[Updated in August 2019 to reflect changes in the new tax law. 90% of taxpayers take the standard deduction now.]
Reader Dan left this comment on my post about paying a 30-year loan on a 15-year schedule:
Having your house paid off in 15 years instead of 30 will provide peace of mind in 15 years. But at what cost?
The opportunity cost of locking that money up in the equity of your house could be significant if you invest the difference.
Reader Heidi also asked:
Although it would be nice to sell the house at that time and have no mortgage, I struggle with tying up the funds in a paid off mortgage. My retirement accounts are maxed out, but my taxable investment account could use some additional funds (hopefully earning a higher rate than what I’d pay on the mortgage). Your view?
Many think that because mortgage rates are at historical lows, it’s cheap money, therefore it would be smart to stretch the repayments and invest the difference. To borrow a phrase from buying life insurance — “buy term and invest the difference” — I call this strategy “borrow 30-year and invest the difference.”
Let’s run the numbers and see if it’s a good move.
Example: Bob refinances a $400k mortgage in Arizona. He can get a 30-year fixed rate mortgage at 3.5% or he can get a 15-year fixed rate mortgage at 3.0% at comparable closing costs. The 30-year mortgage requires a payment of $1,796 per month. The 15-year mortgage requires a payment of $2,762 per month.
Bob decides to take the 30-year mortgage and invest the difference of $966 per month in a “side fund.” We assume Bob earns 5% on this side fund. Due to the new tax law that expanded the standard deduction, Bob no longer gets additional tax savings for the higher mortgage interest paid with the 30-year loan. For simplicity we assume the side fund is perfectly tax efficient. All gains will be long-term capital gains when the side fund is liquidated. When Bob finally sells his house, he liquidates the side fund, pays the capital gains tax (15% federal plus 4% state), and uses the proceeds to pay against the mortgage.
We want to compare the increase to Bob’s net worth. That is (a) the principal paid off if Bob took a 15-year mortgage versus (b) the principal paid off on the 30-year mortgage plus the money in the side fund after paying capital gains tax. Whichever strategy results in a larger number wins.
I have detailed calculations in a spreadsheet. You can double-check my math or enter different assumptions. I summarize the net worth increases here:
| Year | (A) 15-year | (B) 30-year plus side fund | (B) – (A) |
|---|---|---|---|
| 1 | $21,441 | $19,484 | -$1,958 |
| 3 | $66,300 | $60,744 | -$5,555 |
| 5 | $113,929 | $105,295 | -$8,633 |
| 10 | $246,270 | $233,122 | -$13,148 |
| 15 | $400,000 | $389,034 | -$10,966 |
At the end of 1, 3, 5, and 10 years, the “borrow 30-year and invest the difference” strategy is increasingly worse off than just taking out a 15-year mortgage. At the end of 15 years the side fund is finally catching up but still not quite there yet.
What’s going on? How come borrowing money at 3.5% to invest at 5% return with perfect tax efficiency and favorable long-term capital gains treatment doesn’t pay off for 15 years?
The answer lies in the higher rate on the 30-year mortgage. Although a 0.5% difference between the 15-year rate and the 30-year rate looks small, it applies to the entire mortgage balance. The higher investment return on the difference in monthly payments is on a much smaller base.
For instance during the first year the 30-year mortgage will cost roughly $400,000 * 0.5% = $2,000 more. Investing $966 a month at 5% return will only earn about $290. Paying $2,000 more for the privilege to earn $290 on investments is a losing proposition.
Over time, as the side fund builds up, the investment earnings start to overcome the extra cost on the mortgage, but it takes a long time, more than 15 years in our example.
The assumptions in the calculation actually favor the “borrow 30-year and invest the difference” strategy in several ways. First there is risk. The side fund may not be able to earn 5% a year. Even if it does on average over 15 years, there’s a sequence-of-returns risk. If the returns are good in the beginning when the side fund is small but bad in later years when the side fund is larger, the side fund won’t benefit as much. We also assumed perfect tax efficiency. In reality the side fund will have to pay some taxes along the way.
Mortgage Interest Deduction
Now, if you are one of the 10% who still itemize deductions under the new tax law, the higher interest paid on the 30-year loan will give you a higher tax deduction. If you also invest the tax savings into the side fund, the side fund will catch up faster.
For someone in 39% combined tax bracket (35% federal + 4% state), it takes 7-1/2 years to catch up to the 15-year loan. For someone in 26% combined tax bracket (22% federal + 4% state), it takes 10-1/2 years to catch up. That’s assuming you can itemize in all years. As the principal balance is paid down, the interest paid will also come down, while the standard deduction goes up each year with inflation adjustment. It’s possible you will stop itemizing at some point. If that’s the case, you won’t have as much to invest into the side fund.
Higher Investment Returns
I picked 5% as the investment return for the side fund because Vanguard’s median projected long-term return for a globally balanced 100% equity portfolio is only 5.3%. That’s the nominal return, with inflation included. That also includes the effect of a higher projected return for international equity. For a 100% U.S. equity portfolio, Vanguard’s median projected long-term nominal return is more like 4%.
Source: Vanguard economic and market outlook for 2019, pages 33, 37
Now, if you think you can earn a higher return in the side fund, say 7% per year, because you are able to beat the market, or you think Vanguard’s projected returns are wrong, without the mortgage interest deduction, it still takes 10 years to catch up to the 15-year loan.
Conclusion
I would take the sure thing in a 15-year mortgage for its lower rate. A slightly lower rate on a large balance makes a bigger difference in absolute dollars than a higher return on a small balance.
Note this is not a typical “should I prepay my mortgage or invest” situation. Merely prepaying your mortgage does not lower the rate on the entire outstanding balance. You get the lower rate on the whole balance only when you make a firm commitment to make a higher monthly payment each and every month. It’s a gift to the committed.
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AM says
Good post, thanks. I did a similar calculation and decided that I am much more comfortable carrying as little mortgage balance as possible.
In fact, I am currently refinancing from 15-year fixed into a 30-year 7/1 ARM, for a lower rate (and no cost, of course). I will keep paying the same monthly amount (actually I am increasing my monthly payment), in order to pay off the loan faster. After 7 years my principle will be small enough that I will simply pay it off if rates jump too high. Plus there is a good chance we will move within 7 years. PLUS it gives me more flexibility in case I experience cash flow problems.
Dan says
Great and timely article on a great website! I especially like this point that you made: “A slightly lower rate on a large balance makes a bigger difference in absolute dollars than a higher return on a small balance.” It could take a long time to come out ahead by investing the difference because the amount starts out so small.
There are so many variables to consider in this decision. If an investor is an appropriate age, they could invest the difference in globally diverse set of index funds in a Roth account which would offer protection from future taxes provided that congress does not change the rules on Roths.
Life has thrown us a few curve balls already and as much as we try to plan, I just have no idea what is coming around the corner. The lower payment keeps more options available. For example, if we have to move due to a job transfer, the lower payment may allow us to rent our house out instead of selling it at a potential loss.
There are risks involved with both the 30 and the 15. By investing the difference, we still have the ability to access the money and have control over it. I don’t have a crystal ball, but the 30 seems less risky to me and it is possible that we may come out ahead in 15 years by investing the difference.
Ace says
TFB – I wonder if you could do a breakeven analysis on a related topic. I’ve used your “resetting the clock” calculator to analyze the difference between sticking with my current 30-year mortgage at 4.00% (with 28 years left), versus refinancing to a new 30-year at 3.625% (at zero cost, of course). Your calculator tells me that if I keep making same payment, effectively prepaying my new mortgage a little each month, I’ll pay off the new mortgage in about 26 years and save $40k in interest. Alternatively, I can simply pay my new mortgage off according to its own terms and still save about $10k in interest over the 30-year life of the loan.
My question is this: Is there a breakeven point for these two scenarios? Although nothing is in the foreseeable future, statistically I likely will not pay this loan for its duration. Chances are, I’ll move in 5, 10 or 15 years. If we sell in, say, 10 years, will I have saved or lost money by resetting the clock?
(I actually plan to do something in between the two scenarios with my monthly savings: For the next few years, I intend to put my extra $100 per month towards paying off higher-rate student loans. After those are gone in about six years, I’ll pay my old payment towards my new mortgage.)
Dan says
Ace,
If you are refinancing to a lower rate and it will cost you nothing to do so, it seems to me that you’ll come out ahead right away as they are both 30 year terms. The bank may be able to set your term to 26 or 28 years, if you prefer.
Or, if you have enough equity, you may consider taking some cash out to pay off the higher interest rate student loan debt.
Another thought, once you get within a year or so of paying off the student loans, is to transfer the balance to a 0% credit card. We paid off a property that way. We only had to pay a $100 transaction fee and it was 0% for 12 or 18 months. Read all of the fine print and make sure that it makes sense to do so.
Investor Junkie says
TFB,
I while I agree with the formulas, I disagree with the numbers entered. If you are going out 10-15 years shouldn’t you go with the historial average return of 7-8%? That changes your numbers quite a bit.
What seems of greater importance is your age. If you have 20-30 years till retirement you more than likely will come out ahead not getting a short term mortgage. While there is no guarantee of returns for any investment various issues could also happen with paying down a mortgage faster as well (property going down in value, inability to get money out of an illiquid asset, etc.) So paying down a mortgage isn’t risk free either.
I also posted an article similar to this one and came out with different results.
http://investorjunkie.com/13979/fool-prepay-mortgage/
Investor Junkie says
Let me add while both 15 year and 30 year both are tax deductible, the 30 year gives slightly more back since there is more interest expense. So compared to the two you would get slightly more back at the end of each year. Not enough to dramatically affect the decision of mortgage term, but really a consideration with your effective taxable rate.
Financial Advice for Young Professionals says
This is a very complex and detailed analysis that I think you could skew towards either side based on the assumptions one makes. Personally, I like the flexibility a 30 year mortgage gives. I don’t like investing my after tax money in stocks so I choose real estate instead. And one of the benefits of real estate is you only need to put 20-30% down and you can still get 100% of the returns on capital appreciation(with thanks to the banks for the rest).
Harry Sit says
@Ace – Mortgage Professor’s calculator 3a does the type of breakeven analysis you are looking for.
Student2 says
First, I would like to say thank you for such valuable information! I was lucky enough to stumble across your site while researching Roth IRA conversions and have now read enough to know I will be back! Thanks for your contributions and valuable insight.
Second, regarding the 15-year mortgage vs. 30-year mortgage + investing the difference, it seems to me that the key assumption here, as Investor Junkie alluded to, is whether the investments you are making are tax-advantaged long-term retirement-type or not. If you are considering whether or not to invest additional money into a retirement account, then it looks like a no-brainer to me (and I’m fairly green so maybe I’m missing something). The increased return at longer investment periods is clearly going to have a huge impact on the total available at retirement. The paid off mortgage and deferred contributions (assuming you will begin investing the mortgage amount + the side amount when the mortgage is paid off) will take longer to get you to the same place (and make for a lot scarier ride).
On the other hand, if the side investment is for something else with a shorter period, specifically for less than 12 years by your calculation, then, by all means, pay off the mortgage first.
In short, other assumptions on returns, etc. aside, the key point is the investment period.
Harry Sit says
Student2 – I agree if paying a 15-year mortgage makes you unable to fund tax advantaged accounts adequately or max them out, you should not get a 15-year mortgage. For those who can do both, it’s a viable option versus investing in regular taxable accounts because you get a lower rate on a large sum.
bcarney says
“We assume Bob earns 5% on his side fund.”
Where the hell is anyone making 5% on anything that’s non-gambling risk?
Harry Sit says
bcarney – I know some want me to use a safe, guaranteed rate of return to compare to the certainty in paying off debt. Some others, as in the comments by Investor Junkie above, want me to use a higher “historial average return of 7-8%.” I just picked a middle-of-the-road 5%, not guaranteed of course, but likely achievable in a diversified balanced portfolio. The linked spreadsheet allows anybody to plug in their own assumptions.
Lily says
Great article on a topic that many people have never given serious thought to. Given that 30 year treasuries are only yielding 3%, I think 5% is a reasonable guestimate for medium risk investment return. Most people sell or refinance in less than 10 years so it seems like investing the difference is a risky move that is unlikely to yield rewards.
Heidi says
Thanks for a great post! I ran my own model, and agree that I’m better off refinancing to a 15 year mortgage rather than pre-paying on the 30 year or making the regular payments without refinancing.
I like this blog. It makes me think!
Marcus says
Another thought to take this out further would be to have the person with the paid off 15 yr mortgage immediately invest the freed up monthly mortgage payment of $2,859.53 into the same investment and assumptions that the difference has been going into and see how long this takes to catch back up or if it even would.
Shawanda @ You Have More Than You Think says
I think it’s interesting how confident people are of their ability to find an investment that generates higher returns than the effective interest rate on their mortgage.
Also, I wonder how many of them actually get around to investing the difference that’s going to yield them all these stellar returns.
bp says
Let’s not forget all of the young professionals with over $100,000 in student loans at and unshakable rate of 6.8%…and there’s a lot of us! Do the finance gurus out there realize that the graduate student loan rate is that high?
Anyone in that situation should be advised that a 30-year mortgage is a no-brainer.
JoeTaxpayer says
The higher rate on the 30 does cost you. If the 15 year leaves enough money each month that the risk of needing to borrow at a higher rate is minimal, I might agree to go 15.
What I’ll take issue with are those who are so extremely anti-debt that they forgo matching 401(k) deposits, claiming that after 15 years, they’ll have a huge monthly deposit they can afford. Or those whose budgets are tight to begin with, and think the numbers work in their favor by paying off their mortgage faster while still owing money at 18%. I dare say, the sub-4% mortgage money may be the lowest rate we see in our lifetime. When rates go back up to ‘normal’ it would be nicce to be buying 8% CDs while paying the bank 4% for years to come.
bp says
Also…
Most arguments of 15-year vs. 30-year mortgage ignore the performance of the asset i.e. the house. You are assuming more of the risk when you choose to put more money into a house on a 15-year mortgage. If the house value goes up, this will work in your favor. If it goes down, however, it works against you because now the bank has more of your money than if you had chosen a 30-year mortgage.
Tim Richmond says
This is a fascinating analysis. I wonder if home buyers in general would be less confident with investing the difference simply because it is psychologically more satisfying to pay off something so tangible like a home.
Lee says
I was reading about mortgages on your website, what I do is I borrow $10,000 from my paid off car and place the money down on my mortgage. As soon as I pay the car loan off I borrow from the car again. I save big bucks from reducing paying interest on my mortgage.
J says
You are forgetting one vital factor – Inflation.
While I am paying a large dollar value for the first 10 years, the value of the money changes over time.
In a 15 year loan you are paying more in terms of nominal dollars upfront, where as in a 30 year loan you are paying much less because inflation has eaten away the value of that dollar.
Since the majority of interest on a loan occurs in the first 1/2 of the term, you get to deduct the highest nominal dollar amount – then reap the rewards of your 5% investment later (minus inflation at 3%). Otherwise you are just paying today’s dollars upfront in principal with minimal benefits in terms of rate reduction.
Harry Sit says
The analysis compares the value at the end of X years. You look at the amount you still owe, offset by any investment side fund. Whichever strategy makes you owe less at that time wins. It’s not affected by inflation, unless you say inflation drives the investment return. If you assume a 15% return instead of a 5% return then sure, invest the difference wins.
Ben says
Harry,
Thanks for the article. Two points, the mortgage interest tax deduction is not well understood. The statement “Because Bob pays more interest in the 30 yr he gets more tax deductions.” while technically correct, should take into account the interest cost vs amount of deduction. Since a dollar in interest paid reduces taxable income by a dollar. One pays a dollar in interest to avoid paying $0.15-0.35 (marginal tax rate) to the government.
Second,
The 15 and 30 year examples have differing amounts of leverage. One is not just comparing a net dollar amount to determine which option is “better”, but one needs to consider the increased risk as well. This increased risk is understandably hard to value numerically, but should be considered none the less.
Chris says
Regarding consideration of effective interest rate after tax deductions, you should consider that benefit only to the extent that your itemized deductions exceed your standard deduction. If you had lower interest expense that puts you below the standard deduction, you’ll get the standard deduction, anyway. So, the only part of the interest expense that provides a tax benefit is amount that exceeds what you’d get, anyway, with a smaller mortgage.
Stephen says
What the blogger failed to do was calculate returns at the end of the 30-year period. Just think – those last 15 years the 15-year fixed is generating $1700+ a month whereas the 30-year is paying into the mortgage. Investing that $17K per month will generate large returns.
Assuming an 8% annual return on a $100k mortgage within the 25% tax bracket/5% state and using today’s average rates (3.09 15, 3.89 30), the 15-year outperforms by $25,804. This is not counting Itemizing, which isn’t all that significant anyways. Little if any of an interest payment will help with itemizing expenses, as it is somewhat hard to be able to itemize unless you make significantly higher than median income.
However, in the example the blogger used, at the end of those 30-years the 15-year would VERY SIGNIFICANTLY outperform the 30-year because with a house that much, the person is likely paying 40%+ in Income taxes every year.
Tom says
Your point is moot as the 30 year mortgage holder pays a smaller payment for the first 15 years compared to the larger payment by the 15 year mortgage holder. Would you rather have a smaller fixed amount of money to invest for 30 years or a larger fixed amount of money to invest for 15 years? I ran the numbers with my 30 year mortgage payment of 2200/month vs. my 15 year mortgage payment of 3500/month. Assume a 7% return on 1300 for 30 years (savings difference between two payments) or 3500 for 15 years. The 30 year loan always wins even without including any tax benefits. Simple math with simple to understand consequences. People really want to believe paying off the mortgage early will benefit them but in the end how do you access your money after the home is paid off? You don’t unless you sell the house or take out a reverse mortgage. Liquidity and a higher rate of return is usually a better option. If you’re the type of person who won’t actually invest your extra monthly savings then you should go with the 15 year loan as investing in nothing won’t earn you a benefit.
Banks make serious money off home loans but they make even more off the fact that people are unlikely to stay in their homes for 15 or 30 years. Restarting the front end loaded interest game over and over again on the same money with a different house.
Bloblu says
Thank you so much for posting this article and the spreadsheet that I could customize with our own data. I had done the maths over 30 years and found the 30 year option to be better for us – except it is very unlikely we will ever stay 30 years in any house (more likely 5-10 years). I had the gut feeling 15 years was better for us but now have data to back it up. Thanks!
The White Coat Investor says
Great post. First time I’ve seen it for some reason.
One other aspect that is overlooked is the Dave Ramsey philosophy:
“The paid off home mortgage has taken the place of the BMW as the status symbol of choice.”
You’ve really made it when your net worth is so high that paying off your mortgage is something you can do just for the status of it, even if it costs you a little extra.
Tom says
A not so wise co-worker of mine once asked the naive question, How do banks make money? He was perplexed how banks could offer such low rates on loans and still make money. Before one even considers a 15 year or 30 year mortgage, one should realize that banks don’t offer any loan options that don’t benefit them over the consumer interests. They will make money on both loan options which means you will lose money on each loan option.
I think a 5% annual return on investments is too low of an assumption as referenced in the article. I have averaged at least 7% annual return after taxes on my entire investment portfolio over the past 30 years. Running the numbers with a more reasonable rate of return (7%) makes the 15 year loan option much less attractive.
How does it make one sleep better at night when your mortgage has been paid off? You have little to no access to your principle investment and added market value unless you sell your home or take out a reverse mortgage. Are people so worried about monthly cash flow that they’d prefer lumping a large amount of their total savings into an neutral growth asset like a primary home (primary home as an investment is generally an awful investment return compared to secondary investment properties which are great for cash flow, market appreciation, tax sheltering, etc.)? I get it, people don’t like disruptions in their monthly cash flow. What difference does it make if you lose money over a 1-2 year period but end up with an annual return of 7% over a 3, 5, 10, or 20 year period? No matter how many times I run the numbers I haven’t been able to show that a 15 or 30 year mortgage on a primary home investment will outperform the stock market (balanced fund performance: 40:60, 50:50, or 60:40 asset allocation). You might get lucky flipping a primary home in the short term (like buying in 2009 and selling in 2015) but you won’t make more money over the long term on a primary home investment compared to a similar investment in the stock market with the same time horizon.
You can’t really make a bad choice whether you choose a 15 year or 30 year – they are both bad choices albeit necessary if you want to own a home.
Alexander Crossman says
One topic not raised is the impact of diversification and liquidity when the monies are used to invest.
I'mDUN DDS says
A 7/1 interest-only arm gives a low interest rate, 6 month ago at 3.5%, and is always 100% deductible, and saves over 50% of the traditional monthly total P and I payment. The difference is invested (and other $ too) AFTER maxing out all deferred-tax plans. This deductibility gives a bar, after deductions, of say 2.5 % that investments need to overcome to be ahead of the game; not a high bar. The one issue is that you must refinance (or sell home) BEFORE the 7- year period when rate can jump. I leverage my taxable acct, and this additional taxable investment $ combined w/ this margin has been wonderful – you do need to hold investments that are ideally negatively correlated (or at least minimally correlated) so that you can’t get burned from the margin leverage in a down market. I truly believe mortgage debt is a ‘good kind of debt’. Read “The Value of Debt in Retirement”, great book.
simplesimon says
Harry, I was revisiting this in light of the new tax law and current interest rate environment. Based on my calculations, the side fund diminishes significantly for most people/smaller mortgages because of the increased standard deduction. Maybe not in the early years while interest payments are higher, but definitely in the later years. Is that what you see?
Patrick Law says
1. Will interest rates remain so low for 30 years? Which 30 year period in history have we had that allows for these assumptions?
2. Most people don’t live in a single house for 30 years. Employment conditions tend not to remain that consistent.
3. Borrowing money certainly increases returns when the investments are making money, but it increases loses when the investments are losing money.
Borrowing to invest is risky, but I look forward to picking up some investment and rental property bargains if the majority of people follow this advice!
Brendan says
so why is it called “borrow 30 and invest the difference” when your conclusion is the opposite? I like the concept, the math, and agree with your conclusion…but I was expecting something different from the title!
Harry Sit says
Any suggestions for a better title? “Effectiveness of …”?
David Kelsey says
Overall, good article. But like many other similar articles it falls into a category I like to call “the tyranny of numbers”. You get an absolute answer that fails to take into account other variables that may have a significant impact. I see at least two:
1) It assumes a “side fund” has a positive absolute value but a zero relative value in the analysis. A side fund has greater liquidity than a fixed mortgage, and that liquidity could be valuable at some future point even though you can’t put a monetary value on it at the present time. There is something to be said for options and flexibility in the face of uncertainty.
2) Building on #1, the analysis does not take into account the age factor. A retiree might argue that the lower monthly outlay is far more critical over time than a reduced future net worth. A 50 year-old might argue the opposite, as maximizing net worth in the next 15 years over a planned retirement at 65 is a perfectly legitimate and rational goal.
Based on my experiences on our own retirements and working with clients on the issue, I can state only one thing with certainty – decisions should be made based on an individual’s total financial circumstances and needs. This can be a tricky business!
Brian says
Love your stuff Harry, and great analysis here! I do think you should be even more clear that your conclusion really only applies to someone taking the standard deduction. E.g., someone in 35% federal marginal tax bracket itemizing deductions should almost surely arbitrage the rates; break-even at ~4.2% return (ignoring sequence of return risk) doesn’t seem herculean for instance.
Harry Sit says
Being able to itemize deductions and making a higher return in the side fund will help the case for getting a 30-year loan and investing the difference. It still takes a long time to come ahead though. I added two sections to address these two points.
Ben says
Harry,
Great analysis. I used your worksheet and ran this at 0% Sales Tax for my State and a 7% growth assumption and reached a different conclusion.
Jake says
Great material! (Slow response because I saved it after reading on my phone so I could come back and check the numbers in your spreadsheet). I’m amazed how many people neglect the impact of taxes on unrealized gains, $100k with $50k in unrealized gains is not the same as $100k in equity. I’m also depressed about Vanguard’s 10-year outlook but it seems like a reasonable assumption to use.
This makes me think that it’s key to project how long you’ll be in the home. 3/5/7 years? Get the corresponding ARM. 7-15 years? Get the 15 year mortgage. 15-30 years? OK get the 30-year mortgage. (But less than 5 years do you really want to buy? And more than 15 years are you really sure you’re locked into this place for a huge chunk of your life?)
Harry Sit says
This shows the effect of a small difference in the rate applied to a large principal. The initial rate on a 3/5/7 ARM can be lower than the 30-year fixed rate but higher than the 15-year fixed rate.
rp says
Thanks for the analysis. I have a related question. Which is the better option of the following, if you had all the cash to buy a house?
1. buy house with cash
2. take out 30 yr mortgage and invest the cash
Has anyone done this analysis?
Harry Sit says
That’s a different question. As usual it depends on other assumptions. How much money will you still have if you buy the house with cash? Are you one of the 90% who will still use the standard deduction even if you take out a 30-year mortgage? To me, at today’s 3.5% rate for a 30-year mortgage, when I’m taking the standard deduction either way, when I have enough liquidity, and when the long-term expected return is only 5% for 100% stocks, I would pay cash and earn the 3.5% after-tax with certainty. Someone who will itemize, need or like the liquidity, or think they can make a higher return would go for the mortgage.
rp says
Thanks Harry. Thanks makes sense for 5% annual pre-tax returns.
How did you come up with 5% expected return for 100% stocks?
Harry Sit says
See link under the sub-heading “Higher Investment Returns.”
Bill says
One thing that investors should consider when weighing the question of whether to pay down debt versus invest is whether they’re comparing apples and oranges. The return available from paying down a mortgage is a guaranteed return, and comparing it with projected returns on a non-guaranteed investment isn’t a direct comparison.
At present the highest available guaranteed return on a long term investment is less than 2% – that which can be expected from Treasury securities. This is the correct apples-to-apples rate for comparison with other prospective guaranteed returns such as those available from paying down debt. If investors choose to use speculative figures on other forms of securities investments, including especially those based on past performance, they should at least keep firmly in mind that they’re not using a risk free rate.
M says
I have two big issues with the argument you presented.
First, the mixing of real and nominal returns skews your conclusion toward taking a 15 year mortgage. Vanguard’s forward return estimate is before inflation, while all mortgage rates are after inflation. A more apples to apples comparison would be 7.3% (5.3%+2%) total investment returns vs 3.5% mortgage rate. To have returns be 5% after inflation for 15-30 years would be exceedingly unlikely, although possible.
Second, if your goal is to compare ending net worth between the two strategies, it’s unnecessary to incur capital gains tax on the investments. Measuring net worth doesn’t require liquidation. If you want to compare the two strategies with the condition of a paid off home, you need to run the analysis for 30 years. At that point, taking the longer loan will only outperform further.
In my opinion, the only quantifiable reason to have a paid off or paid down home is to hedge against sequence of returns risk when drawing from a portfolio. Otherwise, it’s one of the ultimate risk off moves. Not bad, but not optimal.
Harry Sit says
Heading on Table C at the bottom of page 37 in the Vanguard report published in December 2018:
“Projected ten-year annualized nominal returns as of September 2018”
Nominal returns are returns with inflation included. Median for 100% equity in a globally balanced portfolio in that table is 5.3%. You are talking about before adding inflation. That’s not the case.
We will see how the numbers change when Vanguard publishes a new report.
M says
I stand corrected on the first point then. You might want to reword your summary “Vanguard’s median projected long-term return for a globally balanced 100% equity portfolio is only 5.3% before inflation.” I took that at face value.
Still, even if correct, those Vanguard 10 year returns are not 15-30 year returns, which is what matters for this question. After 30 years, both scenarios will give a paid off house and an investment portfolio. It’s highly likely that the 30 year mortgage person will have a larger portfolio, in addition to having more liquidity the entire time.
Harry Sit says
Like taxes, when people talk about before inflation they are usually talking about before subtracting inflation, not before adding inflation. To make it super clear, I will edit it to say nominal returns, with inflation included.
Yes investing the difference can come out ahead after 30 years. Just it doesn’t come out ahead for as long as 15 years may be a surprise to many people.
$iddhartha says
I chose a 30 year because when I started my career the market had just crashed, and I wanted to max out my retirement accounts while stocks were still low. My balance was over 90% stock index funds at the time.
$iddhartha says
I don’t look at the stock market as something that yields an annual return because of its cyclical nature. Ramsey’s advice is too simplistic for me.
Basically, if we are in a bear market and rates are low, I say borrow and invest the difference in your tax advantaged retirement accounts. However, if we’re deep into a bull market, it’s hard to argue the safe bet is to pay down a ~4% mortgage.
William Law says
Most people on these blogs will rebel at $iddhartha’s Oct. 4th comment because it describes a case of timing the market, but this is the right way to go about it. Although we can’t time the market exactly, we can determine the price of the market. If the price of the market is higher than the mean, we are more likely, if the future is at all similar to the past, to have a low return on a fully diversified portfolio. Why do we continually ignore this in our analysis? The future will not be like the past, but it is more likely to be like the past than not! In some cases, there are 15 year periods where the market is flat! How would you feel in that situation? Better to work hard and pay down the debt or consume less.
Lobo says
Thanks for this article. It kinda inspired me to build my own calculator. You can find it here – https://praveenlobo.com/blog/mortgage-loan-and-refinancing-comparison/
There is an error in your calculation. The first “side fund balance” cell J23 is not adding the interest for the first month. It would be $970.08. Once you fix it, the numbers you show in this article above change by a few dollars.
As you stated, the 30-year loan catches up eventually and over takes the 15-year loan around 22 year mark.
Harry Sit says
Thank you for confirming the results. I didn’t include the interest for the first month because mortgage payments are due on the first of the second month. That’s when the side fund receives its first deposit. Either way, it’s only a few dollars. It’s amazing that it takes 22 years for investing the difference to finally catch up. And that’s assuming someone consistently invests the difference. In real life, people are likely to slip, and some of the difference will go toward more spending.
LD says
Here is what I get when I modify some of the assumptions to make them more relevant to me and I believe to others too. I want to see which scenario results in more wealth after 30 years. So, assume that Bob has the $2,762 available each month for the next 30 years.
1. With the the 15 year mortgage, he has none of that left over to invest for the first 15 years, but has the full amount to invest for the second 15 years of that 30 year period. The $2,762 invested each month for the last 15 years at that 5% rate gives Bob $669,542 at the end of year 30.
2. If he got a 30-year mortgage and paid the $1,796 each month for 30 years, he has the difference of $948 that he invests each month over 30 years. And this time, at that 5% rate it gives him $772,861 at the end of year 30. Which is $103,320 more than with the 15 year mortgage.
So the 30-year wins.
I don’t deduct 15% capital gains tax because if Bob files as married filing jointly and has under $80k TAXABLE income (Line 15 on tax Form 1040, which is the case for me, especially after I deduct IRA contributions for me and my wife and my contribution to my employer retirement account which I max out at around $20k/year), so if he sells the investment assets a little at a time, he won’t exceed the $80k/yr and not pay capital gains tax. Also, if he does earn over $80/year, he can then leave the assets to his kids when he passes, paying no tax, assuming he leaves his kids under around $11 million or so, which is the tax-free limit/exemption for inherited wealth.