What is the magic pay down your mortgage rate?

[arebelspy]

Gotcha.  Something's off in that math for sure, looks like something got weird when they tried to overcomplicate it.

[frugaldrummer]

Seems to me, 2 crucial items keep getting left out of most of these analyses:

1) Taxes - if you're in a high tax bracket, the value of paying off a mortgage early may be less than it is for someone in a low tax bracket.  Essentially, if two people have the same mortgage but one person's income is so low that they pay 0% in income taxes, and the other person has a high income and gets a 35% tax break on the mortgage interest, the low-income person has a better benefit from paying the loan off early.  For a mortgage payment of $1,000 a month with 900 of that as interest, the low-income person pays $1,000, but the high-income person only pays $700 (because of their tax break).

2) Risk - many people are comparing pre-paying the mortgage versus investing in the stock market.  This is a false analogy as the risks are far different.  Pre-paying the mortgage is a low-risk, guaranteed rate of return.  If I prepay a 4% mortgage, I am guaranteed to save 4% interest.  The stock market can go up or down (historical averages notwithstanding, as past performance is no guarantee of future performance). The true comparison would be between the mortgage interest rate, and what you can currently get from safe fixed investments like high-grade bonds or CDs (or possibly one might include dividend paying stocks in super-safe giants like Disney, if you only counted dividend income and not stock appreciation). 

Also, I think everyone should at least try to pay down their mortgage to below 70% to protect them against the possibility of being trapped in a location by an underwater mortgage, unless you have enough assets already to ride out that scenario.  A lot of people suffered in the last downturn because they lost jobs and their stock investments dropped at the same time - their houses were underwater and they had to move to get a new job.  This financial meltdown could have been avoided by a paid-off home.

[DoNorth]

Put another way:

Original term   30 Years @ $100,000
Remaining   20 Years left when you begin extra principal payments
Annual interest rate   4%
Prepayment amount   $100 per month
Normal payment (PI)   $477
Accelerated payment (PI)   $577
Total scheduled payments   $171,868
Total accelerated payments   $162,545
Prepayment savings   $9,323
Prepayment shortens mortgage by   4 years, 9 months
Over 20 years; $24000 extra in principal reduction; $9323 in interest savings:  total $33,323

----------------------------------------------------------------------
simple compound interest example

Current Principal:   $   0
Annual Addition:   $   1200
Years to grow:       20
Interest Rate:       4 %
Compound interest   time(s) annually: 12

Total  $36799
--------------------------------------------

Although there may be some out there, it's difficult to find a 20 year period where the S&P returned less than 4% annualized with dividends reinvested.

[MDM]

Original term   30 Years @ $100,000
Remaining   20 Years left when you begin extra principal payments
Annual interest rate   4%
Prepayment amount   $100 per month
...
Prepayment shortens mortgage by   4 years, 9 months

After 303 months (4 yr 9 mo short of 30 years), with a final month payment of ~$166, the mortgage is fully paid.  There were 182 months with an extra $100 pre-pay.  Because the final month needed only a partial payment, there is $311 in the investment account.

If the $100/mo had instead been invested at 4%, after 303 months the mortgage balance would be $24,746.  After 182 months of $100 invested at beginning of the month, the investment account has grown to $25,057.

At which time the investment account could be used to pay off the mortgage, keeping......$311 in the investment account.

Again, taxes, liquidity, risk, peace of mind, etc. are all valid considerations - but on an "all other things being equal" comparison, pre-paying a mortgage at X% is identical to investing the prepayment amount at X%.

[Midwest]

Original term   30 Years @ $100,000
Remaining   20 Years left when you begin extra principal payments
Annual interest rate   4%
Prepayment amount   $100 per month
...
Prepayment shortens mortgage by   4 years, 9 months

After 303 months (4 yr 9 mo short of 30 years), with a final month payment of ~$166, the mortgage is fully paid.  There were 182 months with an extra $100 pre-pay.  Because the final month needed only a partial payment, there is $311 in the investment account.

If the $100/mo had instead been invested at 4%, after 303 months the mortgage balance would be $24,746.  After 182 months of $100 invested at beginning of the month, the investment account has grown to $25,057.

At which time the investment account could be used to pay off the mortgage, keeping......$311 in the investment account.

Again, taxes, liquidity, risk, peace of mind, etc. are all valid considerations - but on an "all other things being equal" comparison, pre-paying a mortgage at X% is identical to investing the prepayment amount at X%.

MDM - Thanks for doing the math.  4% is 4%. 

Donorth - I agree the S&P most certainly will return over 4% in time.  The S&P yield, however, involves substantially more risk than the mortgage.  Unless you believe you plan on defaulting on the loan (in which case you should pay as little as possible towards the mortgage principal), the yield on repaying the mortgage is risk free. 

You do need to calculate the after tax rate in making your decision, but repaying a mortgage can be part of a diversified portfolio in the right situation.  For instance, if you had a 800lk net worth, a home with zero equity and a 4% loan, $600k of stocks and $200k of savings bonds yielding 2% or same net worth, same stocks, $100k less on the mortgage and $100k in treasuries. 

In the second situation, if your after tax yield on the house is 3%, you are still a point ahead compared to the savings bonds. 

[southernhippie]

I feel that debt is debt no matter what it is in.  Yes mortgage rates are typically low, especially today. There is nothing more liberating than knowing that you own everything including your home outright.

[viper155]

If you did not have a mortgage would you go and borrow money against your house at 4% or under to invest with? I wouldn't, and it's the same thing

[Cheddar Stacker]

If you did not have a mortgage would you go and borrow money against your house at 4% or under to invest with? I wouldn't, and it's the same thing

I would. I'm not suggesting everyone should. But right now, if I were in that position at this stage in my life and at this net worth, hell yes I would.

Also, +1 to what MDM and Midwest just said. 4% has the same efect whether you are adding income or adding expense. I've been confused reading this thread throughout the day by how many people are trying to squeeze blood from a turnip here. If your calculations are telling you 4% prepayment beats 4% investment return, you did something wrong

[Spondulix]

If you did not have a mortgage would you go and borrow money against your house at 4% or under to invest with? I wouldn't, and it's the same thing

I would. I'm not suggesting everyone should. But right now, if I were in that position at this stage in my life and at this net worth, hell yes I would.

Also, +1 to what MDM and Midwest just said. 4% has the same efect whether you are adding income or adding expense. I've been confused reading this thread throughout the day by how many people are trying to squeeze blood from a turnip here. If your calculations are telling you 4% prepayment beats 4% investment return, you did something wrong

It's not about squeezing blood from a turnip - for me, I just want to see some proof in numbers. We don't make progress financially by just throwing numbers to the wind and hoping that vague answers to a vague question will get us where we need to go. I know that in all likelihood, compounding is always going to beat paying anything down (with time) - I wanted to see it backed up with some actual accounting.

[Guses]

I know that in all likelihood, compounding is always going to beat paying anything down (with time) - I wanted to see it backed up with some actual accounting.

That is wrong.

Compounding happens the same in both instances it's just that you don't see it because it's a debt that is paid off.

[DoNorth]

to clarify; I agree if you're talking about investing in a fixed rate investment like a CD or savings account that compounds on the same exact schedule as the mortgage amortizes , then the difference between the two decisions would be negligible. Too many other factors like taxes/loss of tax deduction, dividend reinvestment rate, home price appreciation or loss after mortgage payoff vs. investment appreciation or loss, the fact that mortgages are finite and investments are not still indicate there would likely still be some significant variation in the overall return from making one decision over the other; hence why I would still be skeptical to make an apples to apples 4% to 4% comparison in those terms.  I'm still thinking high 6% to 7% is probably a safe bet for making the decision to pay off.  I just made the last payment on a 5.75% note-- not because I thought it was a good investment, but more so because I wanted the predictability of expenses going into FIRE.


 

[GoldenStache]

Compounding happens the same in both instances it's just that you don't see it because it's a debt that is paid off.

Correct.  The difference between paying off early and investing is the rate of return. 
Many of the examples here are showing 4% and 4%.

My real numbers. 
2013 - Mortgage about 4%, Investment return about 27%
2014 - Mortgage about 4%, Investment return about 13%

[Cheddar Stacker]

It's not about squeezing blood from a turnip - for me, I just want to see some proof in numbers. We don't make progress financially by just throwing numbers to the wind and hoping that vague answers to a vague question will get us where we need to go. I know that in all likelihood, compounding is always going to beat paying anything down (with time) - I wanted to see it backed up with some actual accounting.

I don't mean people should ignore the numbers/accounting. Run them, just double and triple check. Compounding does not/can not beat debt pay down if the interest rate is equal (net of tax). It just doesn't work. It's the same end result.

[Midwest]

to clarify; I agree if you're talking about investing in a fixed rate investment like a CD or savings account that compounds on the same exact schedule as the mortgage amortizes , then the difference between the two decisions would be negligible. Too many other factors like taxes/loss of tax deduction, dividend reinvestment rate, home price appreciation or loss after mortgage payoff vs. investment appreciation or loss, the fact that mortgages are finite and investments are not still indicate there would likely still be some significant variation in the overall return from making one decision over the other; hence why I would still be skeptical to make an apples to apples 4% to 4% comparison in those terms.  I'm still thinking high 6% to 7% is probably a safe bet for making the decision to pay off.  I just made the last payment on a 5.75% note-- not because I thought it was a good investment, but more so because I wanted the predictability of expenses going into FIRE.

We agree that a) you can do better than 4% (although possibly with higher risk) and b) you need to calculate the after tax yield on both mortgage paydown and the investment in making a comparison.

With regard to home appreciation, why do you feel that is relevant to the decision to reduce a mortgage once you have purchased the home?  If your $300k house with a $200k mortgage is worth $200k or $1.0M, you still have a $200k mortgage that you are paying interest on. 

[DoNorth]

Because  I'm looking at the trade-off and it's fundamental to the way in which I invest my capital.  If I put the funds towards the mortgage and pay the mortgage off, then I have a fairly illiquid asset (hopefully an appreciating one) in which I can live and from which I can possibly leverage equity.  Maybe it's appreciating at 3% or maybe less.

Example--I just bought a home with a VA loan; 0 down; no equity to start with.  I bought the house two years ago at 3.375% at $395,000.  It is currently valued at $445K.  I simultaneously invested what I would have otherwise used to pay down the mortgage or put as a down payment and ended up with whatever the returns were for the next two years.  I should be able to either rent or sell the house at a profit.  The house was leveraged at over 100% due to a VA funding fee at purchase; now the leverage is somewhere around 88%.  It provides shelter, a tax deduction and the prospect of future profitability.  Makes no sense to prepay and tie up liquidity in something that's already doing the work for me.

In your example, if the house if worth $1M, then I would tap the equity at a lower rate (if one is available) and clear the mortgage (if a higher rate) or invest it and let it compound (hopefully).  For example, I just took a $25K credit card convenience check and exchanged the last $25K of a 5.75% mortgage for a 1.9% 12 month rate.  This allowed me to take $25K of my own money and max out 2-529's, an IRA, 401k, and my wive's solo 401k + drop the absurd insurance policy.  It would be hard to calculate the overall return over time of making this decision, but it should be favorable.

I have another house that I bought in 2009; 3.75%--same deal over 100% LTV; five years later, it's still underwater by a little, but steadily rented.  Appreciation prospects are average, so again I'm not going to pre-pay because i don't want to tie up my funds in something so illiquid.  I'll take the depreciation in taxes and unload it when I can sell at or above the mortgage.  in the meantime, rent covers PI&T.

I'm not saying everyone should do it, but  home appreciation prospects are something i always consider when determining whether or not to prepay.

[brooklynguy]

To everyone who is making the point that prepaying your mortgage offers a guaranteed return while investing funds in the market offers only uncertain returns:

Don't forget that if you are planning a stash-based MMM-style early retirement (which I assume is true of many of the folks reading and participating in this forum), your entire retirement strategy is already built on the assumption that market returns will greatly exceed today's low mortgage rates.  If your portfolio will not generate returns that vastly outperform your 4% mortgage over an extended time period, then your retirement strategy is doomed.  So why are you willing to accept this assumption about market returns for the fundamental purpose of planning your retirement, but not for the purpose of deciding whether to allocate funds towards investments rather than mortgage prepayment?

As some people have said, treating low-rate mortgage prepayments as equivalent to (and taking the place of an equal amount of) investments in the conservative portion of their portfolio allocation makes perfect sense and is a valid choice.  But do it consciously and realize that that's what you are doing.  If you had no mortgage and were deciding what to do with some available cash, would you stick it in a bank account paying interest equal to your mortgage rate instead of investing it in stocks?  Because that is equivalent to what you are doing when you prepay your mortgage.

[tomsang]

It is crazy to see people thinking that paying off a 30 year fixed rate mortgage at 3.5% is a good idea. In the last post on this I put together a spreadsheet that shows the math. The thing that people tend to overlook is that part of their mortgage payment is principal.


http://forum.mrmoneymustache.com/investor-alley/paying-off-mortgage-early-how-bad-is-it-for-your-fi-date/200/

[Tyler]

This topic comes up all the time. IMHO, two common over-simplifications trip people up.

First, the stock market may average 10% over thirty years but it does not make that every year. There have been many periods of ten to twenty years where it had a negative compound annual growth rate. That is usually preceded or followed by a very good period that helps things average out well, but the ride is not at all smooth.

Second, a 30-year mortgage does not always have a horizon of 30 years. Unless you refinance to a new 30-year mortgage every year (which would be stupid as fees would eat you alive), your loan will get shorter as you gradually pay it off.

As a result, the typical advice that you'll make more investing in the stock market over 30 years with a low-rate mortgage than buying a house in cash is solid. However, when you've owned for a while and only have ten years left on your mortgage, the profit from investing is much more of a crapshoot. With three years left, it's basically a coin flip.

So for most young people buying a house, it makes good financial sense these days to get a mortgage and invest the difference rather than to pay cash. However, it's important to revisit the decision every few years to see if your assumptions have changed. There will eventually come a time where it may make perfect sense to pay off the mortgage and move on to a new financial phase in life.

[mistershankly]

Another factor to throw into the mix is that a house is highly illiquid. Once you put money into the house, you can't get it out nearly as easily. By contrast, publicly-traded stocks can be liquidated at any time. That is another reason I am reluctant to prepay any loans, unless the interest rate is obscenely high.

You can set up a HELOC that will transfer to your checking account within seconds.  I think the main question is if you had your house paid off, would you borrow against it to invest in the stock market?  That is what someone is effectively doing in the question of paying off a mortgage vs investing.  It's a matter of risk tolerance and the scenario above (a Dave Ramsey coined scenario) places the risk tolerance factor into play.

I paid my house off because of my personal situation years ago (caring for an ill parent with unpredictable health care costs) and it suit my risk tolerance to have a house free and clear with what I was dealing with.  Now (parent passed away), I like the freedom of being able to quit my job at any time without the worry of the biggest debt hovering over me.  I have a HELOC open and ready in case I need to tap into the equity but every time I consider it, I compare the risk of debt I will take on to the purpose of taking it on.  If I were to take all of the equity out of my home and invest, I could FIRE in two years and that option is always on the table. 

There are many arguments for and against my approach and most are valid since it also has to do with risk tolerance in every individual's situation (i.e. it's not only about the math involved).

[arebelspy]

There have been many periods of ten to twenty years where it had a negative compound annual growth rate.

Uh, what?

Name those periods, please.

Make sure dividends are included, because obviously you can't own stocks over that period and decline receiving the dividends.

EDIT:
To save you time, there has NEVER been a period of twenty years with negative CAGR, let alone your claim of "many periods".  The worst 20-year period was a 2.5% return (nominal).

Source:
http://observationsandnotes.blogspot.com/2009/04/best-worst-20-years-in-stock-market.html

As for 10-year returns, 95% of them have been positive, with 5% (4 periods) negative.

Source:
https://www.franklintempleton.com/funds/2020vision/history-favors-long-term-investing

I'd hardly call that "many periods."  5 years is short term, yes.  1 year is absolutely short term.  But once you start talking decade(s), it's not a comparison.  Stock market does great.

(And the above are the WORST.. it's more likely you will be closer to the average than being worse than it's ever been.)

[Tyler]

Here's a link.  (warning -- PDF)

http://www.crestmontresearch.com/docs/Stock-Matrix-Tax-Exempt-Real3-11x17.pdf

Note that these are real returns.  If you only want to look at nominal, here's the link for that:

http://www.crestmontresearch.com/docs/Stock-Matrix-Tax-Exempt-Nominal4-11x17.pdf

I agree that using the words "many periods" doesn't apply to the nominal returns.  I was thinking of the real returns when I wrote that, but it's valid to prefer nominal returns when discussing mortgages (as your house payment doesn't increase with inflation).  Still, stocks did go negative on an annualized basis for as long as a decade as recently as the 00's.  It does happen.  The great depression sucked the life out of stocks for two decades.  And there was a cold spot throughout the 60s where any mortgage at more than 5% interest didn't look so hot for a long while (average rates were around 6% at the time).

FWIW, I'm not arguing that stocks are a bad investment.  Just that when discussing mortgages, one should not always look at 30-year average returns when you have less than that left on your mortgage.  Stocks do have downswings, and your forward-looking risk depends a lot on your remaining timeframe. 

[tomsang]

Just to be clear. When talking about investing vs paying down your mortgage you should be talking about nominal returns not inflation adjusted or real returns. Your fixed rate 30 year mortgage eliminates any inflation issues. In fact the greater the inflation the better off you are having a fixed rate loan. Since tracking investment returns within the United States there has never been a time where the market has returned less than 5% over a 30 year period. The SWR and the shockingly simple math calculations are using 5%+ because there have never been times where the market has not achieved greater than 5%+ over these long periods. If you believe that the future is going to be different and that the market will return less than your mortgage rate at 3.5% then you should not retire until your SWR is 1%. If you think the world is going to spiral downward you should not own a house or other longterm investments. You would be better off renting as the rents would decrease with time if you think that the markets are going to crash.

[boarder42]

^^^ oh thats just great.  I love the last sentence. 

Fear mongering apocalypse.  If you believe the market will crash and we will go into a great depression you should be investing nothing. 

In the end though this is all about risk.  And i'm at the super risky end of that spectrum.  So its hard for me to understand anyone prepaying a sub 5% mortgage.  And to those with 3 or below thats just asinine.  Due to inflation.  but to each his own i guess.  i'll bet on the 95% odds 100% of the time. 

Anyone have time to show how many years someone loses from being retired if they pay off their mortgage vs invest at standard market rates.  Assuming Avg annual spending of 30k (this seems to be pretty middle of the road for most here)  and a SWR of 3.8%, the avg mortgage of 170k lets assume no PMI and 4% on a 20 year, and an avg salary of 65k. 

[boarder42]

if someone wants to modify those numbers to real avg's i'm cool with that but i thought those were pretty decent ballpark numbers

[Spondulix]

I know that in all likelihood, compounding is always going to beat paying anything down (with time) - I wanted to see it backed up with some actual accounting.

That is wrong.

Compounding happens the same in both instances it's just that you don't see it because it's a debt that is paid off.

This makes no sense - how is a payment towards a debt compounding? Are you referring to the actual debt that's compounding, or the equity you have in your home?

[MDM]

I know that in all likelihood, compounding is always going to beat paying anything down (with time) - I wanted to see it backed up with some actual accounting.

That is wrong.
Compounding happens the same in both instances it's just that you don't see it because it's a debt that is paid off.

This makes no sense - how is a payment towards a debt compounding? Are you referring to the actual debt that's compounding, or the equity you have in your home?

May be a semantic issue regarding "compounding happens."  I might say that pre-paying a debt "prevents" compounding from happening on the portion I prepay.  The issue of paying an X% debt vs. investing at that same X%, however, is unambiguous: the effect on your net worth is identical.

The worked examples above don't seem to have been persuasive.  Let's try a thought experiment instead. 

Say you owe a debt to person A who is charging you 5% on that debt.  Person B wants to borrow money from you and offers to pay you 5%.  You have some extra money. 

Q1. Should you loan the money to B while paying A at the same rate, or should you use the extra money to pay A?
Q2. What if A is charging 6% while B offers to pay you 4%?
Q3. What if A is charging 4% while B offers to pay you 6%?

A1.  It doesn't matter - the effects are identical
A2.  Paying A is better
A3.  Loaning to B is better

Note that "loan the money to B" is the same as "invest the money in a stock index fund." 

Does it makes sense that, everything else being equal, paying a mortgage at X% is of identical value to investing in something paying the same X%?

[Spondulix]

May be a semantic issue regarding "compounding happens."  I might say that pre-paying a debt "prevents" compounding from happening on the portion I prepay.  The issue of paying an X% debt vs. investing at that same X%, however, is unambiguous: the effect on your net worth is identical.

The worked examples above don't seem to have been persuasive.  Let's try a thought experiment instead. 

Say you owe a debt to person A who is charging you 5% on that debt.  Person B wants to borrow money from you and offers to pay you 5%.  You have some extra money. 

Q1. Should you loan the money to B while paying A at the same rate, or should you use the extra money to pay A?
Q2. What if A is charging 6% while B offers to pay you 4%?
Q3. What if A is charging 4% while B offers to pay you 6%?

A1.  It doesn't matter - the effects are identical
A2.  Paying A is better
A3.  Loaning to B is better

Note that "loan the money to B" is the same as "invest the money in a stock index fund." 

Does it makes sense that, everything else being equal, paying a mortgage at X% is of identical value to investing in something paying the same X%?

Thank you for clarifying, and I totally understand your point, but there's a flaw in the example. Person B would be paying back with different rules than Person A. Person A only pays interest on his balance; Person B would be making paying interest on the balance, PLUS making an interest payment on the interest they had already paid you. Using those rules, Person B would be the one you'd want to loan to in all three examples (especially if you have time).

That's why I keep saying it's not a matter of comparing interest rates, because the rules don't work the same when you're paying down mortgage vs investing in an index fund (assuming you are leaving the balance in to compound). The answer to the question is completely dependent on the time frame you're looking at.

[Peacefulwarrior]

I would pay it off even if it was at 1%. Becoming FI is about mindset not solely about math, and being in any kind of debt is not part of a good mindset.

[MDM]

Thank you for clarifying, and I totally understand your point, but there's a flaw in the example. Person B would be paying back with different rules than Person A.

Not true: same rules of compound interest apply.

Person A only pays interest on his balance; Person B would be making paying interest on the balance, PLUS making an interest payment on the interest they had already paid you.

This actually is true.  Except you are paying person A, not A paying you, but I think I understand what you are trying to say.  But you seem to drawing incorrect conclusions from these facts.  Yes, when you pay a mortgage you pay interest only on the remaining principal - but your payment is calculated based on the compound interest formula.  See http://en.wikipedia.org/wiki/Amortization_calculator if you aren't familiar with the derivation.

Using those rules, Person B would be the one you'd want to loan to in all three examples (especially if you have time).

If you think so, I'll be happy to loan you money at 6% and you can loan back to my kids' college fund at 4%.  The more the merrier. :)

That's why I keep saying it's not a matter of comparing interest rates, because the rules don't work the same when you're paying down mortgage vs investing in an index fund (assuming you are leaving the balance in to compound).

The rules of compound interest work exactly the same when you are paying a mortgage vs. investing in an index fund.  That's why the numerical answers match in the worked examples in previous posts.  E.g. see http://forum.mrmoneymustache.com/ask-a-mustachian/what-is-the-magic-pay-down-your-mortgage-rate/msg509347/#msg509347: it's not a coincidence that paying vs. investing leads to an identical result.

[train_writer]

One big assumption here from the not-paying-off? 100 % discipline and determination of investing exactly the same amount as the amount one would be paying off.

Yes, the math tells you how it adds up in a perfect world, but it ain't..

If you commit yourself to say 250 euros per month extra payment to the principal, how can you know you would be as determined in investing? Personally, I have committed myself to a semi-annual principal payment and at the same time to a monthly investment of 400 euros in index funds. It is only guestimation, but I suspect I would not invest the surplus of not-paying-off in stocks/ index.

[tomsang]

I would pay it off even if it was at 1%. Becoming FI is about mindset not solely about math, and being in any kind of debt is not part of a good mindset.

Wow. Math is what defines when you are FI. Your actions could be causing you to pull a huge anchor to the finish line. If you can borrow at sub 4% and invest at greater than 7%, then surely you can see that you are screwing over your future self by paying down a 1% or even a 4% 30 year fixed rate mortgage.

I think Mustachian is about making logical choices, not buying consumeristic trinkets and not making bad financial decisions.  With your mindset you would put zero in your 401k and not invest in after tax investments until all of your debt was paid off. This would cost you years to FI with the loss of tax benefits for the 401k and mortgage and the lost returns on your investments exceeding today's low mortgage rates.

Would you invest in businesses with debt?  You are a business. If used properly debt is a wonderful thing.

You will get there with your method, but it will take significantly longer. Interesting perspective.

[Peacefulwarrior]

I would pay it off even if it was at 1%. Becoming FI is about mindset not solely about math, and being in any kind of debt is not part of a good mindset.

Wow. Math is what defines when you are FI. Your actions could be causing you to pull a huge anchor to the finish line. If you can borrow at sub 4% and invest at greater than 7%, then surely you can see that you are screwing over your future self by paying down a 1% or even a 4% 30 year fixed rate mortgage.

I think Mustachian is about making logical choices, not buying consumeristic trinkets and not making bad financial decisions.  With your mindset you would put zero in your 401k and not invest in after tax investments until all of your debt was paid off. This would cost you years to FI with the loss of tax benefits for the 401k and mortgage and the lost returns on your investments exceeding today's low mortgage rates.

Would you invest in businesses with debt?  You are a business. If used properly debt is a wonderful thing.

You will get there with your method, but it will take significantly longer. Interesting perspective.

If investering instead of having a paid off house is such a good idea, would you recommend everybody to borrow against house equity as much as possible and spend the money on investments?

And no, with my mindset I wouldn't do that. Because I wouldn't have a mortgage in the first place. I don't borrow money.

I'm not saying that "your" model is stupid or anything. It's just not how I do things myself.

[Tyler]

Rather than continuing to argue about theory, here's my testimony. I'd love for others to share their own.

I'm currently FI and have enough saved up to own a house with no mortgage and still have enough invested to support my conservative 3% SWR. Like MMM, I've chosen to pay off the mortgage (my last remaining debt) and enjoy the fruits of the good decisions that got me here rather than continue chasing additional money in the markets I really don't need. I'm very satisfied with my financial decisions to date, and have zero interest in mortgage debt anymore.

I've had two mortgages in the past, spanning about eight years of my fifteen year career. In retrospect, investing the difference in the stock market really made very little progress towards my goal. I basically broke even. If it took me thirty years to retire that would have been a much different story and my investments would have most likely kicked in. But my retirement timetable couldn't wait thirty years. ;).

Referencing the "shockingly simple math" graph, my income from investing my mortgage balance was pretty much dwarfed by my aggressive saving. This certainly has influenced my views on the whole mortgage/payoff debate, and may not apply to everyone. YMMV. I have no problem at all with anyone who looks at their own plans and decides that a mortgage is a great financial decision. In many cases, it is!

[bacchi]

If you believe that the future is going to be different and that the market will return less than your mortgage rate at 3.5% then you should not retire until your SWR is 1%.

This is the really the only thing that needs to be written.

[Spondulix]

That's why I keep saying it's not a matter of comparing interest rates, because the rules don't work the same when you're paying down mortgage vs investing in an index fund (assuming you are leaving the balance in to compound).

The rules of compound interest work exactly the same when you are paying a mortgage vs. investing in an index fund.  That's why the numerical answers match in the worked examples in previous posts.  E.g. see http://forum.mrmoneymustache.com/ask-a-mustachian/what-is-the-magic-pay-down-your-mortgage-rate/msg509347/#msg509347: it's not a coincidence that paying vs. investing leads to an identical result.

Thanks for sticking with me to explain that - now I get it, and see that you're totally right. I think I've been confused about how debt compounds (and I still don't entirely understand it - it totally works by your math above, but it doesn't look how I'd expect when you graph a curve of payoff over time). The amount your investment goes up is not the same amount that the loan goes down by (at the same interest rate). It appears as though the earnings are increasing at a faster rate than loan balances are decreasing, but obviously that must not be the case.

[rmendpara]

Obviously there is lot's of back and forth on whether to pay down a mortgage or instead invest those assets at what will hopefully be a higher after tax return.  My question is, what do most people feel is the magic number (mortgage rate) that would justify paying down the mortgage vice investing the money elsewhere?

10 yr treasury rate + 150 bps.... I would pay the minimum

10 yr treasury rate + 350 bps.... I would pay something toward paying it down

in between 150 and 350 bps... it's up to you

Of course other factors are important as well. Your overall risk tolerance and portfolio expected returns, the lost opportunity of whatever you would invest in otherwise, the $ amounts of the mortgage relative to your investments and income, etc, could all contribute to whether and how much it makes sense to pay down a mortgage.

[MDM]

...it doesn't look how I'd expect when you graph a curve of payoff over time). The amount your investment goes up is not the same amount that the loan goes down by (at the same interest rate). It appears as though the earnings are increasing at a faster rate than loan balances are decreasing, but obviously that must not be the case.

Yeah, definitely not straightforward at all.  One doesn't need to know all the gory details of Future Value, loan payment calculations, etc., just as one doesn't need to know the inner workings of each company to make money with a total stock market index fund.  But it the right situation it can be helpful.

Not all that long ago I couldn't have explained this.  One reason (among several) this forum is useful is because "you never learn something as well as when you try to teach it."  If it interests you, stick with it and you can learn much from others here - we all can and do, at least when we keep our ears/eyes wide open and restrain our mouth/fingers. ;)

One thing about loan payments: only the principal amount "counts as an investment."  Think of an interest-only loan: you would make payments forever, but never "earn" (i.e., decrease the principal) anything.  In a real loan the early regular payments go overwhelmingly to interest so the "amount invested" (the principal payment) is low.  But when we talk about pre-paying the principal, that is 100% "investment."  Does that help?

[Spondulix]

MDM For some odd reason I find all the inner working really fascinating right now. :) I've been paying my mortgage with the amortization schedule for years (using that to calculate extra principal payments, follow how it's shortening the loan, etc.) What I don't quite understand is if there's a benefit to paying a loan vs investing (if the interest rates are the same) but the balances are significantly different. You've been saying there's not, right?

[MDM]

MDM For some odd reason I find all the inner working really fascinating right now. :) I've been paying my mortgage with the amortization schedule for years (using that to calculate extra principal payments, follow how it's shortening the loan, etc.) What I don't quite understand is if there's a benefit to paying a loan vs investing (if the interest rates are the same) but the balances are significantly different. You've been saying there's not, right?

Right - assuming (as we have been) that all other things (tax treatment, etc.) are equal.

There has to be some combination of loan interest vs. investment return that makes the choice equal to you, correct?  Here the answer happens to be the "obvious" one: when the interest rates are equal.

You can force the balances to be equal by dividing either the loan or the investment (whichever is larger) into two pieces.  Let's say you split your investment into two pieces, one equal to your loan balance and the other holding the remainder.  The performance of the remainder is irrelevant, correct?
If you are getting 5%, the applicable algebraic identity is  (A + B) * 1.05^n = A * 1.05^n + B * 1.05^n.   Thus the total balance has no effect on the comparison.

[Jags4186]

Would it ever make sense to treat your mortgage as a bond allocation and to pay it down in accordance to your chosen asset allocation?  If you keep say an 80/20 equity/bond portfolio, and say you choose to hold BND for you bond holdings, why would you invest money at a 2.75% yield when you can get a guaranteed return on additional mortgage payments of 3.5%-5%?

[TheNewNormal2015]

The rate cannot be the only factor in determining whether to pay down a mortgage, be it with either periodic payments or a lump sum.

The risk of financial ruin also has to be taken into account, and that % chance of ruin increases disproportionately with the size of the debt as a % of income to service the debt.

The propensity to pay down debt vs (hopefully) investing at a spread (based on historical returns) should dramatically increase the closer one gets to the FIRE date and also with age.  This decision has to be different for someone who is 65 vs 25yo.

Additionally one should take into account whether the investment alternative to paying down the mortgage already has a significantly large allocation in one's portfolio, as well as how the it became so large (recent appreciation vs recent large lump sum investment vs steady investments over a long period of time).  If your portfolio is already heavily invested in stocks, you are simply concentrating your risk even further in investing extra principal instead of paying down the debt.  And, I would argue, that concentrating risk in an asset class that has recently had a bigger than normal appreciation OR in an asset where you have recently invested a large sum increases your propensity to act emotionally and make a mistake if markets were to fall sharply.  And yes I believe financial markets mean revert in the long run.

Lastly, a lot of ppl (myself included) are very close to FIRE due to the recent strength of the stock markets.  You only need to get rich once.  In my opinion there is no reason to take chances when 1) the finish line is in sight and 2) I am in this position BECAUSE OF the recent larger than normal gains from the markets.  Historical averages are great to use in setting a general asset allocation, but I think it would be foolish not to consider the fact that markets tend to mean revert over time and the prospective returns investing today are not the same as even 5 years ago.  Does this matter if your time horizon to retirement is 20 or 30 years?  No - but it certainly does if it is you are looking to FIRE in the next 5. 

[NICE!]

In retrospect, investing the difference in the stock market really made very little progress towards my goal.

This is an excellent point I haven't seen discussed much on these forums.

I plan for my working career to be 6-8 years total. With that kind of timeframe, investment gains during your working career are, on average, unlikely to affect your time to retirement compared to just using a 1% savings account. If you get lucky, investment gains might shave some time off, but it could also be the opposite. The expected value is basically a wash, unless you choose very aggressive investments (for example, highly leveraged real estate).

However, it's not just the accumulation phase where investments matter. You also need to support yourself for the rest of your life and that will definitely require real investments, not a savings account. And that's where the 30 year timeframe on these mortgages is very useful, because the mortgage can far outlast your working career and continue to provide additional money during your retirement.

Cathy/Tyler, I think that this is a good point for extremely aggressive savers. Yes, it isn't discussed here but it is certainly discussed over at ERE. During the accumulation phase, Jacob's model was 100% based upon saving and not investing. In fact, I think he did have his money in savings, CDs, or something along those lines before he went heavily into equities/dividend investing. Jacob retired 5 years into his working career.

MMM covers this in the Shockingly Simple post. 80+% savings rate net you a working career of 5 or less years. In that timeframe you could have a great market, like 2009-2014. That would certainly cut your working career a decent bit. Alternatively, you could have 2003-2008 and not be able to retire right after the crash.

I'd say that this means people with extremely high savings rates need to change their strategy, but unfortunately they have to make their money last in perpetuity like the rest of us. As such, I think they still need to be heavy in equities.

Jacob said something pretty astute in his post on savings rates:
"Therefore you gotta ask yourself a question: How much of your retirement strategy is based on things, like your savings rate, which you can control, and how much of your strategy is based on things, like the future return and inflation rates, which nobody know and which are out of your control?"
Source: http://earlyretirementextreme.com/what-should-my-savings-rate-b.html

[newnewman]

+ to what Astatine said.

I'm in Canada, and our situation is different here too. No tax benefit from the mortgage, and we can't lock in a rate for 30 years. Instead, everyone renews their mortgages at the new balance at the end of the mortgage term, 1-7 years. The longest fixed rate terms are around 7 years, and the rates are higher for the peace of mind of having such a long term.

We are maxing out our retirement savings and only carry mortgage debt, so even though our rate is low now, we are paying fairly aggressively, and hope to be done with our mortgage at 12-13 years after we bought our home (we'll be just over 40). From a pure investing and opportunity cost perspective, sure we could do better investing our extra principal but we'd have to learn a lot more than we know today about investing, and we're pretty financially conservative. It works for us.

Also Canadian here and agreeing with you. We are still working on paying off two lines of credit (yes- embarassing!) but after that our plan is to max RRSP/TFS and tackle the mortgage. We aren't knowledgeable about investing. Perhaps I will learn a thing or two from all of you on this board. So happy to have discovered MMM yesterday!!!

[Cheddar Stacker]

We aren't knowledgeable about investing. Perhaps I will learn a thing or two from all of you on this board. So happy to have discovered MMM yesterday!!!

Welcome to the party. There's a lot to learn around here.

[Spondulix]

The risk of financial ruin also has to be taken into account, and that % chance of ruin increases disproportionately with the size of the debt as a % of income to service the debt.

I just ran across an article the other day that explains this exact concept (using mortgages as an example) - I wasn't familiar with it before. For anyone interested, start reading page 11, "Example of why debt adds risk to equity" (warning pdf)
http://wpui.wisc.edu/docs/effect_of_debt.pdf

[Kyle Schuant]

We always pay down, no matter what. Unless the rate is fixed for the entire 20-30 year term of your loan, you never know what the interest rate might be in a few years. In my lifetime I've seen it as high as 17%. By paying less we'd be gambling on the long-term stability of the economy. Recent history shows this is not a good gamble.

[Astatine]

We always pay down, no matter what. Unless the rate is fixed for the entire 20-30 year term of your loan, you never know what the interest rate might be in a few years. In my lifetime I've seen it as high as 17%. By paying less we'd be gambling on the long-term stability of the economy. Recent history shows this is not a good gamble.

The more posts and threads I read on here discussing paying off mortgages vs investing, the more I think the threads should be country-specific. US seems to have low interest rates (at the moment) and fixed interest rates, and very different tax rules. The arguments about not paying off the mortgage fast seem to be based entirely on those assumptions, and don't seem to ever reference the risk of variable interest rates, or the fact the primary residences in Australia, for eg, don't have tax deductions. So may be all of these threads should be "pay down mortgage or not? US" or "pay down mortgage or not? Australia" and so on. 

[Kyle Schuant]

I said that over the 20-30 year period of a mortgage, rates might go very high. This is not particular to Australia.

[MDM]

I said that over the 20-30 year period of a mortgage, rates might go very high. This is not particular to Australia.

Kyle, in the US once you have a 30 year (or whatever length) mortgage the rate for your mortgage never changes.  Unless it is an Adjustable Rate Mortgage, but conventional mortgages are at a fixed rate for the mortgage term.

[Lmoot]

Personally I'd say if you can pay it off in less than 5 years, I'd be more inclined to do that. THEN after that you can invest if you'd like, without worrying if you missed out too much.