Question: I enjoyed your recent Consumer Views column on fast mortgage payoff, but I think there was a mistake. The explanation about the first payment and additional principal-only payment was correct. The problem is in the explanation of the second monthly check: When you pay the $11.56 extra principal, you remove that payment; so, the next month when you pay $553.10, you are making the third loan payment, and the second check should be for $11.81 (not $11.56). Next month you would send your $553.10 and a check for $12.07. See the enclosed photocopy.--B.S.

Answer: About half a dozen of you raised the same point and, with my razor-sharp, toe-counting, mathematical mind, I bravely dodged the issue and simply tossed it back in the lap of Kenneth Scott, president of Boston-based Financial Publishing Co., who devised the mortgage prepayment plan a number of years ago.

For the latecomers, however, we should explain that the column dealt with a strategy for cutting a 30-year mortgage in half--to 15 years--by simply including with every month's regular monthly payment a second check for the * next* month's principal only. Here is the key chart and the explanation of the strategy (showing the first five months of an amortized 30-year mortgage for $50,000 at 13% interest and calling for monthly payments of $553.10) that triggered your comment:

Payment Interest Principal Loan Balance 1 $541.67 $11.43 $49,988.57 2 $541.54 $11.56 $49,977.01 3 $541.42 $11.68 $49,965.33 4 $541.29 $11.81 $49,953.58 5 $541.16 $11.94 $49,941.58

"And so on to the final, 360th payment. With the home buyer's first $553.10 payment, that is, he includes a second check marked 'Principal Only,' in the amount of $11.56, representing the principal due on the * second * month, which has the practical effect of reducing the length of his mortgage by one full, additional, month--not from 360 payments to 359 but from 360 to 358.

"With his second monthly check of $553.10 he includes a second check in the amount of $11.68 (the third month) and so on until, in the 15th year, he's completely paid it off."

So far, so good, but you--and other good readers--spotted what would seem to be a duplication that, over a number of years, would seem to throw a serious distortion into the whole thing. If I can paraphrase the point made in half a dozen similar letters (and several phone calls), it is this:

Everything is well and good with the first payment--you would, indeed, be paying the first month's principal and interest * and* the principal only, due on the second month's payment.

But isn't it true that by repeating this process the second month (paying the regular amount due that includes principal and interest * and* the principal due on the third month), aren't you paying the second month's principal * twice* ?

Wouldn't the correct procedure be to make the payment the first month as outlined above but, on the second month (since that month's principal has already been paid with the first month), "catch up" by skipping the third month's principal and prepaying the * fourth* month's principal along with your regular payment?

Except for getting terribly confusing, early in the game it sounds logical enough, and in our subsequent correspondence with Scott and a follow-up phone conversation, he concedes that, technically, you all have a point. But that it is immaterial and also involves a bit of sleight of hand because, "in effect, they're never making the second payment. What they are doing that first month, purely and simply, is paying the first month's principal and interest and the second month's principal, and they've dropped down a line. For them, of course, it's the second month of this strategy, but it's actually the third month on the schedule."

Like you, I'm sure, I find this a pretty exotic explanation, but the acid test--as Scott emphasizes--is that the procedure * works* just as outlined in the previous column.

"In the first accelerated payment," according to Scott, "you are paying the first and second principal. In the second accelerated payment you are paying the third and fourth, etc. If you were to continue this process to the end, in the 180th accelerated payment you would be paying the 359th and 360th principal payment. That's why you shorten the term to 15 years."

Under the month-by-month acceleration advocated by Scott, here is how the first six months (we've added a month to my original schedule) of the same $50,000, 30-year, 13% mortgage breaks down:

Payment Interest Principal Loan Balance 1 $541.67 $22.99 $49,977.01 2 $541.42 $23.49 $49,953.52 3 $541.16 $24.01 $49,929.51 4 $540.90 $24.53 $49,904.98 5 $540.64 $25.06 $49,879.92 6 $540.37 $25.60 $49,854.32

It should be noted, Scott adds, that in the figures given above, the real litmus test (as to whether it works or not) is not really in the breakdown between interest and principal payments--and the mechanics of how that breakdown is achieved--but in the "Outstanding Balance" column. Where, you will see, Scott continues, "at the end of month No. 1, I have reduced the balance to that scheduled for month No. 2 ($49,977.01); at the end of month No. 2, I have reached the balanced schedule for month No. 4 ($49,953.58); at the end of month No. 3, I have gotten to balance No. 6 ($49,854.32), and so on."

All of which is a little bit like trying to explain why the humble honeybee--the aerodynamic impossibility of it notwithstanding--still manages to fly very well, thank you.