Final answer:
To calculate the minimum gross monthly income for purchasing a house, one must consider the loan amount after down payment, interest rate, loan term, and other mortgage-related expenses. For a $295,000 house with 3.5% interest rate, 30-year term, and extra escrow payments, the gross monthly income must be high enough so mortgage payments do not exceed 40% of it. The specific minimum income required can be derived by dividing the total monthly mortgage payment (including escrow) by 0.40.
Step-by-step explanation:
To calculate the minimum gross monthly income necessary to purchase a $295,000 house given the lender's requirements, we must first calculate the monthly mortgage payment. Since the engineer will make a 12% down payment, the principal loan amount would be 88% of $295,000, which is $259,600. The interest rate is 3.5% per annum, compounded monthly, and the maximum loan term is 30 years.
The mortgage payment also includes a $500 escrow payment which covers expenses like property taxes and homeowner's insurance, becoming part of the total monthly mortgage payment.
Using the formula for a fixed-rate mortgage, the monthly payment for the principal and interest can be calculated. Then, by adding the $500 escrow payment, we find the total monthly mortgage payment. Since the lender allows this payment to be no more than 40% of the engineer's gross monthly income, we can find the minimum income by dividing the total monthly mortgage payment by 0.40.
If the calculations show a total monthly mortgage payment of $1,664 (including principal, interest, and escrow), the minimum gross monthly income required would be $4,160 ($1,664 divided by 0.40).