Step 1 :The problem is asking for the interest amount that Miguel will have to pay Julio. To calculate this, we need to use the formula for simple interest which is: Interest = Principal * Rate * Time.
Step 2 :In this case, the Principal is the initial amount of money that was borrowed or invested, which is $300.
Step 3 :The Rate is the annual interest rate, which is $6.6\%$ or $0.066$ in decimal form.
Step 4 :The Time is the length of time that the money is borrowed or invested for, which is 6 months or $0.5$ years.
Step 5 :We can plug these values into the formula to calculate the interest: \(Interest = Principal * Rate * Time = 300 * 0.066 * 0.5\)
Step 6 :Calculating the above expression gives us the interest amount.
Step 7 :\(\boxed{9.9}\) is the interest that Miguel will have to pay Julio.