Author Topic: Trying to calculate the benefit of paying off the mortgage...  (Read 13331 times)

bo_knows

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Trying to calculate the benefit of paying off the mortgage...
« on: January 03, 2013, 02:53:59 PM »
So, the general thought that floats around a lot of finance forums (including this one) is that if you expect to make a higher percentage return in the market than the percentage of your mortgage, that you should not put any extra money toward your mortgage.

Generally, I have been following this principle, but am about to refi our mortgage and starting to have my doubts.  Can someone help me with the math here?

$285k mortgage, $380ish value home.
Refi @ 3.25% over 30 years.
Minimum Payment: $1240/mo.


Assumptions
If we cut our Roth IRA contribution to zero, cut our 401k contributions down to whatever our company match was, and counted up the general extra money we have, we would have ~$2500-3000/mo.  I'll stick with $2500 for this example.
I'll assume a rate of return on potential market gains as 7%

Maths
Paying the minimum payment on the mortgage for 30 years will net $161521 in interest.  If, during that time, we invested the $2500/mo "extra" in the market (ignoring pre-tax investments for simplicity), we could make a return of $67,794 (I used yearly compounding) in 7 years.

However, if instead we dumped that $2500/mo into our mortgage, our mortgage would be paid off in 2020 (7 years), and the total interest payment on that would be $34,637... meaning that our $2500/mo "investment" netted us $161,521 (original interest payment) - $34,637 (newer interest payment) = $126,884 savings.

So, Scenario 1, investing all the extra money, nets $67,794 in profit.  Scenario 2, dumping it into the mortgage, nets $126,884 in profit over the existing situation.


I know that mortgage interest deductions and market flucuations all make this a more difficult exact answer, but it seems that the common advice doesn't hold water here.  Is this because it's a larger mortgage principal in comparison to our "extra" income?  I'm not sure where to go from here.

Self-employed-swami

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #1 on: January 03, 2013, 03:01:14 PM »
I struggle with the same issue.  I have been doubling up my mortgage payments (2.99% interest for another 3 years) while also putting $$$ into my RRSP (Canadian 401K).  And just to cover the spread, I borrowed $65,000 from my HELOC for investments, and I can use that interest as a deduction.

bo_knows

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #2 on: January 03, 2013, 03:09:08 PM »
I guess when you start pushing out the timeline to 20 and 30 years, of what that 7yr headstart of investing in the market gives you, you start to come out ahead over the mortgage payment... But that's if 7% return holds true. 5% return makes them just about even scenarios at 30yrs, and the early mortgage payoff edges out the other scenario at 20 years.

Sigh.  Decisions, decisions.

Khao

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #3 on: January 03, 2013, 03:17:55 PM »
I think the correct way to think of this is to calculate vs the original length : 30 years. Why? Because your interest saved calculations take into consideration all the interest you would have payed in the next 23 years so to make a real comparison you should calculate your investments for 30 years

Compare :
 - 2,5k per month for 30 years at 7% = ~2mil earned
vs.
 - interests saved by paying your mortgage early (126,884 in your case) + 2,5k per month for 23 years at 7% = ~1,1mil earned
(another option)
 - interests saved by paying your mortgage early (126,884) + 3,7k per month for 23 years at 7% = ~1,4 mil earned

3,7k comes from your extra 2,5k per month and your minimum mortgage payment 1,2k that is now cleared and which is a sum you could put towards saving

My calculations were done really roughly but I still think paying the mortgage off is clearly NOT the best option as it only yields 3,25%

Edit: Another thing to consider which is purely a matter of preferences : By putting all of your extra money in a mortgage, you have zero liquidity. If something huge comes up in your life your have to either : refinance, use a HELOC or sell the house. By investing, you always have access to that money. What if in 5 years you see a nice duplex for sale and you want to purchase it to rent it out? By putting all of your extra in your mortgage this option is not as easy.
« Last Edit: January 03, 2013, 03:21:48 PM by Khao »

Lagom

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #4 on: January 03, 2013, 03:20:03 PM »
Oops, accidentally deleted my post when trying to edit. Anyway, I had never considered things the way you put them here, but it does make sense given that mortgages are usually front-loaded with interest payments, meaning you will generate a far higher ROI than the loan interest rate would initially imply.  Very interesting to think about!

Of course, as you note, things like tax deductions and the value of real estate make the exact numbers harder to calculate, but it seems to me, that if you can afford to significantly accelerate mortgage payments (say by at least $1000/month), and you are still in the early stages of a 30 year loan, it may in fact be the wisest move to do that instead of investing in the stock market. Unless Iím missing something obviousÖ
« Last Edit: January 03, 2013, 03:23:54 PM by Lagom »

Lagom

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #5 on: January 03, 2013, 03:23:30 PM »
Ah, good points, Khao. That puts it in perspective. I knew it seemed a little too good to be true...

tooqk4u22

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #6 on: January 03, 2013, 03:25:07 PM »
I guess when you start pushing out the timeline to 20 and 30 years, of what that 7yr headstart of investing in the market gives you, you start to come out ahead over the mortgage payment... But that's if 7% return holds true. 5% return makes them just about even scenarios at 30yrs, and the early mortgage payoff edges out the other scenario at 20 years.

Sigh.  Decisions, decisions.

This is what your math is missing....you need to match the terms. You are comparing 30 years of mortgage interest against 7 years of investment returns. 

Matt K

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #7 on: January 03, 2013, 03:27:50 PM »
The idea is right, but the numbers are off because you are saying "In seven years I'll pay off my mortgage saving me $126k that would have accumulated over 30 years." But in your investment scenario you are saying: "At the end of 30 years, I will have a return of $67k". To make it a true apples to apples comparison you need to then let that investment sit (without additional funds) for another 23 years, and then see what number it gives you.

MMM talked about this in an article, it's a win-win situation. Either you bank a tonne of cash, or you pay off your house, either way, you win.

Right now I'm very early in my mortgage, so if I pay an extra 1/3rd of a month's payment, it reduces the amount of time I have the mortgage by one month (yes, my payment is 2/3 interest 1/3 principle). Personally I find that very rewarding. But then, I also like seeing my RRSP account jump up due to nice dividend payments, so I do that too. I've done the math, and going whole hog into either investing or house would result in FI faster, but sometimes the feelings of progress and accomplishment are worth more than the mathematically perfect solution. Besides, I consider it diversification.

tooqk4u22

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #8 on: January 03, 2013, 03:31:34 PM »
My calculations were done really roughly but I still think paying the mortgage off is clearly NOT the best option as it only yields 3,25%

Edit: Another thing to consider which is purely a matter of preferences : By putting all of your extra money in a mortgage, you have zero liquidity. If something huge comes up in your life your have to either : refinance, use a HELOC or sell the house. By investing, you always have access to that money. What if in 5 years you see a nice duplex for sale and you want to purchase it to rent it out? By putting all of your extra in your mortgage this option is not as easy.

These two things....paying off your mortgage at these low rates will never make sense from a financial perspect unless you think we are going to be in a deflationary environment.  And liquidity and diversification matters. 

That said I have been paying off my mortgage and have a HELOC for liquidity.....it kills me to do this but I have investments, too much cash, and really don't like where the market is right now and rental properties (which is really what I want) don't pencil out better than a 4-5% cash on cash return in my area (and that is not worth the effort).

Bottom line is when paying off your mortgage for your personal residence it is usually an emotional choice more so than a financial one.  I would never pay off a rental though.


Lagom

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #9 on: January 03, 2013, 03:32:03 PM »
All of this begs another question regarding what is the optimal path for reaching early retirement ASAP. Obviously, eliminating a mortgage drastically reduces living expenses, so depending on your retirement income goal, is it really always suboptimal to pay the mortgage first? If I want to retire in 10 years, then a 30 year horizon for investment returns matters much less. Am I off base? If not, does anyone have a good rule of thumb for figuring out how much should go towards paying the mortgage early?
« Last Edit: January 03, 2013, 03:34:41 PM by Lagom »

Richard3

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #10 on: January 03, 2013, 03:34:42 PM »
Oops, accidentally deleted my post when trying to edit. Anyway, I had never considered things the way you put them here, but it does make sense given that mortgages are usually front-loaded with interest payments, meaning you will generate a far higher ROI than the loan interest rate would initially imply.  Very interesting to think about!
Of course, as you note, things like tax deductions and the value of real estate make the exact numbers harder to calculate, but it seems to me, that if you can afford to significantly accelerate mortgage payments (say by at least $1000/month), and you are still in the early stages of a 30 year loan, it may in fact be the wisest move to do that instead of investing in the stock market. Unless Iím missing something obviousÖ

You are missing something obvious:

Mortgages are not "front loaded" with interest payments. The interest is a percentage of the outstanding balance. This is the same whether the balance is $1,000,000 or $10,000. A higher percentage of early payments are interest because the outstanding balance is higher and people tend to choose a fixed payment amounts over the life of the mortgage. It would equally be possible to structure repayments so you always paid the interest plus $100 - this way the payments would get smaller and smaller as the mortgage declined.

You are not going to magically generate a higher ROI by making an extra payment earlier in the life of a mortgage. If you pay off $10,000 from a mortgage at 7% you save $700 of interest payments a year. If you buy a $10,000 bond (or share or whatever) that pays 7% you will get $700 a year. The effect is identical.

What I think you've done is only apply the benefits of compounding to the mortgage option in your head and not to the investing option.

Whether or not to pay off a mortgage early (actually whether or not to devote this $X to mortgage or investing) depends on your rate, whether interest payments are tax deductible, and what your alternative investment would return.

tooqk4u22

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #11 on: January 03, 2013, 03:37:09 PM »
All of this begs another question regarding what is the optimal path for reaching early retirement ASAP. Obviously, eliminating a mortgage drastically reduces living expenses, so depending on your retirement income goal, is it always suboptimal to pay the mortgage first? If I want to retire in 10 years, then a 30 year horizon for investment returns matters much less. Am I off base? If not, does anyone have a good rule of thumb for figuring out how much should go towards paying the mortgage early?

Somewhat but remember that if you are in a position to pay off the mortgage and you keep it you will then have those proceeds invested to support your mortgage payment given where rates are today.  If they go back to 5-7% then paying off would be better. 

Mola

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #12 on: January 04, 2013, 10:41:22 PM »
I pondered this myself and eventually answered it for myself with an elaborate spreadsheet.  As Khao and others pointed out you need to compare the same time frames.  But that timeframe doesnt have to be 30 years.

Think of it in terms of net worth.  You have a net worth of 95k in that house today (380 value - 285 loan).  You can either increase your net worth by paying down that loan faster or by investing that money.  You can make that comparison for a 30 year time period, a 7 year time period, or a 1 month time period.

But in any period if you have a 3.25% loan but assume an investment return of 7% than you will ALWAYS be better off investing.  Because what you're basically doing is arbitrage.  If I offered you $280k at 3.25% interest and you could turn around and loan that to someone else (say to vanguard) at 7% interest you would always profit.

The real question is do you want a GUARANTEED return of 3.25%, or an assumed return of 7%.  Over 30 years I would take the 7%.  Over a only a year or two I would take the 3.25%.  So it depends on your timeframe and risk tolerance.

Tyler

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #13 on: January 05, 2013, 01:06:34 PM »

The numerical answer: 

The spreadsheet will tell you that if you average 3.5% over your interest rate over 30 years and are always saving money rather than drawing down, then you'll make more money with a mortgage.


The life answer:

Do you really plan on working 30 more years?  In years when your investments lose money in retirement (it will absolutely happen), you'll wish that house was paid off.

The best answer may be somewhere in between: Play offense with a mortgage while accumulating money and then play defense by paying it off when you make "enough" and elect to retire from full time work.

arebelspy

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #14 on: January 05, 2013, 01:41:14 PM »
In years when your investments lose money in retirement (it will absolutely happen), you'll wish that house was paid off.

I'd rather have a huge chunk liquid in tough times than trapped equity.

Not to mention a loan at 3-4% when inflation hits is amazing.
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Tyler

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #15 on: January 05, 2013, 08:51:50 PM »
Fair enough.  Everyone's situation is different.  And to be honest, those with the real option of paying a mortgage in cash are probably already pretty good with money, and those who prefer to get a mortgage in order to invest wisely are also smarter than average with finances.  Both will be fine compared to the typical debt-laden consumer.

This article comes down on the "pay off the house" side.  I found it pretty interesting and it has some points I haven't seen elsewhere. 

http://www.mint.com/blog/investing/paying-down-your-mortgage-vs-investing-more-112011/
« Last Edit: January 05, 2013, 08:56:18 PM by Tyler »

GoStumpy

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #16 on: January 05, 2013, 09:17:13 PM »
Question:  Do these calculations include the fact that once the mortgage is paid off early, the extra payments from the mortgage can also be put towards investing? 

If one puts $1500/mo towards a mortgage for 30 years, and $2000/mo towards investments..

What if the $3500/mo went to the mortgage, paid it off, and then $3500/mo went towards investments?

Can't do the math, sorry :(

arebelspy

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #17 on: January 05, 2013, 10:50:29 PM »
Yes.
We are two former teachers who accumulated a bunch of real estate, retired at 29, and now travel the world full time with two kids.
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sherr

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #18 on: January 05, 2013, 11:18:47 PM »
Question:  Do these calculations include the fact that once the mortgage is paid off early, the extra payments from the mortgage can also be put towards investing? 

If one puts $1500/mo towards a mortgage for 30 years, and $2000/mo towards investments..

What if the $3500/mo went to the mortgage, paid it off, and then $3500/mo went towards investments?

Can't do the math, sorry :(

Let's assume for the sake of consistency with the original comment that the stock market pays 7% every year and the mortgage interest is 3.25%. Things like taxes / home insurance will be the same either way, so ignoring escrow we can calculate that a $1500 payment translates into a $345,000 initial loan.

Option 1: Pay minimum on mortgage, invest rest.
Thirty years later: House just got paid off, spent a total of $540,426 for it. You have $2,454,175 in investment accounts thanks to compounding interest.

Total assets: house and $2.45 Million. No debts.

Option 2: Pay all on mortgage till it's gone, then invest entire amount
Nine years and seven months later: house is paid off at a total cost of $401,855. You begin investing.
Total of thirty years later: You have $2,010,077 in your investment account.

Total assets: house and $2.01 Million. No debts.

Given known future interest rates with no risk and equal tax treatment it is always mathematically best to invest / pay off as much as you can in the investment / loan with the highest interest rate. It may not be the best emotional / psychological choice for you however, and the interest rates are not always known, the risk is not always zero, and the tax treatment is not always the same.

Edit: useful calculators (so you don't have to do the math yourself):
http://mortgage-x.com/calculators/extra_payment_calculator.asp
http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php
« Last Edit: January 05, 2013, 11:23:13 PM by sherr »

The Money Monk

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #19 on: January 05, 2013, 11:23:22 PM »
Question:  Do these calculations include the fact that once the mortgage is paid off early, the extra payments from the mortgage can also be put towards investing? 

If one puts $1500/mo towards a mortgage for 30 years, and $2000/mo towards investments..

What if the $3500/mo went to the mortgage, paid it off, and then $3500/mo went towards investments?

Can't do the math, sorry :(


well it would actually be slightly different because without including the current payment its less. They are talking about putting an EXTRA 2500 towards the mortgage for 7 years.

SO the two options are really:

1. Pay 1240 mortgage payment every month for 30 years
Simultaneously pay 2500 into investments every month for that same 30 years

2. Pay 3640 toward mortgage for 7 years, then entire 3640 into investments for the next 23 years


so I guess my question is, does investing 2500 a month for 30 years beat 3640 a month for 23 years? my guess is that with compounding interest it does, but I am not good at these calculations.

bo_knows

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #20 on: January 07, 2013, 06:51:57 AM »

so I guess my question is, does investing 2500 a month for 30 years beat 3640 a month for 23 years? my guess is that with compounding interest it does, but I am not good at these calculations.

The answer is yes, the 30 year investment plan (minimum mortgage payment) does beat out the other plan.  However, to throw another monkey-wrench into possible calculations, as with most people on these forums, I plan to be long retired before 30 years comes.  So, after 10-15 years, I wouldn't actually be able to invest a whole lot (since I'll be either completely finished with my earning years, or drastically reducing them). 

I have to check back with my spreadsheet.  BRB.

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #21 on: January 07, 2013, 07:05:30 AM »
So, I redid the numbers, assuming that after 15 years, you stop making income (and retire or semi-retire) since this is a more likely scenario in these forums (and for me).

Scenario 1: Pay minimum mortgage, invest extra in market, stop investments after year 15, take mortgage payment out of investments after year 15.  At year 30: $1.8M in investments, No debt.

Scenario 2: Pay max mortgage payment, pay it off in 7 years, then invest 100% into market, stop investing at year 15. At year 30: $1.3M in investments, no debt.

Seems to still be a no brainer toward investing (rather than paying the mortgage). Especially considering that we're still in a recessionary period (stocks are cheap?).

Lagom

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #22 on: January 07, 2013, 08:17:46 AM »
Yes, I have also convinced myself that investing is better. Even with a near-term retirement timeframe, the math is more clear-cut than I expected. At current low mortgage interest rates, you will be able to retire earlier by investing all of your money, even if you still have a mortgage in retirement. This line of thought does make the assumption that market returns will adhere to historical averages over a relatively short timeframe. Assuming average+ market returns, paying off the mortgage first delays retirement, even when you take into account the reduction of your expenses.

That said, beyond the psychological benefits of reducing debt, the fact that so many of us have 5-15 year retirement target dates means that it is far riskier to assume average+ market returns than if we planned to retire in 30-35 years. Thus, I still donít think itís necessarily a bad idea to pay down mortgage principle instead of investing, especially if your mortgage rate is on the higher end of the market (4.5%?). It may be the lower EV play, but itís also less risky and does not excessively delay early retirement even if you do miss out on some returns.

tfordon

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #23 on: January 07, 2013, 09:21:41 AM »
I decided to pay off my mortgage early.  I recognize that I am probably going to lose money in the long term though.  It is mostly an emotional decision.  Here is some of my reasoning/rationalization:

  • Great guaranteed return.
  • Emotional security
  • Less liquidity

I know liquidity is usually a good thing, so I should probably explain my stance on the last item.  I like lowering my hedonistic temptations by making it harder to get to my money.  Way less tempted to overspend if I don't have a huge brokerage account.

It is also worth pointing out the advantage of not paying taxes on your earnings.  To earn from your investments what you save by paying down the mortgage, you need to earn 3.88% in the market (assuming 15% tax).  Still, this is a pretty easy goal to hit.

I list out my reasons a little better in my blog:
http://hedonistic-sukka.blogspot.com/2012/11/die-mortgage.html

Obviously, MMM had a great article last year on the subject:
http://www.mrmoneymustache.com/2012/02/24/pay-down-the-mortgage-or-invest-more-a-winwin-question/

alandjackson

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #24 on: January 07, 2013, 10:00:26 AM »
Glad to hear what you ended up doing.

The whole pay off mortgage vs invest the money is really just a question of leverage. Do you take out (or leave) one loan to finance an investment. When I finally realized that, I was finally able to articulate why I like paying off the mortgage (I'm not a huge fan of leverage in personal finance).

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #25 on: January 07, 2013, 10:15:39 AM »
I list out my reasons a little better in my blog:
http://hedonistic-sukka.blogspot.com/2012/11/die-mortgage.html
Tfordon, I am of a similar mindset to you with our mortgages (primary and rentals). I know that paying them down is statistically not likely to provide the same returns as investing in broad index funds, but my wife is extremely debt averse. Even having mortgages on our investment properties causes her stress. Paying down debt brings her more satisfaction than earning (larger) returns on stocks. We've found a compromise to have the mortgages all paid off here the kids reach college (12 more years), and invest the rest.

I'm curious why you are holding on to a rate of 4.375% on a 15 year fixed. That's great historically, but not great now. We recently refinanced our primary residence at 2.75% for a 15 year fixed with our local credit union. With closing costs, we break even in 6 months if I recall.

tfordon

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #26 on: January 07, 2013, 11:39:19 AM »
@Hamster: My wife is very debt averse and we decided to pay off the mortgage this year.  We shopped around a little recently to see if a refi made sense given the short life left on the loan.  We would save ~$50 by our estimate.

Our current loan is though our credit union, and is really nicely integrated with our current accounts.  We are concerned with how much time is involved with a refi, and how difficult it will be to make payments.  That said, I should stop being a wussypants, do the refi, and save $50.

Congrats on the 2.75%!
« Last Edit: January 07, 2013, 03:25:42 PM by tfordon »

The Money Monk

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Re: Trying to calculate the benefit of paying off the mortgage...
« Reply #27 on: January 11, 2013, 12:48:20 PM »
I decided to pay off my mortgage early.  I recognize that I am probably going to lose money in the long term though.  It is mostly an emotional decision.  Here is some of my reasoning/rationalization:

  • Great guaranteed return.
  • Emotional security
  • Less liquidity

I know liquidity is usually a good thing, so I should probably explain my stance on the last item.  I like lowering my hedonistic temptations by making it harder to get to my money.  Way less tempted to overspend if I don't have a huge brokerage account.

It is also worth pointing out the advantage of not paying taxes on your earnings.  To earn from your investments what you save by paying down the mortgage, you need to earn 3.88% in the market (assuming 15% tax).  Still, this is a pretty easy goal to hit.

I list out my reasons a little better in my blog:
http://hedonistic-sukka.blogspot.com/2012/11/die-mortgage.html

Obviously, MMM had a great article last year on the subject:
http://www.mrmoneymustache.com/2012/02/24/pay-down-the-mortgage-or-invest-more-a-winwin-question/


I think I would do the same thing in your position. The emotional peace that comes with having a paid off house has a huge value in my mind. And it is also an instant huge drop in your monthly living expenses, so you maintain the benefit even if the stock market crashes, or you lose your job, etc.

The alternative is based on steady income AND steady market returns for 30 years, or even 15 years. Hardly guaranteed. Nice work.