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First, I'm not a professional investor, so take my info as a starting point, not the final word.
There are two schools of thought, and you've seen them both. One, own your house outright, and use it as the investment for the money you spent on it. Two, borrow at a good rate and use the money you would have bought the house with as an investment to compound interest over a long period of time.
The first option has the advantage you just pointed out. You own the house. When things go horribly wrong, you don't run the risk of losing it (providing you pay taxes and keep it insured properly). There is a lot to be said for that, especially for the peace of mind and the flexibility it brings.
The second option carries more risk. If you get hit with a bad economy, loss of savings, and a loss of income all at once, you could lose the house, and even if you didn't, you could spend a big part of your savings paying the note on it, so that you don't really come out ahead, anyway. That's the risk side of the investment.
A lot of investment advisors can mathematically show you how option two CAN accrue a lot more money--as I said, two to three times more--over a 30 year period. Their arguments are very seductive, and I recommend finding a good book on the subject just to see the possibilities. These advisors will make you feel silly and naive for worrying about the little risk involved, and will show you graphs and charts about how even during times of depression your investments would in the long run balance out.
More cautious investors will say that there is still risk, and that the risk is not figured into the mathematical formula. Any business would consider the risk as a factor in such investments, so you should too. You are more solid and safe owning the house outright, and investing money not tied to your home. At the very least, you will have a home when all is said and done. The downside to that is the only way to cash in on a home is to sell it or borrow against it, so if it is your only investment, you may still wind up without cash, whereas with the mortgage option, you would have cash saved up--barring bad investments.
So basically, it depends on how much risk you want to undertake, and it depends on how you see your employability. If you have a profession with a pretty certain future of steady income, your risk would be better if you work in a field that could change, that could leave you making less, etc. It also depends on what you plan to do at retirement. Sell your home and travel? Live in your home until you die? The second option will require cash in addition to your home, so maybe the mortgage route would be better.
Also, keep in mind that if you aren't sure, but you have the money, neither decision is irreversible. You can pay off your loan at any time, or you can borrow against the equity in your home if you need. Taking one route and sticking to it, though, will probably give you the best returns.
Anyway, in other words, it really depends on you and what you want and what you can stick to over many years. I can't think of any good books right now, but Google or search your library or Amazon for books on personal investments, and you'll find someone with a title like "How you can retire a millionaire on an average income." If you need to know in a hurry, find a good financial advisor who can advise on both routes based on your goals.
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