To find the total amount that Amy paid for the box of chocolates, we need to follow these steps:
- Calculate the amount of the discount.
- Find the purchase price after applying the discount.
- Calculate the sales tax on the discounted price.
- Add the sales tax to the discounted price to find the total amount paid.
Step 1: Calculate the discount. The original price of the chocolates is $14 and the discount is 15%.
\[ \text{Discount} = \text{Original Price} \times \text{Discount Rate} = 14 \times 0.15 = 2.1 \]
Step 2: Calculate the purchase price after the discount. Subtract the discount from the original price.
\[ \text{Discounted Price} = \text{Original Price} - \text{Discount} = 14 - 2.1 = 11.9 \]
Step 3: Calculate the sales tax on the discounted price. The sales tax rate is 4%.
\[ \text{Sales Tax} = \text{Discounted Price} \times \text{Sales Tax Rate} = 11.9 \times 0.04 = 0.476 \]
Step 4: Calculate the total amount paid. Add the sales tax to the discounted price.
\[ \text{Total Amount Paid} = \text{Discounted Price} + \text{Sales Tax} = 11.9 + 0.476 = 12.376 \]
Rounding to the nearest cent, the total amount Amy paid for the box of chocolates is:
\[ \boxed{12.38} \]