Step 1 :Given the principal of the student loan last month was \$21700, the annual interest rate was 15\%, and the method for calculating the minimum monthly payment was the finance charge plus \$30 plus 3.5\% of the principal.
Step 2 :The finance charge is calculated by multiplying the principal by the annual interest rate and then dividing by 12 to get the monthly interest. So, the finance charge is \(\frac{21700 \times 0.15}{12} = \$271.25\).
Step 3 :The minimum monthly payment is calculated by adding the finance charge, a flat fee of \$30, and 3.5\% of the principal. So, the minimum payment is \(271.25 + 30 + 0.035 \times 21700 = \$1060.75\).
Step 4 :Final Answer: This month's minimum payment is \(\boxed{\$1060.75}\).