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Which is Better: a 15-Year or 30-Year Mortgage?

By JLP | January 31, 2006

This is a post that I moved over from my old blog.

The quick answer is: it depends. The main factors to consider when deciding which mortgage is best are:

1. The interest rate on the mortgage.
2. The rate of return that can be received on the money that would have gone towards paying off the mortgage early.
3. Personal financial constraints.

For example, let’s say someone has a choice between a $100,000 mortgage with a 30-year fixed rate of 6% or a 15-year mortgage at 5.5%. Let’s also assume that the house appreciates in value at 3% per year. We know from a historical perspective that the stock market (using the S&P 500) has returned on average about 10% per year over the last 30 years. The following steps can be used to calculate which mortage looks better on paper (there are other factors to consider that I will discuss later):

1. The 15-year mortgage would have a monthly payment of $817 while the 30-year mortgage has a monthly payment of $600 for a monthly difference of $217 ($817-$600=$217). This $217 we will assume is saved in a Roth IRA and invested annually in the stock market and getting an average return of 10% per year. We will also assume that $817 per month will be saved after the 15-year mortgage is paid off (also in a Roth IRA and getting a 10% return per year).

2. Calculate the total amounts paid towards principle and interest over the two time periods.

(15 years X 12 payments per year) X $817 payment = $147,075

(30 years X 12 payments per year) X $600 payment = $215,838

The 30-year mortgage results in $68,763 ADDITIONAL interest expense. Most people stop here and proclaim that the 15-year mortgage is the best way to go. However, they are missing one VERY IMPORTANT factor.

3. Calculate the investment earnings on the monthly difference.

$217 monthly savings X 12 = $2,610 savings per year invested annually in a Roth IRA.

$2610 invested per year and getting a 10% rate of return will be worth $472,334 in 30 years. For those interested in the math the formula is [$2610 X (1 + .10)^30].

4. Calculate the investment earnings on the monthly savings ($817) after paying off the 15-year mortgage.

$817 monthly savings X 12 = $9,805 savings per year invested annually in Roth IRAs (this amount of money would require 2 Roth IRA accounts).

$9805 invested per year and getting a 10% rate of return will be worth $342,682 in 15 years. The formula is [$9805 X (1 + .10)^15].

5. Now compare the two scenarios to get the full picture. In 30 years, the home will be worth $242,726 ([$100,000 X (1 + .03)^30].

To find the net worth under each scenario simply add the home’s value and the investment balance:

15-year mortgage: $242,726 home value + $342,682 investment balance = $585,408 net worth.

30-year mortgage: $242,726 home value + $472,334 investment balance = $715,060 net worth.

So, in this example a person gains an additional $129,615 in net worth by going with the 30-year mortgage instead of the 15-year mortgage.

How is this possible? Well, since the mortgage rates are 4 – 4.5% lower than the assumed rate of return on the stock market, going with the 30-year mortgage and investing early allows for 15 years of additional compounding. This is the difference maker. But, this ONLY WORKS if the person is dedicated to investing the difference and not spending it on something else like a car note.

Now, even given all that, are there still reasons to go with a 15-year mortgage? I suppose there is a certain peace-of-mind in knowing that the house is paid for. Also, there is no guarantee that the stock market is going to return 10% per year for the next 30 years.

So, there it is. Each person has to decide what is best for them.

Good luck!

Tags:

Topics: Mortgages | 19 Comments »


19 Responses to “Which is Better: a 15-Year or 30-Year Mortgage?”

  1. David Porter Says:
    January 31st, 2006 at 2:11 pm

    JLP,

    This gets even more interesting when you consider that Uncle Sam
    is going to help make the payments with a tax deduction.

    Nice Job!

  2. RS Says:
    January 31st, 2006 at 3:19 pm

    I also decided to take a 30-year mortgage for the peace of mind. I felt that a 15-year mortgage would be harder as you have to pay a higher amount each month. With the 30-year, I can just pre-pay each month to acheive a quick pay-off (I realize that the interest rate would have been lower with the 15 year). This way, if anything happens or my wife decides to stay home when we have kids, there isn’t as much pressure.

  3. Cathy Says:
    January 31st, 2006 at 6:31 pm

    JLP – I really enjoyed this post since I had never thought things through quite this way. I would be interested to know just how many people out there have the discipline to follow through on the investments :)

  4. BrookMan Says:
    January 31st, 2006 at 10:13 pm

    As many have stated many times, the best way to follow through on investing is to make it automatic – just about every company offers an automatic investing program of some sort.

    But I think the better way to do this analysis is to determine the break-even market return, and then ask the question: do I think the market will return more over the time period? How about it, JLP? (figuring out the tax benefit would be extra credit). Great stuff!

  5. some body Says:
    January 31st, 2006 at 10:57 pm

    what if your roth is already maxed out or you are ineligible for it? then you will need to
    calculate taxes on the above-referenced returnsfor the 30-yr mortgage savings!

    also, don’t count uncle sam’s eggs before they hatch. to wit, if you get a 28% (1040 tax form)
    savings on the marginal mortgage interest, don’t forget that it will be a wash if you put the
    same money into your savings account where you get a rate of interest that matches your mortgage
    rate of interest but end up paying tax on this interest. the only way you will come out ahead
    is if you get a good stock market return, which will happen more likely than not when you are
    well diversified; not, for instance, if you were long on goog yesterday before it took a 12%
    after market bath.

    ciao,
    s.b.

  6. Erik Says:
    February 1st, 2006 at 7:11 pm

    I think one major thing to consider here is that people should not be content with waiting 15
    or 30 years to pay off their mortgage. Become debt free and free up your income. Then, you can
    make double payments on your mortgage and pay it off in 7 years. This tips the scale on the investment
    example above if an individual frees up his or her income to get serious about having a paid for house.
    Don’t settle for keeping your mortgage around forever. The tax advantages are not worth it simply
    because the interest is a DEDUCTION and not a credit. Someone making 100,000 a year that deducts
    10,000 from his taxes does not recieve a huge tax savings compared to someone investing an
    entire mortgage payment for 12 months. Personally, I think the only people winning with the whole
    tax advantage and investment argument are the banks. That’s just my take.

    thanks, take care.

  7. some body Says:
    February 2nd, 2006 at 9:25 am

    erik,

    i disagree. if you are confident enough of your investment skills and can get a better deal
    out of your investments, or if your mortgage is a low enough rate, then you should be better
    off holding the mortgage and using the savings in investments or elsewhere.

    say your mortgage is 4.75 % (it was available not more than a year ago!), and the rate is
    sufficient for you to be well over the standard deduction, you should probably invest your
    savings. why, even the treasury direct is right now giving a better rate than 4.75 (i bonds
    are going for 6.73 through april, i believe, and the rate is guaranteed for six months, and
    might even go up with the fed upping the rates).

    what do others think?

    ciao,
    s.b.

  8. retireat30 Says:
    February 2nd, 2006 at 4:08 pm

    erik,

    I’ve got to echo some body. If you’re looking to maximize long term returns, you should put all available money towards the highest possible rate you can. Count debt at its interest rate too (Negative money to negative rates ends up being a positive contribution to your net worth, so you should just put as much), and you will ALWAYS end up ahead mathematically.

    Someone making 100,000 a year deducts 10,000 from their taxes, saving them $3,000 from federal taxes alone. In what world is $3k “not a huge savings”? Can I come visit?

    The net effect this has is lowering your effective APR on your home mortgage by your highest tax rate (since deductions come off the top, not the average). If you’re making 100,000 w/ 10k of deductions, a 6% rate becomes 4.2%. A 4.5% rate becomes 3.15%.

    Currently average mortgage rates for a 30 year fixed are 5.78% (bankrate.com), and treasuries are yielding 4.33 on the low end (for 1 month). 5.78% * .7 = 4.046%. Since 4.33 > 4.046, you would be better off taking the longer mortgage and putting the money into a retirement account.

    If you’ve maxed your retirement, then you need to factor in taxes on your returns. A conservative way to do this would be to deflate your returns by your highest tax rate. So the same person making 100,000 a year who had an increase of 10% would get 10% * .7 = 7% expected return. Even with this, the most conservative way of calculating the tax bite of non-retirement growth, and an average return says that taking longer on your mortgage is a good deal.

    Using this method of accounting for the tax savings is a bit tricky. These measure net effects, not the monthly effect. Leveraging these advantages to help you build wealth would require putting away the savings from a 30 year term + the savings from taxes each month (or year for the taxes) and not spending them.

    Of course, the psychological benefits of having no debt might outweigh the psychological benefits of more money in the future. That’s a personal decision. Furthermore, the TIME benefits of not having to do these intricate calculations and balancings might further outweigh the advantages if you don’t like playing around with numbers in your spare time like JLP seems to do.

  9. Erik Says:
    February 2nd, 2006 at 9:07 pm

    I understand where you both are coming from by crunching the numbers and finding the better rate. However, my point has been missed, and I may have done a bad job at making my point in my previous post. The one MAIN thing that most people do not factor in when talking about playing with the numbers and leveraging their debt is the RISK involved. I would NEVER advise someone not to pay off their mortgage early and aggressively, because by paying it off early and living debt free, that family has significantly reduced their risk. Risk has an economic value that factors into financial calcuations, and it reduces the overall return on investment when leveraging debt. Playing with the numbers look good on paper, but we are not thinking in terms of the real world where people lose their jobs and still need to make a mortgage payment. I know it seems unreal with the current housing market that it is tough to sell a house, but it happens. If it were me, I would rather be sitting in a paid for house when Murphy’s Law moves in rather than having a big, hairy mortgage payment. But, I guess if you are already financially independent then it does not matter that much, but the sad thing is that
    most people live pay check to pay check.

  10. retireat30 Says:
    February 5th, 2006 at 1:39 pm

    Erik,

    Great point. Hadn’t thought of that. I’ll figure out a way to factor that into the analysis.

    TT

  11. Steven Says:
    June 9th, 2006 at 4:33 am

    I have been reading the postings and agree whole-heartedly with Eric. I am a few months away from paying off my 15 yr mortgage (in 7 years) and the positive psychological impact that this allows is immeasurable.

  12. Steven Says:
    June 10th, 2006 at 5:21 am

    Eric,
    Just wanted to let you know that the Ibonds are now at 2.43 from the 6.73.

  13. AllFinancialMatters » Blog Archive » The Top 5 Reasons to Pay Off Your Mortgage? Says:
    May 14th, 2007 at 10:31 am

    [...] Which is Better: a 15-Year or 30-Year Mortgage? Bookmark to:   [link] [...]

  14. Me Myself And I Says:
    June 22nd, 2007 at 2:56 pm

    Personally, having a mortgage paid off before my retirement is in my best interest. I wouldn’t feel comfortable having a mortgage payment when I choose to retire.

    As you said, to each his own.

    For kicks, I set up an Excel spreadsheet to do the calculation you mentioned, on the original balance of our current mortgage. And the results are (using current interest rates of 15/6.03% and 30/6.33%), that I could have created an additional networth of $10,991. And, yes I had the spreadsheet spit out the text that you see at the bottom

    Mortgage Amount $237,000.00
    30 year rate/payment: 6.33% $1,471.60
    15 year rate/payment: 6.03% $2,003.78
    difference: $532.18

    Investment ROR: 10% Networth change
    15 year $100,443.64
    30 year $111,434.82
    Better choice is 30 years, because it increases networth by $10,991.18

  15. Money Magazine Takes on Six Financial Dilemmas—� AllFinancialMatters Says:
    December 12th, 2007 at 6:44 pm

    [...] Which is Better: a 15-Year or 30-Year Mortgage? [...]

  16. joe investor Says:
    February 8th, 2008 at 1:12 pm

    Based on the post # 14, are you forgetting that by paying off the 15 year mortgage after only 15 years that will leave you with $1472.60 to invest over the next 15 years. Shouldn’t that vastly outweigh any negative of the 15 years higher payment.

    Also, I think you have to assume that very few people live in a house for 30 years, especially if they are able to afford a 15 year mortgage. So assuming that when you move, you would like to have the greatest equity in your home to use as a down payment for your next bigger and better house, I think there is no contest that the 15 year is a better choice, IF you can afford it, which most new buyers cannot.

  17. duke Says:
    August 6th, 2008 at 3:08 pm

    I think you forgot to take into account the 15 years after you pay off your mortgage and the investment of the full payment for 15 more years. . .

  18. JLP Says:
    August 6th, 2008 at 3:14 pm

    duke,

    No, I did take that into account.

  19. Paul Says:
    December 28th, 2009 at 10:52 pm

    Dear JLP,

    I’m missing something here. You point out that during the first 15 years, the lower monthly payment for the 30 year mortgage saves you $217 per month and $2610 per year. But when you calculate the benefits of a 30-year mortgage, you assume you are saving $217 per month for the second 15-year period. But how is it that you are you saving that amount? The 15-year mortgage has been paid off, so you aren’t saving $217 in comparison with it any longer. What am I missing here? Best, Paul

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