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July 24, 2000
�A
lender in our area is promoting a biweekly payment program by claiming that the
reduction in interest payments under the program is the equivalent of a
reduction in interest rate. Can
this be right?�
Lenders
promoting biweekly payment plans often blur the distinction between interest
payments and the interest rate.
Suppose
you currently spend $24 a month to buy 12 pounds of flour at $2 a pound.
Your spending could be reduced to $12 a month if you purchased only 6
pounds, or if the price was reduced to $1 a pound.
If
someone told you that these were equivalent ways to reduce your flour spending,
you�d pass it off as nonsense. But
when exactly the same argument is made regarding mortgages, you aren�t so
sure. And judging from my mail,
your confusion is widely shared.
The
interest rate on a mortgage is the price of money, which is analogous to the
price of flour. The interest
payment is the rate times the amount borrowed, just as spending on flour is the
price of flour times the amount purchased.
What
makes the mortgage (or any financial claim) a little different is that the �amount�
has two dimensions: the initial
loan amount and how long you have it. But
this does not affect the basic principle that was so obvious in the case of
flour: Reducing interest payments by reducing the amount borrowed is very
different from reducing interest payments by reducing the interest rate.
Here are some illustrations.
Case
1: You borrow $200 for two months at 1% a month.
At the end of month 1, you pay $2 interest.
The interest payment is calculated by multiplying the interest rate times
the loan balance -- .01 times $200 = $2. At
the end of month 2, you again pay $2 interest, along with the loan balance of
$200. Total interest payments on
this loan are $4.
Case
2: Reduce the loan amount to $100. The
interest payment is now .01 times $100 = $1 for month one, and another $1 for
month 2, for a total of $2.
Case
3: Shorten the same $100 loan to one month.
At the end of the month, you pay $101, with interest payments of $1.
Case
4: Reduce the interest rate on the $100 loan to 0.5% a month. At the end of
the month, you pay $100.50, with an interest payment of $.50
In
Case 2 the interest payment is reduced by taking a smaller loan, in Case 3 by
borrowing for a shorter period, and in Case 4 by paying a lower interest rate.
But only case 4 provides a clear benefit to the borrower.
In the other two cases, the borrower pays less because he receives less.
The
amount borrowed on a mortgage depends on the initial loan amount, and on how
long you have it, which in turn depends on how rapidly you repay it.
Thirty-year mortgages that convert to a biweekly payment plan add an
extra monthly payment each year. This
pays off the loan more quickly, reducing total interest payments.
Lenders typically charge for conversion to a biweekly.
There
is nothing wrong with a biweekly plan, if you understand what you get for your
money. Your interest payments
decline because you reduce the amount borrowed, but that�s not equivalent to
reducing the rate.
Furthermore,
if you want to reduce the amount borrowed by paying off early, you can do it
without the cost of setting up a biweekly plan.
Just add to your regular monthly payment an amount equal to 1/12 of the
payment.
Consider
a biweekly plan if you want to pay off your loan faster but don�t have the
discipline. A biweekly provides the
discipline, and that is all it provides.
Copyright
Jack Guttentag 2002
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