inflation until 2020. Add another 1% inflation for the first three quarters of the year and you're down to around $543K. Though the figures are close enough I really don't care about the cause of the 1% discrepancy.)

We don't know what will be in the next 30 years but I like to make predictions NOW since we are talking about retirement now.
My assumptions of 2.5% and why I used 7% are close to yours of 4.5% withdrawal and then using adjusted for inflation. Both are close...Mine=$876K...yours=$847K.
I ONLY CARE about numbers adjusted for inflation.
Basically in the last 22 years this portfolio lost a purchasing power at about 0.5% annually.
In the next 30 years, I think it will get even worse. There is a good chance to lose at least 1.5-2% annually after inflation. I used Savings Withdrawal Calculator, starting with 1million, taking out $15K annually for 30 years left me with $550K.
Still OK according to Bengen.

You can see that my assumptions end results are pretty close to yours.
Remaining portfolio:...Mine=$876K...yours=$847K.
I wrote: "At the end of the 22+ years, it [Bengen's model, not mine] shows a remaining portfolio value of $1.366M, or $847K in inflation adjusted dollars (check the inflation-adjusted box at the bottom of the graph).
Your scheme: $543K in inflation adjusted dollars (check the inflation adjusted box at the bottom of the graph).
From this point it may get much harder not easier. FBNDX(bonds) past performance since 1998 was 5% annually, it's going to be about 2% lower. This means that the same portfolio could make about 2% lower than the above and further erosion
All talk, no numbers. Here's a start.
Take 50% US Stocks, 50% US Bonds. Start with a nominal value of $1.366M, i.e. Bengen's value as of now. Use your 3% nominal return figure for bonds. Use your 7% nominal return figure ("now it's lower 7 - 2 = only 5%") for stocks.
As a starting withdrawal, take Bengen's 4.5% figure ($45K on $1M), adjusted upward for inflation over the past 22 years (about 60%, as I've already shown), i.e. start with a withdrawal amount of $7200. Follow Bengen's scheme, not yours - adjust that withdrawal amount for inflation annually (based on historical inflation, which is likely too high, but that just makes this model more conservative).
Run a simulation based on these parameters for 10 years - a higher bar than the 8+years needed to complete the 30 year span. The survival rate is 1000/1000.
I'm done. You're writing about, to use @davidrmoran's term, what you "feel". I'm writing about numbers.