WASHINGTON – US single-family homebuilding and permits for future construction fell sharply in September as higher mortgage rates suppressed demand, suggesting residential investment resumed its declining ​trend in the third quarter. Single-family housing starts, which ‌account for the bulk of homebuilding, dropped 4.6% to a seasonally adjusted annual rate of 859,000 units last month, the Commerce Department’s Census Bureau said on Tuesday. Single-family building permits decreased 4.0% to a rate of 845,000 ‌units. Mortgage ​rates have surged in recent weeks, with ⁠the 30-year fixed rate ⁠averaging 7.40% last week. …Slumping ‌sales have led to a glut of unsold houses on the market, further reducing the incentive for developers to break ground on new single-family housing projects. Despite the overhang of new ⁠single-family homes, there is a national housing shortage. …Residential investment rebounded in the second quarter, also reflecting renovations. The rise followed five straight quarterly declines.