I'm in the midst of a refinance of my mortgage, a very straightforward one because our equity in the house is over 80 percent of even a low-ball estimate of value. I was talking to the bank representative early in the process and she said, "So your monthly payment will be down from the current $1339 to $720."

I pointed out matter-of-factly that, of course, that large difference between those two amounts is due mainly to the fact that we would be taking on a 15-year mortgage rather than sticking with our original 15-year mortgage that has only about 10 years left on it. The best way to compare, I said, is to look at the saving in interest. I had in mind the 1.25-percentage-point difference between the old 5.5 percent and the new 4.25 percent. On a mortgage of about $100K, that's $1250 a year. When you take account of the tax treatment of interest, it still saves us, net of tax, about $800 a year.

Then she surprised me. "No," she said, "you might not pay less interest. You might pay more because you're paying interest for 5 more years."

I don't think she was playing to what she thought was my ignorance of basic finance, interest, and present value. She knows I'm an economics professor. I think it's that she didn't get it.

The incident reminded me of my "Buyer Beware Consumer Reports" that I appended to the article on Interest in the first edition of the *Concise Encyclopedia*.

David,

Would you be itemizing if not for the mortgage interest deduction? If not, the marginal tax benefit is your interest deduction (plus other itemized deductions that you would not have taken had you not itemized) less the standard exemption that you are forfeiting. Especially if your house is 80% paid off, the tax benefit may not be as large as it seems.

Hmm, I dont' see what's wrong with her statement. She was addressing interest, not anyone's preferences for present vs future value. As a practical matter I think her emphasis was correct. Most people focus too much on third-level issues like what is the interest rate, rather than second-level issues like how much interest are they going to pay, or top-level issues like how do they pay off the principal.

David Henderson, yes maybe you have the top two levels under control so therefore you can focus on the third. In this case you're the exception even for a professional economist.

Maybe I don't get it either, but it seems like she is correct.

I don't know much about the tax treatment of mortgage interest. I know it is supposed to be deductible, but how it effects any given individual might be a more complex issue. Maybe this is where I end up being incorrect.

To get to the point, you haven't mentioned mortgage amortization. If you've made one third of the payments on a fifteen year loan you've already paid more than 62% of the interest, assuming you have a standard mortgage. By refinancing you're likely to pay nearly double the amount of total interest on what you owe.

Perhaps the NPV of the new mortgage payments is lower (I don't know what discount rate you're using), but in nominal terms she seems to be correct.

Am I missing something?

It depends on your goals. If you wish to minimize your after-tax interest cost and you have a little nerve, consider doing what the wife and I are doing.

We are on a glide path to retirement and have a lot of free cash flow. We chose the ARM that would fully amortize during the initial fixed payment period at the maximum payment we could afford. If you stick to the plan you get a very low interest rate. In our case we went with the 5/30 and got a rate of about 3%. If we stick to the plan we will pay off the mortgage in 5 years. If we miscalculated our nerves of steel, we will have a balance when it reprices and run the risk of getting a high interest rate on the residual. We are willing to take the chance. Kind of a forced financial diet with the opportunity of burning the mortgage at the end as an incentive reward.

The only good way to do the comparison is to do the full calculation of the "after 5 years" point on the 15 year note at 5.5% versus all the interest on a 4.25% note. I don't have the energy to calculate it out, but it's probably close. (And I'm ignoring inflation, time-value of money, all those marginal whatevers, etc, although I probably shouldn't - they probably do make the 4.25% note better.)

Also, to figure out the _real_ value of the mortgage interest deduction, you have to deduct the standard deduction, which is something like $10.5K for someone filing married jointly, from the Schedule A total. Since you live in CA, you may well have enough deductions between state tax and property tax, charity, etc to itemize without mortgage interest, but if the rest are less than $10.5K, the real value of the mortgage interest deduction is 10.5K - (schedule A total - mortgage interest).

Free phones with 2 year contracts. Zero commissions on stock trades. Sugar quotas cost the government nothing. Much of successful marketing involves the bait-and-switch. In markets with free competition, these tend to be minimized, but there's always a base level of this because a large fraction of customers are susceptible given the complexities of many transactions. If you are stupid, people will take advantage of you.

The fact that he is paying for an addition 5 years is irrelevant to the the question of how much interest he is saving. Yes he may pay more interest on the loan but he would have access to principle to use today. He could use that additional cash flow to keep the payment the same. In this case, the loan would be paid off faster than 10 years. If he choses to spend the money that would have been paid on principle, he gets the utility of having that money today. It's neither a savings or a cost in dollar terms. The only thing that matters in determining how much he is saving is, how much interest is he paying, this year, on his current balance with the new loan compared to if he hadn't refinanced. He gains a choice with what to do with the rest of would have had to be the principle payments under the old loan. There is economic value in that choice as well. He could chose to amortize the loan over 10 years as before and have a smaller payment.

In order to determine his pre tax savings. All David has to do is compare the present value of his current mortgage payments using the new interest rate to the outstanding principal on his current mortgage.

The present value of the monthly payments on $100,000 remaining principal and a 5.5% mortgage discounted using 4.25% is approximately $105,950. Thus his savings from refinancing is $5,950. Since that savings is interest expense, one only has to apply his marginal tax rate to the savings to determine the after tax savings. (assuming that he in fact does increase his deductions by the full amount of the interest as previous commenters have stated).

Of course one should always do a calculation like this before doing a re-fi. It's the only way to compare the savings if there are closing costs or legal costs involved in the transaction.

Thanks so much for posting this! That about sums up my hatred of the finance industry, the mortgage component specifically: Not only do they make simple comparisons of alternatives unnecessarily complicated (see Scott Adams's "confusopolies"), the field is packed with mouth-breathers who don't have a clue how to make relevant comparisons themselves. Sigh...

I think she was misleading when she said "your payments would be lowered." But she was right when she said that total interest payments might go up, because of the longer term.

To compare a current mortgage to a refinance, you should keep as many things the same as possible. If you want to lower your rate, keep the term the same. You can always do this by making extra payments -- a zillion websites will help you figure out this number without needing to any math.

Then compare the new mortgage at the shortest term with the new mortgage at the extended term.

Working backwards a bit:

Paying $1339 for 10 years at 5.5 percent means you have about $123,500 left. [Total payments: about $161K.]

If you lower to 4.25 percent at the same term, then your payments drop to about $1265 a month, saving about $75 a month or $900 a year. [Total payments: about 152K.]

If you want to re-extend out to 15 years, you would have $929 a month. [Total payments: about 167K.] The total cost of the extended mortgage is about $15,000 more than the shortest term, or $6,000 more than your current mortgage.

So your total interest payments

dogo up if you re-extend your loan.