Need help with a PayOff Mortgage vs. Investing Equivalent Cash Balance

[pac_NW]

Folks - I am having a math fart this morning so thought I would just post the question to get the experts' responses.

Situation - the one thing holding back the RE in the FIRE path is the home mortgage. 
Assume the following - $400k balance on the mortgage.  Cash position is $500k.  Paying off the mortgage would lower expenses such that the remaining investments + cash are more than 25x the annual expenses.  Yeah, happy days...but...
Problem - having a hard time parting with the cash to payoff the mortgage because we like the cash position and the mortgage rate is 3.5% so money is cheap over the long haul.
Question.1 - What would you do in this situation? 
Question.2 - I would like to invest $400k in a safe investment vehicle to meet the mortgage & interest payments over time.  If I did that, I cannot figure out what return I would need.  It is not as simple as 3.5%, is it?  Or, should it be 3.5% plus an inflation factor of 3%.  What am I missing?

[eaw13749]

I am in a very similar situation.  However, a sound investment will produce 6% -8% in a good index fund. That's higher than the 3.5% your paying on the mortgage leaving you with a great net return.  In addition, you get to write off a portion of the mortgage on tax returns lowering your mortgage interest rate even further.  Investments are best left in the market making more money, and depending upon where you live, home values are not going up.  There's also security in knowing you have the money to pay the house off if an emergency should occur, or even sale the house.  That being said, I know there's less stress in being totally out of debt; however, it would take a lot of time to rebuild that kind of investment portfolio.  I hope this helps.  For me, I plan to pay my house off when the intereest is paid down and monthly payments are predominently principal meaning I have less tax advantage.

[CopperTex]

There's no guaranteed return when you put your money in the market.  If your house was paid off right now, would you refinance to invest the equity? The answer to that question usually reveals the answer to the original question.

[pac_NW]

Thanks to you both. I would not take the equity and invest it.  I would let me home continue to appreciate. On the investment, I have so much in the stock market presently, I am concerned about putting more out there.  Any one have expeerience with treasury notes?  I know the rate is not like stocks, but seemingly safer.