We currently rent in CA, but want to buy a place so that we begin to pay down principal, accrue tax benefits, and lock in a monthly housing payment in a rising rental market. 

In the year it was accrued (even if on cash basis)?

We keep this in a high interest savings account so that it's accruing at least a little bit.

For time being it’s an asset of company then after they have the tenure it can xfer to them and they pay a tax on the delta but it acts as a nice bonus they can cash out or let it keep accruing at about 4% per year

Ironically, they were so good at raising funds that it caused serious problems in their business.Because they raised funds so readily (real estate celebrity owner) they had serious pressure to acquire new deals to put the capital to work as the preferred returns are constantly accruing.

Then, once you pay it down you repeat the process - take another $10K chunk over to the HELOC and pay it down.I think the main thing people don't understand is that the interest on your mortgage is accrued over time, but it's not OWED, it's SCHEDULED.

@V.G Jason as I understand it, and still doing research, but you fund your whole life cash value life insurance policy and use that as a savings account accruing 3-5% on your money.

Up to this point the investor has received 100% of the cash flow because 4% accrued from year 1 and didn't get caught up until year 3.As to waterfall structure, hurdles can be based on IRR or Cash on Cash. 

Any additional rescue or improvement funds provided by you during ownership would be preferred and premium, meaning they are paid back first and accrue at 8-10 ish % interest. 

You get your rental property, can withdrawal contributions and conversions at any point tax and penalty free, and your profits accrue tax free (which is a huge benefit over time).