Preheat the oven at 180 degrees.
Prepare a 7 inch cake pan for baking-brush the sides with oil/butter and line with parchment paper.
Mix the baking powder, flour and salt in a small bowl.
Cut the apples into one inch thin slices.
Melt the butter and set aside to cool.
Whisk the eggs in a bowl, once they are frothy add the sugar.
Cream both together until they are pale.Add the vanilla extract and the rum.
Trickle the liquid butter in the egg mixture incorporating all the while with a spatula.
Mix the flour mixture with the liquids in two batches.Add all the apples in the batter.The batter will look more of apples than a cake batter but thats alright.
Spoon it in the prepared pan and bake in preheated oven at 180 degrees Celsius for 40 minutes.
Test with a skewer or a knife,if it comes out clean the cake is cooked, if not bake for another 5 minutes.
Let it cool for 10 minutes before transferring on a wire rack.