Final answer:
Ethan can afford a $600 monthly loan payment by deducting monthly taxes and fees from his max budget. Using the present value of an annuity formula, the maximum loan he can afford can be calculated, to which his $38,000 down payment should be added to determine the total house price he can afford.
Step-by-step explanation:
Ethan can afford $840 per month for a 30-year loan at a 5.5% interest rate, with $240 going towards taxes, insurance, fees, and maintenance. This means he can use $600 per month for the loan payment. By using a monthly loan payment formula or an online mortgage calculator, we can find out the maximum loan Ethan can afford. We will use the formula for the present value of an annuity: PV = PMT [1 - (1 + r)^(-n)]/r, where PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
First, we convert the annual interest rate to a monthly rate by dividing by 12: r = 5.5%/12 = 0.0045833. Then, we calculate the total number of payments over 30 years: n = 30 years * 12 months/year = 360 payments. Plugging these values and Ethan's monthly payment for the loan ($600) into the formula, we can solve for the present value PV, which is the maximum loan amount Ethan can afford.
To find out the total price of the house he can afford, we then have to add his down payment of $38,000 to the maximum loan amount calculated. Bear in mind, the actual maximum price may differ slightly due to rounding or additional costs such as closing fees that have not been accounted for in this basic calculation.