The S&P CoreLogic Case-Shiller National Home Price Index, which measures home prices across the nation, rose 3.9% from a year earlier in September, compared with a 2.5% annual increase the prior month. The September level was the highest since the index began in 1987. Home sales have slumped from a year ago because higher mortgage rates have pushed buyers out of the market. But the decline in demand isn’t causing prices to fall, because the inventory of homes on the market is unusually low.