Preheat your oven to 350°F (175°C). Grease and flour a loaf pan.
In a mixing bowl, whisk together the flour, baking powder, and salt.
In another bowl, mix the sugar, yogurt, oil, eggs, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 50 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.