[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)|
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% before inflation. That includes the effect of a higher projected return for international equity. For a 100% U.S. equity portfolio, Vanguard’s median projected long-term 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.
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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