Question

After graduation, an engineer is trying to determine what the minimum gross monthly income would be necessary in order to purchase a $295k house. The lender requires monthly mortgage payments to be no more than 40% of gross monthly income with a maximum loan term of 30 years. The engineer is accounting for a 12% down payment and the interest rate of the loan to be 3.5% compounded monthly. The mortgage payment also includes a monthly $500 escrow payment.

Answer 1

To determine the minimum gross monthly income needed to purchase a $295k house, calculate the maximum loan amount and monthly payment. Consider the lender's requirement of mortgage payments not exceeding 40% of gross monthly income. The minimum gross monthly income can be calculated by dividing the monthly payment by 40%.

Step-by-step explanation:

To determine the minimum gross monthly income needed to purchase a $295k house, we need to consider the monthly mortgage payments. The lender requires the mortgage payments to be no more than 40% of the gross monthly income. The mortgage payment includes the principal and interest payment, as well as the escrow payment. We need to calculate the maximum loan amount first, and then calculate the monthly payment using the loan term and interest rate.

Step 1: Calculate the maximum loan amount:

Down Payment = 12% of $295k = $35,400

Loan Amount = $295k - $35,400 = $259,600

Step 2: Calculate the monthly payment:

Loan Term = 30 years = 30 * 12 months = 360 months

Monthly Interest Rate = 3.5% / 12 = 0.00292

Principal and Interest Payment = Loan Amount * (Monthly Interest Rate * (1 + Monthly Interest Rate)Loan Term) / ((1 + Monthly Interest Rate)Loan Term - 1)

Monthly Payment = Principal and Interest Payment + $500 (escrow payment)

Step 3: Calculate the minimum gross monthly income:

Minimum Gross Monthly Income = Monthly Payment / 40%