Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy.
Add the egg to the butter and sugar mixture and beat well until fully combined.
Mix in the yogurt and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined.
Fold in the chopped apples evenly throughout the batter.
Pour the batter into the prepared cake pan and spread it out evenly.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.