Step 1 :Let the cost price of the coffee table be denoted by \(C\), which is \$415.
Step 2 :Let the markup be denoted by \(M\), which is 25% of the cost price. So, \(M = 0.25 \times C = 0.25 \times 415 = \$103.75\).
Step 3 :The retail price is the sum of the cost price and the markup. So, the retail price \(R = C + M = 415 + 103.75 = \$518.75\).
Step 4 :Final Answer: The retail price is \(\boxed{518.75}\) dollars.