Mortgage math does not add up.

[bilmar]

I am new to the idea of retiring early and see it a s a real possibility this year.

I am having trouble with the math of the question " Should I pay off the mortgage now"

I have $100K left at 4%, $1k mo for 10 yrs. I have the cash to write a check tomorrow to pay it off without any penalties or tax hits.

Most financial sites say keep the money and invest it at higher rates than the mortgage. This makes perfect sense.


But, when I run this from the expense perspective I see a completely different picture:

If I pay off today then my expenses go down $1k mo or $12K yr - forever
In doing so I have lost $100K of investable money which @ 4% is 4K yr.
This suggests that I save $8k yr by paying off

I know that 4% is way low today and this is a simplistic comparison but the numbers seem compelling - what am I missing?

Bill

[Dragline]

Well, the assumption on the investment side is that you would be making more than 4% on the money, starting today -- say assuming an 8% investment return, you would be making $8K per year off the invested money and only paying $4K per year on the mortgage.

The problem then becomes one of a certain 4% return (the paydown option) versus an uncertain but potentially much higher future return in the investment option.

And there is an immediate emotional component to it that many be more significant than the financial component -- i.e., do you personally value the secure feeling of paying off the debt more than the "but I'll be missing out on higher returns" feeling that is attached to the investment option? No right or wrong answer there.

Since it will only be possible to know if you made the "right" decision in hindsight years later, I would usually some of both in these circumstances -- i.e., take part of the money and pay down the mortgage and invest part of the money.

[Sclass]

Hi,

Your reasoning makes sense the way you asked the question.

Looks like a good deal for the bank right?

But I think your simple interest return of $4k /yr is like comparing apples to oranges. Only banks get to charge compounding?

If you take into compounding the numbers should be closer. I think they should be the same because you're kind of making a loan to yourself or buying a 4% bond and paying out the interest and principle.

All this and what Dragline said.

[M]

Out of curiosity, does the 1k /month mortgage payment include property taxes and home owner's insurance? Even if you pay off the mortgage, these other things may not go away, so your real savings may be significantly less. than 1k /month..

[bilmar]

Thanks for the tips.
Once I considered the magic of compounding then the picture changes :

I used 4% because that seems to be the safe return number to use for projections. Given that I can pay off the mortgage any time I want, I see no reason not to use a current rate so lets go with 8% as suggested

My $1K mo ( P & I only) is a fixed loan @ $12K yr

If I invest $100K @ 8% then I am still down $4k at the end of year one ( $8K return vs $12K paid to bank)
But by year 10 with compounding and a monthly reduction of $1000 to pay the mortgage pay I have $38K left over vs paying off the loan today.

Obviously the market could tank and returns shrink but if they do I can still take my money and pay off the loan anytime and not 'lose' anything.

Bill

[Tyler9000]

It's important to remember your mortgage payment stays constant while the remaining principal and term do not. Each year you have a decision to make on whether keeping the mortgage is worth it over simply paying it off. Let's use Firecalc to demonstrate.

A $160k mortgage at a 4% interest rate has an annual principal + interest payment of $9156. Plugging that $160k amount into Firecalc with annual spending of $9156, no inflation, and a 30-year horizon gives a success rate of just over 95%. That means that historically theres a 95% chance that investing the mortgage balance will make more money over 30 years than paying it off. The mortgage makes a lot of sense.

With 15 years left on the same mortgage, the balance is $103k. Plug that in with the same spending and a remaining 15-year duration, and the success rate drops to 82%. Still not bad, but also no longer a sure thing.

With 5 years left, the balance is $40k and the success rate is 53%. Still worth it?

So unless you continually refinance to a new 30-year mortgage, the risk of the investments lagging the mortgage increases over time. One can still argue the odds are in your favor, but at some point (especially for someone who is already FI) the risk may seem unnecessary. That breaking point is up to you.

[Ego]

Another factor to consider is the way a mortgage is amortized. If the original mortgage was 15 year and you've got 10 left, then the majority of your monthly payment is going toward interest. OTOH, if it was a 30 year mortgage with 10 left, then you have paid the bulk of the interest and most of your monthly payment is chipping away at principal. It makes more sense to pay off in the early years of the mortgage than it does in the later years since those first payments are weighted toward interest vs. principal.

[henrik]

If I pay off today then my expenses go down $1k mo or $12K yr - forever

The difference in expenses (compared to the keep-paying-as-normal scenario) is relevant only for the duration of your mortgage contract, not forever. I.e. after 10 years, your expenses will have gone down $12k/yr whichever way you decide. An investment of the same size will, theoretically, keep paying into year 11 and beyond.