National Interstate Corp., the provider of insurance to the transportation industry, accepted majority-owner American Financial Group Inc.’s sweetened bid of $32 a share to buy the stock that it doesn’t already own. The offer values National Interstate at about $660 million, according to a statement Monday. Investors in the target company will get a one-time special dividend of 50 cents a share before the deal is completed. The combined value of $32.50 is 44 percent more than the Richfield, Ohio-based company’s closing price on March 4, the last trading day before American Financial made its initial offer of $30. American Financial, led by co-chief executive officers Carl Lindner and Craig Lindner of the billionaire Cincinnati family, is seeking to simplify ownership of National Interstate and expand the parent company’s bets on trucking, heavy machinery and moving and storage. The buyer provides property-casualty coverage, including crop, aviation and construction insurance, in addition to some retirement products. The deal “enables us to make an additional investment in a business we know well,” Carl Lindner said in a separate statement. Special Committee American Financial has a stake of about 51 percent in National Interstate after selling stock in the subsidiary for $13.50 a share in a 2005 initial public offering. Following the Lindners’ March offer, National Interstate established a special committee to review the proposal. The parent company boosted the offer to $30.75 in June, and the panel rejected that price two days later. American Financial said July 6 that $32 was its “best and final offer.” National Interstate climbed 3.9 percent to $32.16 at 9:43 a.m. in New York trading. American Financial was unchanged at $72.90, leaving the stock up 1.1 percent since Dec. 31. The deal is expected to be completed in the fourth quarter, according to the statement. Morgan Stanley is the financial adviser to the special committee of National Interstate shareholders that reviewed the bid. The group relied on Willkie Farr & Gallagher LLP for legal advice. The buyer used Skadden, Arps, Slate, Meagher & Flom LLP. Alan Spachman, the founder and former CEO of National Interstate, has agreed to vote his shares in favor of the offer, according to the buyer’s statement. He controls about 20 percent of the stock not already owned by American Financial.