Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x5 inch loaf pan.
In a medium bowl, sift together the flour, baking powder, baking soda and salt. Set aside.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Beat in the banana, then stir in the sifted ingredients until just blended. Fold in the pineapple.
Pour the batter into the prepared loaf pan. Bake for 55 to 65 minutes, or until a toothpick inserted into the center of the loaf comes out clean. Let bread cool in pan for 10 minutes, then turn out onto a wire rack.
Interesting Facts
Bananas are a rich source of potassium, fiber, and other essential vitamins and minerals.
Pineapple is a good source of vitamin C and manganese.
Banana-pineapple bread is a great way to use up overripe bananas.