Home prices have been soaring over the past year, the sharpest gains in seven years; construction activity is picking up nicely. Both trends have been driven in no small part by a steady drop in home mortgage interest rates, which have made homeownership too good a deal to pass up for millions of Americans.

But the trend on rates has reversed abruptly in the past few weeks. This chart shows the average rate on a 30-year fixed-rate mortgage since the start of 2011; the spike on the right shows an increase from 3.4 percent to 4.1 percent since May 1.

Source: Bloomberg/BankRate

So what will become of our precious and long-awaited housing boom? Is it a fragile, delicate flower about to be crushed by the boot of higher rates? Or is the housing recovery now resilient enough that there’s no need to fear? Economists at Goldman Sachs have run some numbers through their models of how the housing market works and have come up with some promising answers.

The Goldman economists, Hui Shan and Marty Young, start with an analysis built on home affordability. Take the median household income in the United States ($50,000), assume a buyer has a 20 percent down payment and that they can only afford debt payments equal to 25 percent of their income. This chart shows how much house they can afford at any given mortgage rate:

It also shows an initial reason for some optimism. At a 30-year fixed-rate mortgage rate of about 3.8 percent, the typical American homebuyer can afford a $279,000 house. That’s 45 percent more than the current price of houses. That suggests that affordability isn’t the thing holding Americans back from buying houses (instead, it may be such factors as tight credit standards, difficulty building up a down payment  or lack of confidence in future job prospects). It also implies that slight increases in the mortgage rate shouldn’t completely undermine the improvement in the housing market; the thing to watch is not rates per se, but what happens on those other factors that are drags on would-be homeowners.

And that bodes particularly well:  As we wrote last week, the rise in rates over the past month appears to be driven primarily by improving economic prospects. If that’s the case, even as homes become a bit more expensive, they will be doing so at the same time those other restraining factors dissipate. So rising mortgage rates, if they’re rising for good reasons, could actually be net positives for the housing market if they result from more people having jobs and being confident in their prospects.

Will higher mortgage rates kill the housing market? Maybe not!.