15 year or 30 year mortgage?
Mortgage rates are hitting all time lows and several people are wondering whether to refinance to 15 year or 30 year Fixed Rate Mortgage (FRM). As with any personal finance choice, there are two types of answers to this question: a psychological answer based on behavior/emotion such as “I will have peace of mind by paying off my mortgage sooner” and the other answer is based on the math and data. This article focuses only on the mathematical answer.
It’s a common knowledge that the 15 year mortgage reduces the overall interest paid due to lower interest rate and lower loan term. However, the monthly payment is significantly higher compared to the 30 year mortgage. Many people who can afford the higher monthly payment, go for the 15 year mortgage to save the overall interest paid. Is that the best choice mathematically? The data in this article clearly shows that the best choice is to “go for a 30 year mortgage and invest the monthly payment savings in the stock market”. Please bear with me to explain with an example before judging this statement.
Let’s take an example of someone with the following loan terms and can afford the 15 year FRM payment.
The proposal is to go for the 30 year FRM, but pretend that it is a 15 year FRM by investing the $22,416 savings annually into a low cost S&P 500 index fund such as VFIAX for 15 years. After 15 years, stop investing and instead withdraw $34,980 annually from the investment account to pay the mortgage until year 30. After year 30, whatever is left in the investment account is a net gain because of this strategy!
One might wonder if this approach is risky because of the exposure to stock market volatility. The risk is greatly reduced because of these three factors:
(1) Investing in a broadly diversified low cost index fund.
(2) Having a 15–30 year long-term investment horizon.
(3) Dollar cost averaging while investing as well as while withdrawing.
One might wonder if “sequence of returns risk” will fail this approach if the withdrawal happens during the bear markets. I ran the numbers for hypothetical cases of someone applying this strategy for various years we have the data for S&P500 index, i.e. for 94 years between 1926CE — 2020CE that witnessed several recessions and bear markets. Even though the “past performance does not guarantee the future returns”, it is interesting to note that all of the sixty-five 30 year intervals have significant positive account value at the end of the 30 year term! Whether the 30 year duration was 1926–1955 or 1991–2020 or any other duration in-between, one would have surplus money left in the investment account after paying off the mortgage as shown in the chart below.
The chart above shows the surplus left after paying off the mortgage in various years. The number corresponding to pay-off year 2020 is $1.25 million, i.e. the person with the example loan terms applying this strategy for the 30 year loan duration 1991–2020 would have $1.25 million surplus after paying off the mortgage.The lowest surplus is $1 million for the 30 year interval 1955–1984 and the highest surplus is $8 million for the interval 1970–1999. The surplus is 1.33x to 10.6x times the original loan amount, which is pretty significant considering that one didn’t have to spend any extra out-of-pocket to achieve these gains. Anyone interested in the raw data used for this chart can refer to this sheet.
Note that the long-term capital gain taxes during the withdrawal phase is not accounted here for simplicity. However, those taxes are counteracted by the higher tax deductions one gets from the 30 year FRM.
