If your current salary is $\$ 41$ per hour and you earn a $3 \%$ raise, what is your new hourly rate? Round your answer to the nearest cent.

Step 1 ：Calculate the new hourly rate by multiplying the current salary by \(1.03\)

Step 2 ：\( \text{new\_hourly\_rate} = 41 \times 1.03 \)

Step 3 ：\( \text{new\_hourly\_rate} = 42.23 \)

Step 4 ：Round the new hourly rate to the nearest cent

Step 5 ：\( \text{rounded\_new\_hourly\_rate} = 42.23 \)

Step 6 ：\( \boxed{42.23} \)