15-Year vs. 30-Year Mortgages (Part 2): Which is Better for You?

Tuesday, October 29, 2013 at 5pm
By John Friedman

Quick! Which would you rather have: a 30-year mortgage at 4% or a 15-year mortgage at 3.25%?

I thought I knew the answer — the 15, right? — until I recently spent a good deal of time what-if’ing the numbers. And what I found surprised me.

*  *  *

Let’s analyze this in terms of a $100,000 mortgage. Mortgages in that low-six-figure ballpark are rare for recent home buyers on the coasts, but they exist for recent buyers in, say, Iowa (a wonderful place and home to moi during my college years) and for older folks on the coasts who started with a smaller mortgage than people do today and/or who’ve had a decade or more to pay the mortgage down quite a ways. Plus, using $100k as our basic starting point is helpful because $100k is a nice round number, easily multiplied to arrive at your own mortgage reality. So, for example, if you have a $200k mortgage, when going through the numbers down below, you can just multiply everything by 2 and if you have a $2 million mortgage you can multiply everything by 20 because, as it happens, this scaling all happens in a linear fashion (which is often not the case in the financial wonk realm . . . ).

OK?

So here are some numeric couplets comparing the 15-year fully amortizing $100k mortgage at an annual interest rate of 3.25% to the 30-year fully amortizing $100k mortgage at an annual interest of 4%:

   Monthly Payments

The 15: Your monthly payment will be $702.67
The 30: Your monthly payment will be $477.42

 Total of All Payments Made at the End of 15 years

The 15: After 15 years you’ll have paid $126,480.60
The 30: After 15 years you’ll have paid $85,935.60

  Amount Owed at the End of 15 Years

The 15: After 15 years you’ll owe $0.00 — zilch — on the mortgage
The 30: After 15 years you’ll owe $61,541.64 dollars on the mortgage

 
So what’d’ya see?

Hmmm . . .

*  *  *

What I see is that, at the end of 15 years, two main differences have come about. The first difference is that, if you’ve gone with the 30-year, then you’ll still owe the bank $61,541.64, while if you’ve gone with the 15-year, your mortgage will be a not-so-fond memory in the rear-view mirror, paid in full, finito, done, expired. And paid in full is a big Big BIG deal!

The second difference is that, if you’ve gone with the 30-year, then you’ll have $40,545 in your little hands that you would not have in your little hands if you had instead gone with the 15-year. That is, with the 15-year mortgage your monthly payments would’ve been bigger by about $225 each month, or about $2,700 per year, which over 15 years is $40,500 (or, more accurately and using the numbers from the middle couplet up above: $126,480.60 minus $85,935.60 equals $40,545.00). So with the 30-year mortgage, you’ll have paid out $40,545 less to the bank.

And here’s the kicker: that $40,545 that your went-with-the-30-year-mortgage self didn’t pay to the bank can go a long way towards paying off the $61,541.64 that you still owe to the bank. In fact, if you’ve been earning a good return on each of the $225 chunks that you’re keeping on your side of the ledger rather than having given them over to the bank’s side, you can even come out ahead. And, in the meantime, you’ll have had more cash on hand, and, as we all learned during the Lesser Depression/Great Recession, all anew, cash equals power, in the sense that many, many problems can be solved with cash, and in the sense that being able to solve problems is to be powerful, while being a captive to problems is to be unpowerful.

*  *  *

So what kind of “good return” does your went-with-the-30-year-mortgage self need those $225 chunks to generate for you to get that $40,545 of not-given-to-the-bank-yet cash up to the $61,541.64 that you still owe the bank?

I recently updated and improved a tool that I’ve used for many years to help clients make mortgage decisions; it has lots of moving parts and many general applications, and I’m still working on some issues with it which I suspect are truly bugs, not features. But it is, I am pretty sure, mostly right . . .

This new and (mostly) improved mortgage comparison tool tells me that the growth rate at which the 15-year mortgage and the 30-year mortgage produce the same numeric picture at the 15-year mark is when you can generate a 5.826% annual return on each of your $225.25 chunks. So if you can generate higher returns than that, then you’d be better off numerically with the 30-year mortgage (because, aided by, say, a 6% annual growth rate, your $40,545, consisting of 180 chunks of $225 that you save each month for 15 years, will grow into more than the $61,541 you owe the bank at the end of those 15 years), and if you can’t generate higher returns than that, or if you’d spend some or most of the $225 monthly chunks rather than having it earn money for you, then you’d be better off with the 15-year mortgage.

Using a far simpler version of this analysis, the answer to the question of, “How much do I have to grow these $225.25 chunks I save each month for 180 months in order to have $61,541.64 at the end of the 180 months,” is 5.2619%. (The fact that this percentage is fairly close to — but not the same as — the 5.826% figure the grander tool came up with indicates that the grander tool has a thinko or two in it, but nothing too drastic.)

At any rate, if you can earn, say, 6% annually on your stored $225 chunks, and if you are good at storing those chunks rather than spending them, then you should be good-to-go golden, and numerically better-off, even, if you go with the 30-year mortgage.

Admittedly, a 6% annual return is not a rate that you can get on cash — certainly not right now in our 1%-on-cash-at-best world, but also during more normal interest-rate times — but a 6% annual return is a rate that you can often get on smartly designed stock/bond portfolios over a 15-year time frame. And if you fall short of that a bit? That is the cost of having the asset on your side, rather than the bank’s side, as in, you’ve got the cash and the bank doesn’t, and you’re not paying much to have it, either.

*  *  *

That, then, is the math (or should I say maths?). 

In my experience, though, the maths might not be the key determinant because, perhaps in the mortgage realm more than any other, the heart often overrules the head, as most people just really like the idea of being done with their mortgage, even if it does, by the analysis set out above, de-power them some, and often cost them some bucks to boot — especially at today’s incredibly low interest rates.

That last point really is key, in that, in the final analysis, what it comes down to for me is this:Yea, I’d love to have that 3.25% loan. But I’d love even more to have that 4% loan that lasts twice as long.

Which is to say this: we’ve been living for decades in a 6, 7, 8, 9 — even 10% world — so, sure, the three-quarters of a percent lower interest rate sounds good, but the 15 extra years sounds even better, as in, please, suh, I want some more.

P.S. for financial wonks. Yes, I am ignoring all tax issues — both the tax deductability of the bulk of most mortgage payments, and the tax includability of the returns on the $225 chunks. So let’s assume for the time being that they’re a wash, shall we?

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