I Paid Off A Cheap Mortgage And It Was Mathematically Wrong

I paid off a 3.1 per cent mortgage early. There was about $180,000 left on it and eighteen years to run, and I wrote the check knowing it was the worse decision on paper.

Three separate people told me so, one of them at length. They were right.

The case against me

It is simple and it is strong. Money borrowed at 3.1 per cent, invested instead at a long-run expected return of something like 7 per cent, earns you the gap between the two, every year, on the whole balance.

Here is the honest version of that comparison rather than the flattering one. Put the $180,000 into the market at 7 per cent, keep the mortgage, and make the payment out of that portfolio every month.

The payment on $180,000 at 3.1 per cent over 18 years is about $1,088 a month.

Over those 18 years, $180,000 compounding at 7 per cent grows to roughly $608,000. The stream of $1,088 payments, had it also been invested at 7 per cent instead of being handed to the lender, would have grown to roughly $469,000. Take one from the other and the portfolio finishes about $139,000 ahead, with the house paid off on its original schedule either way.

I am not going to pretend that is a small number or that I did not know it going in. I ran it twice.

What the $139,000 bought

A fixed monthly obligation of $1,088 that no longer exists.

That is a bigger thing than it sounds. My required monthly spend fell by $1,088, which means the income I need to get through a bad year fell by $13,056.

I run a business. Revenue is lumpy and always has been. The month a client pays sixty days late, or a deal that was supposed to close in March closes in July, is the month that number decides what I do next.

There is a second thing, and it is the one that gets waved away as emotional. I sleep differently.

I watched a lot of people with perfectly sound spreadsheets make bad decisions in a frightening market because they were frightened. The risk a portfolio actually carries is not the standard deviation in the model, it is whether you sell at the bottom, and anything structural that makes you less likely to sell is worth money the model has no line for.

Where the math was wrong about me specifically

The invest-the-difference case has an assumption buried in it. It assumes you invest the difference. Every month. For eighteen years. Through a bad market, a slow quarter, a year with a new kid in it.

I know myself well enough to know I would have done it for about six years and then something would have come up. A kitchen, an opportunity, a bad stretch where the transfer got paused and never got unpaused.

The comparison everyone quotes puts a disciplined investor next to a paid-off house. The comparison that was actually on offer put me next to a paid-off house, and those produce different answers.

Where I would tell you not to do this

• If you have not captured the full employer match on your retirement plan. That is a guaranteed return that beats retiring a 3 per cent mortgage by a distance, and it goes first, every time, no exceptions.
• If you carry any credit card balance. A 3 per cent mortgage is the cheapest money you will ever be lent. A 24 per cent card is the most expensive, and paying the cheap one down while the expensive one runs is arithmetic backwards.
• If it drains your emergency fund. Home equity is not accessible quickly, and a paid-off house with $800 in the bank is a materially worse position than a mortgaged house with $30,000 in it.
• If you have a stable salary and secure employment. The income-volatility argument that convinced me is much weaker for someone whose paycheck is the same size every fortnight, and the case for investing instead gets correspondingly stronger.

The part I would do differently

I paid it in one lump, and that is the piece I would change.

Writing a single check moved my cash position from comfortable to thin in an afternoon, and there were about five months afterwards where one slow quarter would have been genuinely uncomfortable. I bought the security of owing nothing by temporarily giving up the security of having something.

The better version is to pay it down across eight or twelve months, keeping six months of fixed costs in the bank the entire time, and to make the final payment only once the emergency fund is whole on the other side of it. Same ending, and you never spend a night in the gap.

One mechanical thing to settle before you start. Call the servicer and ask specifically how extra payments get applied. Some apply them to principal automatically. Some hold them as a prepaid future payment, which does nothing to the balance and therefore nothing to the interest. Ask in writing, then check the statement the following month to confirm the balance actually moved.

Decide which of your debts is emotional

Write down every debt you have, with the balance and the rate. Then next to each one, write what you feel when you look at it.

Most will produce nothing. A 3 per cent car loan you never think about is a line in a spreadsheet and should be treated like one.

One or two will produce something real. The student loan for the degree you did not finish. The card from the year everything went wrong at once. The mortgage on a house you bought at a price that still makes you wince.

Those are not irrational for producing something, and paying them down ahead of schedule buys you a thing that exists even though it will never appear in the comparison.

Do it with your eyes open though. Run the number first, write it down, then decide whether the feeling is worth that amount of money. Mine came to $139,000 and I would sign for it again, and the only part I would insist on is that you know your own number before you sign for yours.