Builders cut prices. The mortgage can swallow the discount.

The builder cut the price. The payment is still out of reach. Both can happen when the cost of borrowing moves against you faster than the price of the house moves in your favor.

Almost half the surveyed builders, 43%, were cutting prices in October. The average cut among those making one was 6%. On a hypothetical $300,000 price, that is $18,000 off.

Yet buyer traffic stayed weak. A cheaper sign was not getting enough people through the door.

Sales incentives were offered by 65% of builders, nearly two in every three surveyed. Sellers were reaching beyond the asking price to make deals attractive. The problem shows up when the buyer works out what the offer will cost each month.

The National Association of Home Builders’ overall confidence reading fell to 29, its lowest level since June 2012. That is the industry’s view of conditions for new single-family homes.

The discount can lose to the rate

Take an illustrative $300,000 loan at a fixed annual rate of 6%, repaid over 30 years. Principal and interest would be about $1,799 a month. That is the payment on the borrowed money, before the other costs of owning the home.

Now reduce the amount borrowed by 6%, to $282,000, and raise the rate to 7.5%. That’s not far-fetched: NAHB’s chairman said mortgage rates “have climbed well above 7% in recent weeks.” The principal-and-interest payment becomes about $1,972.

The smaller loan costs roughly $173 more each month.

Those examples use 360 equal monthly payments and the standard loan-repayment formula.

They illustrate the mechanism, rather than an actual offer or a current mortgage quote.

Property taxes, homeowners insurance, mortgage insurance, association charges and closing costs are outside those example payments. An actual comparison also needs those costs and the loan’s full terms.

What the builders are seeing

Builders were most downbeat about people showing up to buy. Buyer traffic scored 18, below current sales at 33 and expected sales over the next six months at 32. Together those survey components produced the confidence reading called the Housing Market Index.

On this index, 50 is the line. Above 50, more builders call conditions good than poor. At 29, far more builders say conditions are poor.

The price-cut statistic has its own boundary. It concerns surveyed builders; the average reduction concerns those reporting cuts. Neither figure measures every American home or establishes what happened to prices in the neighborhood where a particular buyer is looking.

NAHB points to borrowing costs, construction costs and labor constraints as pressures. It represents the building industry, and its explanation should be read with that role in mind. The survey cannot independently assign an exact share of the problem to each cause.

An incentive can move the cost around

A lower price, assistance with closing costs and help with financing address different parts of a purchase. One reduces the amount owed. Another reduces cash needed up front.

A financing benefit may change the payment for some period under its particular terms.

For a buyer, that creates specific questions: what changes, how long does it last, and what is due afterward? An offer that makes the first stage easier still needs to be affordable when a temporary benefit ends.

Builders are offering concessions while traffic stays weak. Completed sales and changes in financing costs will show whether those offers bring buyers back.