Mortgage Math Lesson: A Myth that Shouldn’t be Repeated

by JT McGee

What the world gets wrong about paying off mortgages.I found this article thanks to a helpful email from a Dave Ramsey fan hell-bent on making a great discussion of mortgage debt. I guess you know now why I decided to post a new disclaimer last week.

I figure I should discuss the topic publicly, since the information is incredibly off the mark.

ChristianPF, a personal finance blog with 1,000,000 times more reach than me, posted an article that says:

“Starting to pay off principal at any point during the term of the mortgage loan will help save you money, but start early on to make the most difference – the first half of the payments go toward interest. After the halfway point, the majority of your monthly payment goes to the principal.”

This makes zero practical sense. I say practical sense, because it is true if your only goal is to save money on a mortgage.

It is true is that the first few years of a mortgage payment are mostly interest because the first few years of payments will pay off the tail end of your mortgage debt. A mortgage is an amortizing loan.

Mortgage Math

To say that paying more than the minimum payment on your mortgage earlier and not later nets a bigger positive return is true in much the same way that a 5% return compounded for 20 years creates a bigger return than a 5% return compounded for 10 years.

Of course, in looking at this in absolute terms, a 5% return for 10 years provides more interest than a 5% return for 20 years. Five percent APY compounded monthly for 10 years works out to be 64.70%. The same return, compounded for 20 years, works out to be 171.26%.

If the finance world accepted similar thinking, the yield curve wouldn’t offer higher yields to longer term debt. Instead, longer dates would have lower rates. A 4% rate compounded for 30 years is far more than 100% compounded for one year. You should know that this isn’t how the yield curve works. It works in an opposite fashion, with longer terms naturally having higher rates of interest.

Bad Advice

The article also makes some other faulty generalizations about paying off a mortgage that ignore the benefits of capital structure—namely, the tax benefits of debt.  The article continues by saying:

Another argument against is that the extra money could be put into investments – but you’d have to make at least the same percentage return as your interest just to break even. Right now, that means playing the stock market or putting money into less-risky savings vehicles, such as CDs, which are barely paying 2% in some places. But don’t forget, these investments are taxable. Your mortgage interest can be used to reduce your tax burden.

Most anyone can find faults here:

  1. The tax benefits of debt allow you to generate lower rates on your borrowed cash than you would receive in paying back your mortgage early.  You do not need to make the same percentage return.
  2.  

  3. Comparing 30 year mortgages to 5-year retail CDs isn’t a very fair comparison.  More importantly, homes are not a risk-free investment, and neither is mortgage debt. Bankruptcy/lending laws protect your retirement, but not the whole of your home.
  4.  

  5. The mention of mortgage interest is contradictory. The author is saying that mortgage interest reduces your tax burden, but investment income increases your tax burden. Simple mathematics tells us that reducing a 15%+ tax burden (income) and increasing a 15% tax burden (investment income) by neglecting mortgage prepayments and investing the available cash is a net positive for our net worth. This is bad math right out of the Dave Ramsey playbook. See page 187 of Total Money Makeover where he says CPAs can’t do math.
     

    I can make this really simple. Effectively, what Dave Ramsey and the author are saying is that a grocery store should stop buying 24-packs of Coca-Cola since they rack up a $4.00 charge from the distributor for each case. That sounds fine and dandy, until you realize they receive $5.00 in revenue for each sale. If we focus on the $4.00 loss, this sounds like a pretty miserable deal. If we look at both sides of the transaction, we see that the grocery store makes $1. Dave Ramsey wants to capitalize on this way of thinking with his new book Entreleadership!

I’ll try my hardest to stick with the one point I want to hit: paying more on your mortgage early will net you a higher return in the context of paying off a mortgage, but not in the context of improving your net worth, which is the only real objective. If growing our wealth isn’t an objective, then I’m fine with assuming that the only perennially-available investment opportunity is our own debt. There is no shortage of financial commentators who have, directly or indirectly, come to similar conclusions.

Cynical and simple as it might be, this point is very important: prepayments will always earn you the interest rate you pay on the loan for the length of the loan term remaining. Making X% for 20 years is only better than making X% for 10 years if there are no opportunities to make X% in any other investment vehicle.

{ 13 comments… read them below or add one }

No Debt MBA June 13, 2011 at 09:21

I appreciate your efforts to add complexity and nuance to personal finance advice. I feel like often advice is dispensed without discussing the opportunity cost, tax implications or other details that provide more information but detract from the author’s ability to convey the situation as only black and white.

In that spirit I just want to add that your mortgage only has a tax benefit if you itemize and then the true benefit might only be to the extent the interest exceeds the standard deduction minus your other itemized deductions. There are situations where prepaying your mortgage early will make practical sense though it is certainly not true across the board. A full comparison of investment and refinance options, long-term and short-term goals, and someone’s current financial situation would be needed to make the call.

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JT June 13, 2011 at 16:30

The absolutes are one of the many reasons why I think it’s funny that there are so many people who discuss personal finance that think hiring a financial planner is a crazy idea. Paying for financial advice is the only way to get personalized advice.

Thank you for adding more information about taxes, especially the part on standard deductions. Interestingly, the only people who might cross the SD threshold regardless of their decision to prepay or not prepay their mortgage are people who could very easily afford to pay for financial advice.

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Norman June 13, 2011 at 09:27

I’ll give you another good reason I keep my mortgage. If I itemize on my Federal return then I can itemize on my state return. If I only take the standard deduction on my Federal return then I only get a one-thousand dollar deduction on my state tax return. That’s just how my state’s income tax is set up. I have 75% equity in my home with only 25% of the value mortgaged so I could pay it off, but by keeping my mortgage it saves me an incredible amount of taxes on my state tax return and also some on my Federal tax return. Now if they ever do away with the mortage interest deduction, we may have to talk.

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JT June 13, 2011 at 16:34

Hmm, this is really interesting. A $1000 standard deduction, even with state taxes being generally lower than federal taxes, makes a very big difference. In going through a short list of deductions, I can’t see very many that offer as much utility as the mortgage interest deduction. If they do get rid of it, then there isn’t much of an out for you, is there?

Thanks for sharing. Now I have even more reason to complain about a broken tax code. 😉

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Jeffrey Trull June 13, 2011 at 20:42

This is great, JT! I recently read this argument elsewhere, but it’s great that you went in such depth here to explain it. I think this topic is something that is often misunderstood, which is exactly why the bad advice you refer to is out there.

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JT McGee June 15, 2011 at 22:31

There is a severe shortage of tax related articles out there. Shame, too. I wish I were an accountant, I’m sure there are about 349580034530 things that never get talked about.

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LifeAndMyFinances June 13, 2011 at 20:58

I know there are quite a few variables that go into whether or not we should pay off our house, but I like the idea of owning something 100%. In doing this, I can guarantee that the bank will not be able to take it away. Plus, after it’s paid for, I will have a huge amount of discretionary income at my disposal. If applied toward investment, wealth will be had in a very short period of time!

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Jonathan June 14, 2011 at 09:28

Keep in mind that an even tougher shark than the banks when you don’t pay is the government when you don’t pay your property taxes – there’s no such thing as “owning it 100% so nobody can take it away.” Though I’m sure paying off your mortgage would be a good feeling.

But on to your second comment regarding building wealth with the free cash flow, you can typically build more wealth more quickly by holding onto your mortgage and investing the difference, assuming your mortgage is relatively cheap. I’ve got a 5% mortgage and there’s no way I’d pay it down early unless I felt I couldn’t safely invest excess money to return greater than 5%.

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JT McGee June 15, 2011 at 22:27

Good point on property taxes. We really don’t own anything related to real estate…we rent it.

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Evan June 14, 2011 at 10:17

Most of those pay off your mortgage regurgitated posts completely forget about liquidity concerns as well. Sure you paid off your mortgage in year 17, but what if disaster strikes in year 12 and you need a boat load of cash?

Isn’t it scary when you read posts (not so much Nicole’s because that one wasn’t that bad lol) and everyone in the comments agrees like sheep?

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JT McGee June 15, 2011 at 22:29

If disaster strikes in year 12 then you borrow money at twice the rate you received by paying on your mortgage early to access your equity. Yummy! Great point, though, liquidity is very important since most couples have 2 sources of income and nothing more.

Scary, yes, but everyone pretty much agreed here. LOL. We’re all sheep until we turn into Lemmings, am I right?

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Kellen June 14, 2011 at 16:19

@Evan – totally agree about the cash flow. I could pay off my student loans way faster, but then I wouldn’t be able to build an emergency fund (which I needed almost all of recently for some vet bills.)

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JT McGee June 15, 2011 at 22:30

Student loans are scary debt. I’d probably ignore the low rate on student loans since they can be discharged. I don’t like the idea of owing money to someone who can garnish my wages to get it back, even if I know 100% that I plan on paying it back as agreed.

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