Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.

In a mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt.

In another bowl, cream together the softened butter and sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

Gradually add the dry ingredients to the wet mixture, mixing until just combined. Fold in the chopped apples.

Pour the batter into the prepared cake pan and smooth the top.

Bake in the preheated oven for 45 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.