The sales tax charged on noncommercial boat purchases in New Jersey is set to be cut in half from 7 percent to 3.5 percent early next year under a measure that won Gov. Chris Christie’s final approval yesterday. New Jersey will also cap the total amount of sales tax that can be charged on a boat or yacht purchased in the state at $20,000. The sales-tax reductions are the result of a bipartisan compromise hammered out by Christie, a second-term Republican, and Democrats who control the Legislature. The goal of the new tax policy is to give a boost to a state boating industry that’s been hit hard in recent years by recession and superstorm Sandy.