Interest expense on a $237K mortgage at 3.625 a year is $8,591. Investment income on $237K at 3.625 a year is $8,591. Before taxes, it is a wash. Personally, I would not sleep much better at night paying off a mortgage if the financial impact was zero......
That's only for the first year. Every year the investment grows and earns more interest, while the interest cost on the mortgage drops and becomes home equity principal. If you pay cash for a house the investment only earns appreciation, which the mortgaged house also earns. Each year you pay the house with progressively inflated dollars, while the investment grows to match and exceed inflation. This is a very old and tired argument. The reasons to pay off a house when rates are so low are entirely emotional. There is no financial incentive. I'm not discounting the validity of the emotion. It has a fixed cost to it that many find acceptable.