Final answer:
To determine the total cost of a house you can afford with a 15-year mortgage, calculate the maximum loan amount you can afford using the present value formula. Subtract your down payment from the loan amount to find the total cost of the house.
Step-by-step explanation:
To determine the maximum cost of a house you can afford with a 15-year mortgage, you need to calculate the maximum mortgage payment you can make each month. Since you are only willing to spend 1/4 of your take-home pay on a house payment, you can afford a maximum monthly payment of $667.50. Using the formula for the present value of an annuity, you can calculate the maximum loan amount you can afford. The formula is:
PV = PMT x (1 - (1 + r)^-n) / r
Where:
- PV is the loan amount you can afford
- PMT is the maximum monthly payment ($667.50)
- r is the monthly interest rate (3.75% / 12)
- n is the total number of payments (15 years x 12 months/year)
Plugging in the values, you get:
PV = $667.50 x (1 - (1 + 0.0375/12)^-(15*12)) / (0.0375/12)
Solving this equation will give you the maximum loan amount you can afford. Once you have that, you can subtract your down payment of $15,400 to find the total cost of the house you can afford.