Old Colony Beach Association President Douglas Whalen on Wednesday said the four beach communities that have been involved in devising a shared sewer system are looking for between $6 million and $10 million to bridge the gap between what residents agreed to pay and the ever-rising cost of construction. Whalen said the sewer system will cost residents of Old Colony Beach Association $2,300 a year, based on a 20-year note at 2% interest through the state. The associations governing Old Colony Beach, Old Lyme Shores Beach and Miami Beach, which are chartered neighborhoods and considered their own municipalities, approved the project at separate referendums. The public Sound View Beach came on after a townwide vote. Old Lyme Water Pollution Control Authority Chairman Richard Prendergast on Tuesday told members of the commission that local officials are looking for grants, not loans. “They need to lower the overall project cost,” he said. The effort to secure federal funding is the latest step toward installation of sewer lines to homes in the popular beach area that has been closely monitored for years by state environmental officials.