Thanks very much for the replies and advice, it all helps, especially markci and Weedy. I do know that there are a lot of variables here, which is why I was looking for some way to plug in different numbers and “what ifs” to see what the effect would be.
markci got closest to the gross generalization that I was also looking for. Although in my specific case, when I factor in not only the loss of the tax deduction for paying mortgage interest, but also the additional tax on investment profits, the approximate break even number that I come up with is about 6%. In other words, I would need to be able to get more than a (consistent) 6% return from investing the $400K before that would be more profitable than paying off the mortgage. And even that is on the assumption that the mortgage interest rate doesn’t go up much. If it does, then obviously I would need even more return on the investment to be profitable. These days, that kind of return doesn’t seem all that likely.
On the other hand, the argument in favor of having some readily available cash is a good one. So, in case anyone cares, I think I’m going to hedge and pay off about half of the mortgage, then refinance the rest so that I can have lower monthly payments but still some money in the bank (or stock market).
On that note, I must confess more ignorance: If I do make such a large payment to my mortgage, do they recalculate the monthly payments, based on the now lower balance for the rest of the life of the loan? Or do they keep the same monthly payment and you just end up paying off the mortage sooner? I am assuming the latter, which is why I’m thinking I’ll need to refinance in order to get lower montly payments.