Is this comparison of a 15-year vs. a 30-year mortgage reasonable?

Question

My wife and I are thinking about purchasing a home at some point in the next few years, which has got me reading about mortgages and trying to think through what would make the most financial sense for us.

I have read the other questions & answers on this site regarding 15-year vs. 30-year mortgages, and they are all very helpful. However, what I'd like to do is take a concrete example, assume we go with a 15-year or a 30-year mortgage, and see where either choice takes us. To that end, here are some basic values to start with:

• Let's say we take out a mortgage for $350k
• Interest rates in our area according to bankrates.com are 3.11% for a 15-year mortgage vs. 3.94% for a 30-year
• According to some online mortgage calculator I found, this means that our monthly payments would be $2,436 for a 15-year mortgage vs. $1,659 for a 30-year

Let's imagine that in both cases we allocate the same amount we'd be spending on a 15-year mortgage for the first 15 years, then allocate the amount we'd be spending on a 30-year mortgage for the next 15 years. In the 15-year mortgage case, we'd be paying only our mortgage for the first 15 years, then we'd be investing money in the stock market for the next 15 years. In the 30-year case, we'd be paying our mortgage + investing the difference for the first 15 years, then only paying our mortgage for the next 15.

So our monthly allocations would look like:

+----------------------------------------------------------------------+
| Term    | Monthly allocation 1st 15 years     | Next 15 years        |
|---------+-------------------------------------+----------------------|
| 15-year | $2,436 towards house                | $1,659 invested      |
| 30-year | $1,659 towards house, $777 invested | $1,659 towards house |
+----------------------------------------------------------------------+

So at the end of 30 years, we would have spent the same amount of money on a combination of our mortgage + stock market investments. In the 15-year case the breakdown would be $438k towards the house and roughly $300k invested; in the 30-year case it'd be $597k towards the house and roughly $140k invested (but invested earlier). Either way, we'd be looking at a total of ~$740k.

Obviously our house would be worth the same in either case. By my calculations our investments in these two scenarios would look something like this, depending on the return we got from the stock market, after 30 years:

+----------------------------------------------+
| Return | 15-year mortgage | 30-year mortgage |
|----------------------------------------------|
| 2.5%   | $329k            | $236k            |
| 5.0%   | $390k            | $398k            |
| 7.5%   | $465k            | $670k            |
+----------------------------------------------+

So if our returns from investing in the stock market were only 2.5% over the 30-year period, then we'd have been better off going with the 15-year mortgage. But if our returns were greater than 5%, then the value of our investments after 30 years would be greater if we went with the 30-year mortgage.

Does this overall comparison make sense? I'm not asking for anybody out there to check my math. Mostly what I'm wondering about is the soundness of my comparison.

I like that this approach is apples to apples in the sense that it lets me compare the same monetary amount put in over 30 years to the total value gotten out at the end. On the other hand, it's obviously unrealistic to say that with a 15-year mortgage we'd invest nothing for the first 15 years or that with a 30-year mortgage we'd invest nothing after the first 15 years. But maybe that doesn't affect the overall analysis.

What significant factors have I completely missed? Do these numbers look at least semi-reasonable (are they in the right ballpark)?

There are always bound to be other considerations, e.g. the psychological satisfaction of having a house fully paid off, the discipline required to invest a fixed amount every month, etc. But for the purpose of this question I'm interested in looking at the decision in purely financial terms.

Answer 1

I think your analysis is very clear, it's a sensible approach, and the numbers sound about right to me.

A few other things you might want to think about:

Tax

In some jurisdictions you can deduct mortgage interest against your income tax. I see from your profile that you're in Texas, but I don't know the exact situation there and I think it's better to keep this answer general anyway.

If that's the case for you, then you should re-run your numbers taking that into account. You may also be able to make your investments tax-advantaged, for example if you save them in a retirement account. You'll need to apply the appropriate limits for your specific situation and take an educated guess as to how that might change over the next 30 years.

Liquidity

The money you're not spending on your mortgage is money that's available to you for other spending or emergencies - i.e. even though your default assumption is to invest it and that's a sensible way to compare with the mortgage, you might still place some extra value on having more free access to it.

Overpayments

Would you have the option to pay extra on the mortgage? That's another way of "investing" your money that gets you a guaranteed return of the mortgage rate. You might want to consider if you'd want to send some of your excess money that way.