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Quick Math Check on Paying off Mortgage vs. Investing

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BiggerFishToFI:
Taking on a new mortgage at an interest rate of 4.625% 30 yr fixed. Plan is to invest all excess money in a taxable account, then likely try to pay the house off at or before FIRE to reduce sequence of returns risk and our total expenses (P&I on the loan) by ~30%.

So if I can expect at least a 4.625% TOTAL return (including inflation) in the market it does it always make more sense to invest over paying down the mortgage? I do not expect to itemize my taxes with the current tax laws.

Assuming I can invest an extra $4k per month or put it toward the loan, and assuming a 7% total return. If I invest I will (might?) have enough to pay off the loan around September 2023. If I put it toward the mortgage instead I will pay it off GUARANTEED in November 2023 (2 months later).

If I decide to keep the loan for the entire term (and stop contributing to the investment account ~September 2023), in 30 years I end up with 1.6M -  466k = 1.13M more in future dollars.

So does the question come down to --> Do I want the loan paid off at FIRE (in 5-7 years) or do I want to service the loan for the next 30 years and most likely end up with more money? It seems if  I want it paid off at FIRE it might make more sense to take the "guaranteed" (barring income loss) payoff as opposed to rolling the dice to pay it off just two months earlier. Not to mention having to sell a big chunk of investments to do so and the extra taxes that may bring in.

What am I missing that sways this more one way or the other? Thanks!

Other notes: Mortgage balance is ~300k and am maxing out all tax-advantaged space

One:
Sounds correct, you have to pay tax on the gains plus dividends on the investments but no tax on the pay down mortgage. I'd go with the %4.625 but I'm in the minority here. Could look at doing a combination of both. 

moof:

--- Quote from: BiggerFishToFI on October 10, 2018, 11:23:33 AM ---...
So if I can expect at least a 4.625% TOTAL return (including inflation) in the market it does it always make more sense to invest over paying down the mortgage? I do not expect to itemize my taxes with the current tax laws.
...
--- End quote ---
Compare nominal to nominal, then adjust returns based on expected taxation of those last dollars in the two scenarios.
Will the interest be deductible now?  If so the effective interest rate is lower, in my case it is no longer deductible (itemizing now longer makes sense for our family).  Taxable accounts in retirement are likely going to be at 0% if total withdrawals stays below 100k for MFJ.
So in my case I compare 3% rate on my 12 years of remaining loan to rolling the dice over the next 12 years of the market for the remainder of my loan, and over that time span I chose taxable investments over mortgage.  I ran these through cfiresim.com to compare, and it was clear that my safe withdrawal rate excluding the extra mortgage withdrawals went up by paying the minimum on my mortgage and investing.  Your mileage may vary.

steveo:

--- Quote from: One on October 10, 2018, 11:50:56 AM ---Sounds correct, you have to pay tax on the gains plus dividends on the investments but no tax on the pay down mortgage. I'd go with the %4.625 but I'm in the minority here. Could look at doing a combination of both.

--- End quote ---

I'd go with and went with the guaranteed 4-5% tax free returns. To me that is a no brainer.

Scortius:
A few quick thoughts. Long-term stock return over decades is closer to 10% than 7% without inflation. On the other hand, you're talking about investing only until you have enough to pay it off in full, and then simply moving all the investments into the mortgage principal. This is generally not how it's recommended to be done, usually you are better off going all or nothing. I would recommend holding it the full 30 years, but if you really want to pay it off in 12, then you're probably just better off putting it into your principal directly. Note, this is of course as you mentioned only if you're already maxing out your tax-advantaged accounts (and I would still recommend just holding the mortgage for 30 years).

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