Step 1 :Let's denote the price of the old computer as \(P_{old}\) and the price of the new computer as \(P_{new}\). Given that \(P_{old} = \$410\) and the new computer is 15% more expensive, we can express \(P_{new}\) as \(P_{old} + 0.15 \times P_{old}\).
Step 2 :Substituting the given value into the equation, we get \(P_{new} = \$410 + 0.15 \times \$410\).
Step 3 :Calculating the value, we get \(P_{new} = \$410 + \$61.5\).
Step 4 :Adding these values together, we find that \(P_{new} = \$471.5\).
Step 5 :Final Answer: The price of the new computer is \(\boxed{\$471.5}\).