House prices are hitting new highs due to high interest rates and shrinking supply.

Home prices hit a record high in May, rising 0.7% nationwide from April on a seasonally adjusted basis, according to the Black Knight Home Price Index.

Prices, which have been rising since January, were 0.1 percent higher in May than a year earlier.

The sharp rise in mortgage interest rates last year cooled the overheated real estate market, but that didn't last long. Even with rates still high, home prices are rising again, and growth is accelerating with each new month.

"There's no question the housing market has popped in terms of home prices," said Andy Walden, vice president of research at Black Knight.

"Although the annualized statistic fell to 0.1 percent, the extremely strong 0.7 percent gain in May compared to''The previous month would have corresponded to an annualized growth rate of 8.9%, which means that the annual rate of home price growth will remain around 0% for a short time and then rise sharply in the following months,' Walden added.

Prices began falling last summer after the average interest rate on a 30-year fixed mortgage more than doubled in just six months. They continued to fall until January, when buyer demand returned but faced very limited supply. Buyers may have simply gotten used to higher interest rates.

"I said earlier this year that I believe 6% mortgage interest rates have been accepted as the new normal. I think we are now in an environment where 7% interest''mortgage rates are now the new normal, and people are accepting that,' Robert Reffkin, CEO of Compass Real Estate, said last week on CNBC's "Squawk on the Street" program.

By May, more than half of the nation's 50 largest housing markets, mostly in the Midwest and Northeast, have either returned to their previous peak prices or set new records.

Housing prices are still weak in the West and in many cities that are considered pandemic "boom towns," where many remote workers came in, finding new homes during the early days of Covid.

But those prices are starting to strengthen. Home prices in San Jose, California, fell 10 percent last year, but inventory is starting to dwindle again and prices are rising again. In May, they rose''by 1.4 percent, the second largest monthly increase on a seasonally adjusted basis. San Diego, Los Angeles, San Francisco and Seattle also saw price increases in May.

The exception, however, is Austin, Texas, one of the largest pandemic boom cities.

"Inventories there continue to exceed pre-pandemic levels, putting pressure on prices, which are down 13.8 percent below peak, the biggest gap compared with other markets.

In general, supply is shrinking again. New supply is down about 25 percent from a year ago as owners with mortgage interest rates below 4 percent are reluctant''are selling their homes and potentially paying a much higher interest rate for another home. The total inventory is now about half what it was just before the pandemic, causing a massive explosion in the real estate market.

Sales of used homes are still much weaker than they were a year ago, but that has less to do with less supply than with higher costs. The average price for a used home in May was $396,100, according to the National Association of Realtors. Redfin, a real estate company, reported last week that the median home price is now selling just above its starting price for the first time in nearly a year.

Trades are clearly making a comeback, even if affordability is suffering. As of June 22, with 30-year rates at 6.67%, to pay the monthly''s payment on a median-priced home with a 20 percent down payment and a 30-year mortgage requires $2,258 a month based on principle and interest, according to Black Knight. That's the highest such payment in history, up slightly from the $2,234 required in October.