The third group consists of those who can afford to put more than 20 percent down, perhaps even 100 percent, and must decide how much it should be? They are the subject of this column.

Assume Jacques has $100,000 of surplus cash, over and above the 20 percent he will put down. He can use the $100,000 either to make a larger down payment, or he can continue to hold it as an investment. His objective is to have the most wealth at the end of the period during which he expects to be in the house; or, if his wealth is the same at that point, he wants to select the option that will allow him to spend more over the period.

There is one simple rule that, if followed, will achieve this objective. Take the mortgage if the investment return on the $100,000 is higher than the mortgage rate. If the investment return is lower than the mortgage rate, use the $100,000 as an additional down payment.

This is an application of the standard investment rule, that the better investment is the one providing the higher return. Increasing the down payment is an investment in the mortgage you avoid, on which the yield is the mortgage rate you don't pay. For example, if you put $100,000 down instead of borrowing that amount at 6 percent, your return on the $100,000 is the 6 percent you would have paid on the mortgage. If the alternative use of the $100,000 is to keep it in the bank earning 3 percent, you do better using it to make a larger down payment.

Here is a simple example that will illustrate the principle. If Jacques earns 3 percent on his $100,000 of financial assets, his investment income is $250 a month. If the 6 percent mortgage he is considering is interest-only, it will cost him $500 a month. Net, he loses $250 a month.

If, instead, he uses the $100,000 to increase his down payment, he has no investment income or mortgage interest to pay, so his income from these sources is zero. He thus has $250 a month in disposable income that he would not have had had he taken the mortgage. He can live a richer life by spending it, or he can invest it and end up with more wealth, or some combination of the two.

An investment in mortgage avoidance makes good sense for elderly home buyers whose money is invested very conservatively. Their objective is more likely to be maintaining consumption rather than increasing wealth. So long as the mortgage rate exceeds the yield on their investments, consumption at a given level will deplete their wealth less rapidly if they avoid a mortgage.

Home buyers with excess cash who can earn a return above the mortgage rate may do better taking the mortgage. It may pay to take a mortgage at 6 percent if you can invest at 10 percent. I say "may" rather than "will" because any investments that promise yields above the mortgage rate carry risk, whereas the return on mortgage avoidance has no risk.

Younger buyers with excess cash are in the best position to assume the risks. If they take the mortgage and invest their cash in a diversified portfolio of common stock, they have an excellent chance of earning 9 percent-10 percent over a long period. Because they are young, they can take a long view and ride out short-term fluctuations in the stock market.

But they should have the stomach for it. If they are going to have a gastric upset every time the value of their portfolio drops, they should opt for the safe return on investment in mortgage avoidance.