## Best way to pay off mortgage (considering investment returns)

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Topic Author
newberstiltskin
Posts: 2
Joined: Sun Jan 14, 2018 11:09 pm

### Best way to pay off mortgage (considering investment returns)

I was wondering what the best way to pay off a mortgage is between these three options below. I've used some general numbers:
House Cost \$500k
Mortgage Rate: 5%
7% Stock Market Returns
Let's assume I have \$2,147 each month to do something with and \$150k in cash.

Option 1: \$100k down payment, \$2,147 mortgage payment, \$50k invested lump sum
Option 2: \$150k down payment, \$1,879 mortgage payment, \$268 invested monthly for 30 years
Option 3: \$100k down payment, \$2,147 mortgage payment, \$50k immediate mortgage payment, \$2,147 invested monthly for 7.2 yrs

I've done the math, and it looks like the they are ranked from best to worst.
Option 1: \$401k after 30 yrs + paid off house
Option 2: \$326k after 30 yrs + paid off house
Option 3: \$233k after 30 yrs + paid off house

To me, this makes some sense because I am invested in the stock market for the longest period of time, generating higher returns.

I'm a little concerned though that inflation is making my calculations wrong. Wouldn't option 3 look better once inflation is accounted for, because the \$2,147 monthly payments would be "worth less" 22.8 years from now?

willthrill81
Posts: 7453
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

### Re: Best way to pay off mortgage (considering investment returns)

Mathematically, if the stock market actually does average 7% and the mortgage rate is 5%, then option #1 is best. Multiple studies have shown that lump-sum investing is preferable to dollar-cost averaging into the market two-thirds of the time. Paying down the mortgage early is taking money away from a 7% investment (gain) to prevent a 5% cost (loss). Inflation reduces both of these rates but does not change the conclusion. Tax issues could complicate matters somewhat, but this conclusion is still very likely to hold.

That being said, I and my wife have chosen to pay off our mortgage early. We're still saving 15%+ of my gross income into tax-deferred accounts. Once the mortgage is paid off, we'll divert the money toward investments. Even though projections built on historical data suggests that this is sub-optimal, it's what we're most comfortable with. You have to decide for yourself.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

FiveK
Posts: 6018
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Best way to pay off mortgage (considering investment returns)

newberstiltskin wrote:
Sun Jan 14, 2018 11:23 pm
Mortgage Rate: 5%
7% Stock Market Returns
Once you make this assumption (that your investment returns will be higher than the mortgage rate), any properly done analysis will show that investing beats paying the mortgage. The real question, then, is "will this assumption be true?"

The ongoing "pay mortgage vs. invest" wars discussions tend to have two camps:
a) those who assume historical averages are good predictors of the most likely future results
b) those who aren't comfortable with "most likely" (or disagree completely with that prediction)

Neither "a" nor "b" can be proven correct, except in hindsight. Many members of camps "a" and "b" cannot understand the other position.
I've done the math, and it looks like the they are ranked from best to worst.
Option 1: \$401k after 30 yrs + paid off house
Option 2: \$326k after 30 yrs + paid off house
Option 3: \$233k after 30 yrs + paid off house

To me, this makes some sense because I am invested in the stock market for the longest period of time, generating higher returns.

I'm a little concerned though that inflation is making my calculations wrong. Wouldn't option 3 look better once inflation is accounted for, because the \$2,147 monthly payments would be "worth less" 22.8 years from now?
Inflation is irrelevant to these results, because no matter how much less buying power those amounts may have, \$401K > \$326K > \$233K remains a true set of inequalities.

riverguy
Posts: 454
Joined: Sun May 23, 2010 10:33 pm

### Re: Best way to pay off mortgage (considering investment returns)

Why would you want to take stock market risk for a 2% spread? Seems silly.

Stonebr
Posts: 1468
Joined: Wed Jan 21, 2009 11:19 am
Location: Maine

### Re: Best way to pay off mortgage (considering investment returns)

I paid off my mortgage in 1999, getting lucky with the timing. But paying off in 2000 or 2009 would not have been so lucky.

It's probably better to do it when the skies are sunny, the bulls are running on Wall Street, and all your friends tell you you're crazy. Happy days don't last forever, and I found that those nasty financial meltdowns were a lot easier to handle with a roof over my head. Staying the course was a lot easier with one less worry.
"have more than thou showest, | speak less than thou knowest" -- The Fool in King Lear

Watty
Posts: 14944
Joined: Wed Oct 10, 2007 3:55 pm

### Re: Best way to pay off mortgage (considering investment returns)

There is a wiki on this choice and no consensus on what is best.

newberstiltskin wrote:
Sun Jan 14, 2018 11:23 pm
Option 3: \$100k down payment, \$2,147 mortgage payment, \$50k immediate mortgage payment, \$2,147 invested monthly for 7.2 yrs
This option makes no sense because a lot of the loan costs are based on the loan amount so you would be better with a \$150 downpayment and then just paying extra on the loan each month.

The math gets more complex when you start factoring in things like inflation, taxes, and different interest rates for different lenght loans. It is also very rare for people to actually have a loan for the full 30 years. The vast majority of people will either move or refinance a loan long before the 30 year loan would be paid off.

There is so much that is unknowable that I would not depend on simple math like that.

Nate79
Posts: 3939
Joined: Thu Aug 11, 2016 6:24 pm
Location: Delaware

### Re: Best way to pay off mortgage (considering investment returns)

Rerun your numbers with 4% stock market returns. Then rerun it for 10% stock market returns..... on and on. Since there is no guaranteed stock market return all you are doing is playing with numbers.

willthrill81
Posts: 7453
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

### Re: Best way to pay off mortgage (considering investment returns)

FiveK wrote:
Mon Jan 15, 2018 1:22 am
newberstiltskin wrote:
Sun Jan 14, 2018 11:23 pm
Mortgage Rate: 5%
7% Stock Market Returns
Once you make this assumption (that your investment returns will be higher than the mortgage rate), any properly done analysis will show that investing beats paying the mortgage. The real question, then, is "will this assumption be true?"

The ongoing "pay mortgage vs. invest" wars discussions tend to have two camps:
a) those who assume historical averages are good predictors of the most likely future results
b) those who aren't comfortable with "most likely" (or disagree completely with that prediction)

Neither "a" nor "b" can be proven correct, except in hindsight. Many members of camps "a" and "b" cannot understand the other position.
+1

This is the best explanation of the 'pay down debt or invest' discussion that I've seen.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

Topic Author
newberstiltskin
Posts: 2
Joined: Sun Jan 14, 2018 11:09 pm

### Re: Best way to pay off mortgage (considering investment returns)

FiveK wrote:
Mon Jan 15, 2018 1:22 am
Once you make this assumption (that your investment returns will be higher than the mortgage rate), any properly done analysis will show that investing beats paying the mortgage.
I was satisfied with this answer (Thanks FiveK), until I started thinking about the two replies below:
riverguy wrote:
Mon Jan 15, 2018 5:55 am
Why would you want to take stock market risk for a 2% spread? Seems silly.
Watty wrote:
Mon Jan 15, 2018 9:42 am
newberstiltskin wrote:
Sun Jan 14, 2018 11:23 pm
Option 3: \$100k down payment, \$2,147 mortgage payment, \$50k immediate mortgage payment, \$2,147 invested monthly for 7.2 yrs
This option makes no sense because a lot of the loan costs are based on the loan amount so you would be better with a \$150 downpayment and then just paying extra on the loan each month.
2% does not seem like a lot of equity risk premium. The answer would be obvious with a 0% mortgage or a 20% stock market return, but obviously as these two numbers come closer together, it starts getting more difficult. Option 3 effectively treats your mortgage like a guaranteed rate of return, doesn't it? It's the "pay off your house early" scenario.

So what's the usual equity risk premium on the stock market? It's gotta be more than 2%? All my googling shows equity risk premium based off something like treasury bills. Wouldn't paying off your mortgage be kind of equivalent to buying a 5% bond? (I guess one you can't sell)

FiveK
Posts: 6018
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Best way to pay off mortgage (considering investment returns)

newberstiltskin wrote:
Tue Jan 16, 2018 9:13 pm
2% does not seem like a lot of equity risk premium. The answer would be obvious with a 0% mortgage or a 20% stock market return, but obviously as these two numbers come closer together, it starts getting more difficult.
Indeed it does, and thus the discussions recur, because the equity risk premium is a subjective number.

One can reasonably say "because it's only a little more return from investing, I'll take the sure return from paying the debt."

Another can reasonably say "the extra return is the expected value - could be less, could be more - so the odds are in my favor to invest."