You need to challenge a few of your assumptions.

First of all, the “back of the envelope” calculation cannot be applied to obligations like mortgages that have an end date. That formula is based on the assumption that we need our principle to survive, essentially, forever. Your mortgage, hopefully, will not last forever, and you therefore need less money to achieve FI than is implied by the “back of the envelope” formula in Scenario #1. This is obvious when you compare your calculated FI Goal to the amount you need for living expenses. That is, $600,000 - $390,000 = $210,000 which would provide enough money to buy the house outright with $60,000 left over. Obviously, you do not need this much money to carry a mortgage during FI.

Secondly, it looks like you are only considering taking out a mortgage after FI. Is there a reason for that? Why not buy a house with a mortgage as soon as you have a sufficient down payment, emergency fund, closing costs, etc.? In many ways, this scenario is the best of all worlds. For every year that you pay down the mortgage while working, the amount you need to save for FI decreases as your mortgage balance decreases. Meanwhile you have all of the emotional and, possibly, financial benefits of ownership sooner even than if you saved to buy the house outright.

Third, it looks like you might need to reevaluate some of your numbers. Consider what it actually costs you to rent, what it actually costs to own, and separate out the principle and interest portion of the mortgage from the tax and insurance portion. The tax and insurance should be considered a cost of ownership, since you will, presumably, be paying both your property taxes and your homeowners insurance both with a mortgage and without one. You should also consider the difference between the cost of ownership and the cost of renting as that increased or decreased cost could increase or decrease your living expenses in FI relative to now, and it will affect how much money you can put towards investing for FI after you begin living in your house.

Once you have isolated the principle and interest portion of your mortgage, use the formula,

PV = R*(1-(1.0034073)^(-m))/.0034073,

where R is the principle and interest payment, m is the number of months sill left on the mortgage after FI, and PV is the amount you need to add to your FI goal to provide for the remaining mortgage payments after FI. I can go into the technicalities of where this formula comes from if you’re interested, but this post is already quite long, so I won’t do that here.

Example: If your FI Goal based on living expenses alone (and remembering to take into account all costs of ownership) is $390,000, and you wait until FI to take out a 30 year mortgage with monthly principle and interest payments of $572.90, then you would do the following math,

PV = 572.90*(1-(1.0034073)^(-360))/.0034073 = 118,724.29

to find that $118,724.29 needs to be added to your FI goal.$518,724.29 would be your actual FI Goal which is less than in your Scenario #2.