Preheat the oven to 350 degrees. Grease a 8 1/2 X 4 1/2-inch loaf pan.
Cream the sugar and butter together in a stand mixer until creamy.
Beat in the eggs and bananas.
Whisk together the flour, baking powder, and salt. Add gradually to the wet ingredients.
Scrape the batter into the pan. Bake the bread for 1 hour, or until a toothpick or fork inserted into the center comes out clean. Cool slightly, then unmold.