Bloggers and Mortgage Interest. Really.
In the past week two popular personal finance blogs have posted remarkably convoluted pieces on the relatively simple concept of mortgage interest.
Last Friday Free Money Finance posted an excerpt from The Sound Mind Investing Handbook – A Step-By-Step Guide To Managing Your Money From A Biblical Perspective 5th Ed
If you have the choice between investing with a guaranteed 8% return and paying down your 6% mortgage, choose the investment because it will make you richer.
If you are thinking that my sentence is lacking because it doesn’t explain why you are richer and assumes an unlikely risk-free return, I am not unsympathetic. But my goal was only to replace the FMF post, and that post has both those flaws as well. And a few more.
In a 953 word meandering journey through the topic of saving in a 401(k) versus paying down a mortgage, the author demonstrates nothing so much as that revising his book four times did nothing to increase his knowledge of the subject. For example, he shows obvious discomfort with the effects of taxes. If I was in a kind mood I might say that he assumes his readers are easily confused by it, but I am rarely in a kind mood. He discusses a man who decides to save an additional $273 a month in his 401(k) as follows.
Now here’s where it can really get confusing. To construct an accurate picture, we have to recognize that Rob gets a second tax deduction—this time for putting money into the retirement plan. Rob’s $273 contribution is worth another $85 tax savings, which he could then also put into his 401(k). But then that $85 contribution would save him an additional $26 in taxes, which he could also put into his 401(k). But then that $26 . . . well, you get the idea. If Rob took maximum advantage of this, he could ultimately put $396 into his company retirement plan….
Rob’s marginal tax rate is 31%. $273 / (1 – .31) = $396. Is that really that confusing? Really?
The post discusses Rob and Mort, guys in identical situations with 6% 15 year mortgages and a little extra money to either pay the mortgage down early or invest in a 401(k) at 8%. Mort pays down the mortgage, Rob socks it away in the 401(k). After 15 years Rob is richer. The author has no idea why.
Although they had both saved the same amount in taxes which could then be invested for retirement, Rob’s savings were “front-loaded.” That meant he could put them to work in his 401(k) earlier than Mort could. In this way, Rob was able to take greater advantage of the tax-deferred compounding of profits. …. Mort’s retirement account later came on strong, but Rob’s head start was too great.
Uh, no. It’s a good guess, but it turns out that “front-loading” has nothing to do with it. The author could have figured this out by setting the 401(k) return at 6%, which would have made Rob and Mort equally rich after 15 years. That would have been easy to do in Excel, but something tells me this guy worked the example out with pencil and paper.
But at least the FMF post had basically the right answer. The same cannot be said of a post on a similar topic by Pinyo at Moolanomy this Monday. That post discussed refinancing mortgages with the aid of a higher interest short term loan. He is in favor of it. Really.
The post starts out with the reasonable observation that just because you can lower your interest rate, refinancing is not necessarily a better deal because of the closing costs you may have to pay. Okay, that’s a fair point. Then Pinyo runs the whole thing off the rails by comparing the old and new mortgages based on the total dollar amount of interest and fees paid over the life of the loans. That’s intuitive, and if my 11-year-old suggested it as an approach I would pat her on the back for going the in right direction. But it’s wrong, and anybody who has signed a mortgage, never mind given advice to thousands of others about them, should know better.
(The right way is to adjust the interest rate on the potential refi. You can do this using the mortgage calculator that Moolanomy’s post links to. Use the actual monthly payment and an adjusted principal amount, i.e. the amount of the loan less the fees, and solve for the interest rate. Figuring a precise after-tax rate is harder, since for tax purposes this adjusted rate is not what you pay, but it is a good approximation. ARMs are more complicated.)
To me, it’s not a lot of effort to demonstrate that the total interest dollars paid method is flawed. Would you rather have a five year loan at 20% or a hundred year loan at 2%? The hundred year loan has more than twice the total interest.
I’m hoping most of you saw immediately that the hundred year loan is a much better deal. You could pay it off in five years if you really wanted to. (But you shouldn’t want to.) The proper measure of the cost of borrowing money is the interest rate you pay, not the total dollars paid. Interest is rent on money. Would you rather pay $500 to rent an apartment for a month or $1000 for a year?
This is all apparently too subtle for Pinyo, who concludes in his post that rather than refinancing the entire balance of a mortgage at 4.5%, it might be preferable to refinance a portion with a three year 9% loan and the rest with a 4.5% mortgage. Really. Here’s another link if you don’t believe me.
Just to be clear, I am completely aware that what is appallingly obvious to me is not always obvious to others. (Two days after going up, the Moolanomy post has only one comment, the entire text of which is “Whoa…good post.”) Nor do I think that these two authors are exceptional. Sadly, I think they are typical. Which is a bad thing. Really.
Housing | Frank Curmudgeon | 
April 8, 2009 3:15 pm
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By Josh Yeager, April 8, 2009 @ 4:03 pm
So what if I’m thinking that your sentence is lacking because it doesn’t explain why I am richer and assumes an unlikely risk-free return?
That’s actually something that I’ve been wondering lately as I’ve read more stuff about personal finance. It seems like half the authors out there say you should invest your extra money because it returns 2% more than paying off your mortgage, and the other half say that you should pay off your mortgage first to eliminate the risk of losing your house if something bad happens.
By Rick Francis, April 8, 2009 @ 5:48 pm
I agree that Pinyo’s calculation is flawed- and it isn’t immediately clear when reading the article because it is subtle. The flaw is that he calculates the total amount of interest ignoring WHEN that interest has to be paid. If you had a bill of $1000 to pay wouldn’t you rather pay it in 30 years rather than paying it now?
I suspect some of your readers are still scratching their heads as to why the 2% 100 year loan is a lot better even though you pay more total interest, as I suspect few non-economists really understand the time value of money very well. I thought Wikipedia had a reasonable explanation isn’t too bad:
http://en.wikipedia.org/wiki/Future_value
-Rick Francis
By Chris, April 8, 2009 @ 5:54 pm
I commend you. The easy way is to provide personal finance fluff and act all happy all the time. However this has led to too many of these entrants that will on occasion (or more often) give horrible advice (as you reference). If there is the recognition that someone might call them out, then maybe we actually start to see higher quality articles in the pf blog space.
It reminds of the line: It’s hard work, but someone has to do it.
By SJ, April 8, 2009 @ 6:02 pm
“Rob’s marginal tax rate is 31%. $273 / (1 – .31) = $396. Is that really that confusing? Really?”
I LOVED that part… he proved the geometric series =)!!
“Interest is rent on money.” — I don’t think I’ve heard anyone just out and out say that… but so true…
By abdpbt personal finance, April 8, 2009 @ 9:12 pm
Frank, how do you find these posts? They make my head hurt–it hurts to bend my mind around how they get these numbers. I would have just looked at it and said, “No. No. That’s wrong.” I may not be the best personal finance blogger, but I have confidence now that I’m not the worst, either.
By GPR, April 9, 2009 @ 10:55 am
Whoa…good post.
By LG, April 9, 2009 @ 12:03 pm
Nice, GPR.
Love this blog.
By ObliviousInvestor, April 9, 2009 @ 12:58 pm
But wasn’t this whole financial crisis caused by people who never pay off their mortgage?
By Mr. ToughMoneyLove, April 9, 2009 @ 3:02 pm
Frank: Of course your financial analysis is correct but to be fair to Pinyo, he may thinking in a different space from you. Take for example your rhetorical question about renting an apartment for $500/month or $1000/year. If I only need an apartment for a month, I am not interested in spending an additional $500 to have it for a year, no matter how good a bargain it is (unless subletting is guaranteed!). Nor am I interested in a 100 year loan at 2% unless I have the right to prepay (because I am emotionally debt-averse.) These concepts were no doubt inherent in Pinyo’s thought process, which clouded the economic logic. But overall, I agree that the PF blogosphere is a fertile source of bad money advice. You can probably find some on my site as well!
By Frank Curmudgeon, April 9, 2009 @ 10:42 pm
Josh: First, sorry it took a day for your comment to show up. It got stuck in the spam filter somehow. If you have a risk-free 8% investment and a 6% mortgage (which is the example from the post) you should take the investment. But this would never happen in real life. What does happen is that you have an investment that is expected to average 8% (or more) and a mortgage that will definitely cost you 6%. Then the question is not so easy.
Rick: It’s not exactly a time value of money thing, although that’s a big deal not enough people understand. (And thanks for the link.) It’s really that the value you are getting for your interest dollars depends on how long you are getting to use the money, i.e. the interest rate is what matters.
Chris: Somebody’s has to do this, but it’s not exactly hard work.
Anna/abdpbt: Sorry about your head. These posts are not hard to find. Really.
GPR: How come it took a day for somebody to post that comment?
LG: It loves you too.
Oblivious: No, it was caused by AIG’s bonus scheme.
Mr. Tough: I did mention in the post that you could pre-pay the 2% loan. Generally, I think it is assumed that all consumer debt is pre-payable. And 2% is a very low investing bar to clear, even on a risk-free basis. And I will be reading your blog very carefully from now on.
Everybody: Sorry no post today. Confluence of Red Sox tickets and Passover.
By ObliviousInvestor, April 9, 2009 @ 11:14 pm
haha. Well played.
By Rick Francis, April 10, 2009 @ 6:17 pm
>It’s really that the value you are getting >for your interest dollars depends on how long >you are getting to use the money, i.e. the >interest rate is what matters.
Frank, I think reducing propositions to today’s current $ value (or cost) is the easiest way to compare them.
Here is an example with identical interest rates:
Say the prevailing interest rate is 3% and you are offered the option to take one of two loans:
#1 $1000 for 100 years at 2% (payment of $1.93/month)
#2 $1000 for 50 years at 2% (payment of $2.64/month)
Which would be better? The interest rate is the same so that doesn’t help. But if you have an amortization calculator handy you can calculate that
The payments for #1 could be covered by $733.42 earning 3% leaving $266.58 for you to spend as you wish.
The payments for #2 could be covered by $819.93 earning 3% leaving $180.07 for you to spend as you wish.
I would take #1 as it puts more in my pocket today.
-Rick Francis
By James Sheets, April 11, 2009 @ 2:40 am
Thanks for that, just what I needed kind of. A few modifications and Karl’s Mortgage Calculators I have a calculator I needed & saved me some time!
By gbevis, April 15, 2009 @ 8:32 am
Frank, your problem here is historical in nature. The title of the book clearly states “From A Biblical Perspective”, and much of the Bible was written before Zeno. Therefore, from a biblical perspective, no-one has solved his paradox, and one can never really solve the infinite series to get from $273 to $396.
By Neil, April 16, 2009 @ 6:16 pm
Maybe I don’t properly understand the tax implications – being more familiar with the Canadian tax system – but wouldn’t a 6% after-tax return on paying down the mortgage exceed the 8% pre-tax return on the investment? Or is this another one of those perverse incentive things that the American tax code does with its mortgage deductibility.
By Frank Curmudgeon, April 16, 2009 @ 7:13 pm
The 6% is pre-tax, since mortgage interest is tax deductible. If the tax rate were 25%, then the cost in after-tax dollars would be 4.5%.