The old question about whether you should spend extra money on paying off the mortgage early has a new twist.

In a recent research report, economists for the first time posed a very specific and very common question: "If I have extra money for savings, should it go toward retirement or paying down my mortgage?" Though the report is riddled with dense jargon and algebraic formulas, the conclusion is crystal clear.

"About 38 percent of U.S. households that are accelerating their mortgage payments instead of saving in tax-deferred accounts are making the wrong choice," says the report by economists Gene Amromin of the Federal Reserve Bank of Chicago, Jennifer Huang of the University of Texas at Austin and Clemens Sialm of the University of Michigan.

And as a practical matter, that percentage is much higher, considering the ultraconservative assumptions the economists made. So easily half of all Americans facing this decision could be making the technically wrong choice.

We say "technically" because some people clearly derive a non-financial benefit from being debt-free, which is why they make a priority of paying off the mortgage early. Just because it's not mathematically rational doesn't make it a bad choice. But you should realize what that debt-aversion is costing you, and consciously decide if it's worth it.

"Instead of trying to maximize their wealth, people pay more attention to getting rid of their debt," Amromin said. "They are not a dispassionate comparer of dollars and cents. Somehow a dollar you owe is worth more than a dollar in your pocket."

The study found that U.S. households making the "wrong" choice by paying off the mortgage early cost themselves a collective $1.5 billion per year, forgoing a yield of 11 to 17 cents for each dollar misallocated. "The average household leaves about $300 on the table by not doing the right thing," Amromin said.

Consumers making the "right" choice to prepay their mortgage were largely those who didn't itemize tax deductions and those who already maxed out their retirement contributions, Amromin said.

Using themes from the research paper, below is advice on whether to invest for retirement in a tax-deferred plan--the only type addressed in the research--or pay down your mortgage.

Take the free lunch. You don't need fancy economic formulas to figure out free money is a good thing.

The first step is to invest in your company's 401(k) up to your employer's maximum match. In many retirement plans, you can invest 6% to get your employer's full 3% matching contribution. That's a 50% return before your investments even start growing. No amount of prepaying your mortgage will yield that kind of return.

The study, when it considered 401(k) matching contributions, found that 53% of consumers would be better off with retirement savings than prepaying the mortgage.

Decision formula. Once you've reached the employer's 401(k) match, write down three numbers. Two are easy: your mortgage interest rate and your federal tax rate.

The third number is how much you think the extra money will earn in your 401(k). This needs to be a very conservative number, such as the return on a government bond.

Why? Because each dollar used to pay off your mortgage early is a guaranteed return--you are guaranteed not to have to pay interest on that dollar.

So to be fair, its return should be compared with the 401(k)'s least-risky return.

The formula is to multiply your mortgage rate by 1 minus your tax rate. Compare that return to what you think you can get in the least-risky 401(k) choice. Choose the higher one.

For example, if your mortgage rate is 6 percent and your tax rate is 25%, the math is 6 times the result of 1 minus 0.25 (or 6 times 0.75). The result is 4.5%. That's your real mortgage rate when you consider the mortgage tax deduction. If government bonds are paying 5%, you should choose retirement investing over mortgage prepayment.

Decision formula revisited. Of course, most people don't invest so conservatively in their retirement plans, especially if retirement is decades away. History suggests investing in riskier bonds or stocks will yield a greater return over time than safe government bonds.

So forgoing extra mortgage payments and investing for retirement normally--that is, in mutual funds likely to yield higher returns than government bonds--only skews the choice toward 401(k).

ARMs and exotics. The study only addressed fixed-rate mortgages. The calculation is more difficult for adjustable-rate mortgages and "exotic" mortgages, such as interest-only loans, which have unconventional repayment schedules. You'll have to forecast what your mortgage rate is likely to be in the future.

But in the end, it might not matter much, Amromin said. Because as interest rates rise, paying off your mortgage will be more valuable, but so will investing in government bonds in your 401(k) because rates are higher. So it might be close to a wash. You could use the decision formula and probably be right.

Housing boom. People who have been sending in extra mortgage payments because they figure their house is appreciating faster than their investments in recent years are using misguided logic.

You get to keep the capital gains from appreciation on your house--up to $500,000 if you're married--regardless of how much principal you've paid off. Just because your house value appreciated 10% last year doesn't mean you earned 10% on your extra mortgage payment.

To download a copy of "The Tradeoff Between Mortgage Prepayments and Tax-Deferred Retirement Savings," go to www.nber.org/papers and search for working paper 12502.

By Gregory Karp

The Allenton (Pa.) Morning Call

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