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Is the housing market finally cooling off? Not to judge by home prices, which rose about 20% in April from a year ago.

But many potential buyers are apparently giving up.

Total mortgage application volume fell by 6.5% last week from a week before, according to the Mortgage Bankers Assn.

That’s the lowest mortgage demand in 22 years.

Along with stubbornly high prices — fueled in part by well-heeled buyers willing to make all-cash offers or waive contingencies — mortgage rates are steadily rising as the Federal Reserve pursues a series of rate hikes to ease inflation.

A 30-year fixed mortgage now carries an interest rate of 5.4%.

“The purchase market has suffered from persistently low housing inventory and the jump in mortgage rates over the past two months,” Joel Kan, an MBA economist, told CNBC.

“These worsening affordability challenges have been particularly hard on prospective first-time buyers.”

Expect rates to keep rising and prices to remain stratospheric until more inventory hits the market.

And if you can’t make an all-cash offer for a house, there’s always trying to dazzle the seller with a heartfelt letter or a plate of cookies.

But good luck with that.