Mortgage Payment Reduction Versus Rate Reduction

July 24, 2000, Revised August 28, 2011

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.

In Case 1 the interest payment is reduced by taking a smaller loan, in Case 2 by borrowing for a shorter period, and in Case 3 by paying a lower interest rate. But only case 3 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. The biweekly thus corresponds to interest payment reduction 2 above, where the payment is lower because the borrower has it for a shorter period.

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. See Is a Biweekly Mortgage Better Than a Payment Increase?

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.

“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?”“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.

## Distinguishing the Interest Payment 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.

*Base Case:*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.*: 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.*

Interest Payment Reduction 1Interest Payment Reduction 1

*Interest Payment Reduction 2*: Shorten the same $100 loan to one month. At the end of the month, you pay $101, with interest payments of $1.*Interest Payment Reduction 3*: 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 $.50In Case 1 the interest payment is reduced by taking a smaller loan, in Case 2 by borrowing for a shorter period, and in Case 3 by paying a lower interest rate. But only case 3 provides a clear benefit to the borrower. In the other two cases, the borrower pays less because he receives less.

## The Biweekly Mortgage

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. The biweekly thus corresponds to interest payment reduction 2 above, where the payment is lower because the borrower has it for a shorter period.

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. See Is a Biweekly Mortgage Better Than a Payment Increase?

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.

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