1. **State the problem:** We need to find the new price after applying a 16% discount to the original price of 24. 2. **Formula used:** The new price after a discount is given by: $$\text{New Price} = \text{Original Price} \times (1 - \text{Discount Rate})$$ 3. **Apply the values:** $$\text{New Price} = 24 \times (1 - 0.16)$$ 4. **Simplify inside the parentheses:** $$1 - 0.16 = 0.84$$ 5. **Calculate the new price:** $$\text{New Price} = 24 \times 0.84$$ 6. **Multiply:** $$24 \times 0.84 = 20.16$$ 7. **Round to the nearest cent:** The new price is $20.16. **Final answer:** The new price after a 16% discount is **20.16**.