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So, toss this around -- if we just pay cash for this house, it would be like getting 4% interest on our money (since no 4% mortgage) right?

No, avoiding interest paid is not the same as earning interest. It would actually be putting your cash into an illiquid asset that has the potential to gain at or near the rate of inflation, unless you are in an area that goes through another housing bubble, plus provide you with some dividend type income in the form of the rent net of the costs of maintenance, repairs, improvements, property taxes and insurance. Of course, since there are those additional costs and work, it's not as simple as sitting back and collecting dividends.

So, where else would we get 4% on our money (if we are not putting it in the stock market). So, my question I pose, is why get a mortgage at all? This is almost like finding a CD that pays 4%... isn't it?

Again, avoiding interest paid is not the same as 'earning' interest. At a 4% mortgage rate, if your rental property can't earn enough rent to cash flow to pay for the mortgage, taxes, insurance, maintenance, repairs and improvements, and still provide you some additional income for the work and effort you will be putting in, it's not a good property for a rental.

And that will keep your cash available to invest in other things, like say, target date bond etfs, where you know the rate of interest you will earn, and the term you will earn it for, and what year you will be getting your principal back, assuming you hold to maturity. You will be taking on a risk that some of the bond investments will declare BK and won't pay the full principal back, but even in a BK, bondholders often get some type of a payment or equity in lieu of the full principal repayment.

Or you can do like I am doing, and invest your money in dividend paying stocks, preferred stocks and individual bonds. Even with all of the calls that I have had recently, and having to re-invest capital at a lower rates, I am still earning about 8% on my invested capital (with a nice capital gain), and almost 6% on the current value. Yes, there are risks that some of the issuers will stop paying and/or go BK. But if you have enough cash to buy 'a couple' of rental properties, you should be able to create a diversified enough portfolio that you will limit your risk. Since you will have the rental income to pay the mortgage, you won't need to use the income like I am - to pay the mortgage on my residence - but instead, can use the income for current expenses.

Some would say we should get the mortgage, so we could deduct the mortgage interest

That's a side benefit, but not a reason to get or not get a mortgage. The reason to get a mortgage is to keep your capital available for other types of investments that can pay more than the mortgage is costing you, and/or have the potential to gain more than the rate of inflation. I would agree with others, if you have enough cash to buy 'a couple' of rental properties for cash, you are exposing yourself to the risk of lost purchasing power by holding so much cash. By putting that cash into illiquid rental properties, the gain on your asset (the rental house) is likely to provide a return that's going to keep your purchasing power about the same, once you cash out, and it should throw off some nice rental income, net of costs.

If you aren't willing to put your cash into investments, and instead, would leave it sitting in a CD, then this might be a decent investment for you. But I would strongly suggest that you are taking a significant risk of having an illiquid asset that can't be easily cashed in, compared to more easily marketable investments.

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