April had a record collapse in Americans signing contracts to buy homes, a reflection of the broader shutdown of economic activity in response to the coronavirus outbreak. The National Association of Realtors said Thursday that its pending home sales index plunged 21.8% from the prior month to a level of 69, the largest decline registered in data going back to 2001. Pending home sales have fallen 33.8% from a year ago. The index is a barometer of sales over the next two months when the transactions are completed. There are signs that home sales have reached a trough and could rebound. Low mortgage rates have supported buyer demand, such that the government’s report of new-home sales showed a slight increase in purchases last month.