The Math doesn’t make sense, but the heart says otherwise
I’m a math guy, or some would say a nerd. I know it doesn’t make math sense to pay off the house early when instead you could use the magic of compound interest to grow your wealth. I also know that if you did invest the money and watch it grow, in due time you could still pay off the house. I’ve even run calculations and for the nerds who read this, I have them at the bottom of this post. However, the math doesn’t account for the freedom, financial well-being, release, joy, and calm that comes from not having a mortgage over your head no matter how high of a net worth you have.
This story is mostly about allaying Mrs. Chocolate’s fear of having a mortgage over her head. She hates debt more so than she enjoys watching her net worth grow. Whenever I show her the increase in our 401k or IRAs she always comes back with, “but when will we have this house paid off?” Her safety meter far exceeds her risk tolerance or the need to accumulate more wealth. In essence, she values safety and security over market gains.
At some point, you have to move at the speed of your spouse. Her speed is slow and steady, pay off the house, be clear of any financial pitfalls and then invest. She’s probably going to still be risk averse, but she won’t have to worry about me or her losing our job and not being able to live in our house. Though she doesn’t like Dave Ramsey’s politics, she wants to be on that stage to scream that she’s completely debt free, to include her rental properties and her primary home. To the both of us, paying off the house is a significant step in our financial independence retire early journey. While we are at FIRE now, it will be more real, more tangible when the house is paid off.
So how fast can we pay this house off?
We’ve taken drastic and not so drastic steps to get there faster (but not as fast as humanly possible). We’ve stopped contributing to our 401ks. We each have over 600k in our accounts, we’re ok with letting compound interest increase them over time. Personal finance is personal, if we’ve decided to take this step. We do contribute the max to our Roth IRAs (so yeah, not fast enough). We’ve cut back on some spending, but do enjoy restaurants and taking occasional weekend getaways to destinations we like (again slow and steady with a pep in our step). Also, we plan on taking family vacations over the summer, go on our bi-monthly trips to the beach, and enjoy our anniversary trip to somewhere, depending on COVID restrictions. So while we’ve taken some drastic steps, we aren’t cutting back as much as humanly possible. The math nerds are screaming, cut back on restaurants and trips and put the money in your 401k. Believe me I’m with you.
When we decided to pay the house off early, we had a balance of $320,000 (orginal loan balance of $350,000 at a 3% interest rate for 15 years). We set a goal of paying the house off between 3-5 years. 36 months was unrealistic but we thought if we pushed ourselves, we could get closer to 4 years rather than 5. 36 months would average about 10,000 per month and so we built a model where we would make 72 payments of $5,000. We took a picture of the house and cut it up into 72 subsections. As of February 2021, we’ve paid just enough to own a small part of the grass (the bottom section is complete). We recently refinanced the home, which should help us keep the pace.
Paying off the house vs investing the money
Given the numbers above, we literally have anywhere between $3,000-7,000 per month to put towards this mortgage. For calculation sake, say we had just 5,000 per month, and instead of putting it toward the house, we decided to invest it instead and then pay off the house at a later time. But also consider the fact that you would still send your normal payment in and so the house would eventually get paid off. We choose to go with a 15-year mortgage and so worst case scenario is that the house would have been paid off in 2034.
Math 1
House gets paid at the end of 15 years, and the extra money is invested for the same 15-year period.
Math 2
House gets an additional $5,000 payment, gets paid off early and then the mortgage payment and the extra $5,000 are invested for the remainder of time.
Math 3
(hybrid plan) you pay the house for 10 years, invest for 10 years and pay the house off with some of the proceeds from investment.
I realize that you would incur a very large tax bill to pull the money out of your investments to pay the house off at the 10-year mark.
Oh, don’t forget the interest paid on the loan as well. What you can’t account for is the joy and freedom of having no mortgage for an extended period of time.
What will we do when we pay off our house?
1-Buy our dream car. See this post to find out more.
2-Go on a 2-week trip to Thailand, as depicted on the picture above.
3-Decide whether to go back to work. Literally. After our house is paid, we will be at or near FAT FIRE and can choose to work or not work. See the finances here.
*We also refinanced our house in January 2021 as a way to pay it down even faster. I've outlined actionable tips and lessons that can help you on your journey to refinancing. Check out the blog post here.
MATH NERDS:
As it turns out, paying off the house in 15 years would net a total return of $288,000. Enjoy the math. But we’re still going to pay it off in 5 or less years.
Total interest paid during the 15-year normal payment schedule: $85,066.43
Total interest paid during the accelerated payment plan of 5 years with the additional $5,000 in payment:$22,894.43
Total interest saved on the life of the loan if paid in 5 years: $62,172
Math 1:
Invest$5,000 over a 15-year period, with an 8% rate of return= $1,730,522
This is a lot of money. Factor in the total cost of interest payment over the same period ($85,066.43) and it would be a net difference of $1,645,455.57.
Math 2:
After paying the house off in 5 years, investing $5,000 + the normal mortgage payment of $2,417 ($7,417) over a 10-year period, with an 8% rate of return= $1,357,133
The net difference between $1,645,455.57 and $1,357,133 = $288,322
That’s a difference of $288,322 on the investment side.
Math 3 Hybrid 10-year scenario:
Investment value after 10 years=$914,952
Mortgage balance owed after 10 years=$134,513.09
Assuming there is a possible 35% tax hit as part of the withdrawal amount, you would need $207,000 to get the balance paid (I understand longterm investment is at 15% but your overall tax bill would be higher because of your tax bracket).
Total investment value after paying off house ($914,952 - $207,000)= $707,952
**** After paying the house off in 10 years, investing $5,000 + the normal mortgage payment of $2,417 ($7,417) over a 5-year period, with an 8% rate of return (and adding the starting balance of $707,952)= $1,599,717
Over the 10-year period, you would have paid $78,246.75 (compared to the 5-year payment of $22,894.43, that’s a difference of $55,352.32 (78,246.75 - $22,894.43)
Total return over the 15-year period is $1,544,364
The hybrid plan confused things just a bit because of the tax liability. It’s probably not worth the trouble.
Math 4 (no graph):
Invest long enough to have enough to pay the house and then invest all of the money.
Break even point is likely 6 years of payment and investment:
6 Years of investment value: $460,288
Balance after 6 years on the mortgage: $228,519.00
Total needed to pay mortgage with a 35% tax rate: $353,000
Total investment value after paying off house ($460,288- $353,000= $107,288
**** After paying the house off in 6 years, investing $5,000 + the normal mortgage payment of $2,417 ($7,417) over a 9-year period, with an 8% rate of return (and adding the starting balance of $107,288)= $1,387,545
Over the 6-year period, you would have paid $52,546 (compared to the 5-year payment of $22,894.43, that’s a difference of $29,651 ($52,546 - $22,894.43)
Total return over the 15-year period is $1,357,894
This is almost identical to just putting the extra $5000 towards the mortgage and paying it off in 5 years.
If you simply want to maximize your return, invest the money and pay off the house in 15 years.
If you want the peace of mind, pay it off as quickly as possible and then invest the difference.
None of the calculations account for the tax benefit of itemizing your mortgage interest payment or the tax liability of investing the money outside of tax-deferred accounts which would incur some type of capital gains tax on a yearly basis.
We’re still going to pay off the house early.
What about you, have you considered paying off your house early, why or why not?