Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x5 inch loaf pan.
In a large bowl, cream together the butter and sugar until light and fluffy. Stir in the eggs one at a time, beating well with each addition. In a separate bowl, stir together flour, baking powder, nutmeg, allspice and salt. Blend the flour mixture into the butter and egg mixture a bit at a time, beating well after each addition.. Stir in the banana and vanilla; mixing just enough to evenly combine. Pour batter into prepared pan.
Bake in preheated oven for 90 minutes, until a toothpick inserted into center of the loaf comes out clean. Cool the cake in the pan for 10 minutes and then turn out onto a wire rack to cool completely.