Reader Dan left this comment on my post last week 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.
According to Bankrate.com, the Annual effective interest rate for a 4% mortgage, after taxes are taken into account is 2.76%.
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 California. He can get a 30-year fixed rate mortgage at 3.5% or he can get a 15-year fixed rate mortgage at 2.875% at comparable closing costs. The 30-year mortgage requires a payment of $1,796 per month. The 15-year mortgage requires a payment of $2,738 per month.
Bob decides to take the 30-year mortgage and invest the difference of $942 per month in a “side fund.” Because Bob pays more interest on the 30-year mortgage, Bob gets more tax deductions. Bob also invests the tax savings into the side fund. When Bob finally sells his house, he liquidates the side fund, pays the capital gains tax, and uses the proceeds to pay against the mortgage.
We assume Bob earns 5% on his side fund. For simplicity’s sake, we assume the side fund is perfectly tax efficient. All gains will be long-term capital gains at the time of sale.
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 worse off than just taking out a 15-year mortgage. Only at the end of 15 years does the side fund finally build up enough to overcome the higher loan balance.
What’s going on? How come borrowing tax deductible 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 12 years?
The answer lies in the higher rate on the 30-year mortgage. Although a 0.625% difference between the 15-year rate and the 30-year rate looks small, it’s applied 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 * 0.625% = $2,500 more. Investing $942 a month plus tax savings at a higher return will only earn about $200 more. Paying $2,500 more for the privilege to earn $200 extra on investments is a losing proposition.
Over time, as the side fund builds up, the extra investment return starts to over come the extra cost on the mortgage. But it takes a long time, more than 10 years.
The assumptions in the calculation actually favor the “borrow 30-year and invest the difference” strategy in many 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 the tax savings are invested. If they are not, the side fund will be much smaller. We also assumed perfect tax efficiency. In reality the side fund will have to pay some taxes along the way.
Even with all the favorable assumptions, for a $400k payoff the difference is also very small. After 15 years, Bob is better off by about 2.5%. Not 2.5% per year, 2.5% total over 15 years.
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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