Step 1 :The problem is asking for several calculations based on a family's gross annual income. We'll start with the first question, which is to calculate the maximum amount the family should spend each month on a mortgage payment.
Step 2 :According to financial experts, a family should not spend more than 28% of their gross monthly income on a mortgage payment. So, we need to calculate 28% of the family's monthly income.
Step 3 :To find the monthly income, we divide the annual income by 12. The annual income is \$43,200, so the monthly income is \(\frac{43200}{12} = \$3600\).
Step 4 :Now, we calculate 28% of the monthly income to find the maximum monthly mortgage payment. This is \(0.28 \times 3600 = \$1008\).
Step 5 :Final Answer: The maximum amount the family should spend each month on a mortgage payment is approximately \(\boxed{1008}\).