The difference between the average daily balance of the HELOC by depositing ALL your income into it - and using it as a checking account is what does the trick.The fundamental mathematical principle is not "paying extra on principal" it is REDUCING ACCRUED INTEREST - which results in more money going toward principal. 

Mathematically it would be better to ditch the lease and buy a good used car.Assuming you are keeping the car, then I see nothing wrong with converting the lease to purchase.

I have been in the rental business 15 years and I can prove to you mathematically you will come out ahead just putting cash in reserves.

These might not be the Dave Ramsey recommended routes but mathematically it can be shown that historically the S&P route will provide significantly better ROI than paying down a conventional owner occupied home loan.  

"Regression to the mean" is the mathematical term.Fix and flipping, OTOH, is a job.

@Bill Bonds found a website that shows more of the mathematical way of answering your questions.

The result is a file that acts as a mathematical sand-table, where you can present data in any way you wish - any way folks should check it out - gotta go, takings the kids ice skating.

It was not a mathematical cost calculation like footings, framing, roofing, etc. 

I made a big mathematical error I just corrected.I ran the numbers using 30 years of S&P 500 data. 

Hey,a very interesting historical analysis and model of rents in San Francisco (with data source on GitHub).For numerical guys such as @Brian Burke, @J. Martin, @Minh Le etc etcSome excerpts:"Overall [rents], they wen...