Cream the butter; gradually add the sugar, beating well at medium speed of an electric mixer. Add eggs, one at a time, beating well after each addition.
Combine flour and the next 5 ingredients; add to the creamed mixture, beating until blended. Stir in the apple and pecans.
Pour batter into a greased and floured 13 x 9 x 2 inch baking pan. Bake at 325 degrees for 50 to 55 minutes or until a wooden pick inserted in the center comes out clean. Let cool completely in the pan on a wire rack. Serve with Hot Buttered Rum Sauce.
Hot Buttered Rum Sauce:
Combine the sugar, butter, and half and half in a saucepan; cook over low heat, stirring occasionally, until sugar dissolves. Remove from heat, and stir in the rum extract.