Final answer:
To determine how much you can afford to borrow with a monthly payment of $400 at a 2.88% interest rate for a 15-year fixed-rate mortgage, use the loan payment formula. After computing your borrowing capacity, calculate the home price you can afford by accounting for the required 20% down payment.
Step-by-step explanation:
If you can afford monthly payments of $400 and current mortgage rates are 2.88% for a 15-year fixed-rate loan, we can use the loan payment formula to determine how much you can afford to borrow. This formula considers the monthly interest rate, the number of payments (term of the loan), and the payment amount to solve for the principal amount.
The formula for the monthly payment (M) for a fixed-rate mortgage is M = P[r(1+r)^n]/[(1+r)^n - 1], where P is the principal amount of the loan, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (loan term in years multiplied by 12).
By rearranging this formula to solve for P, you can calculate how much you can borrow based on your $400 monthly payment capacity. To factor in the 20% down payment, we would calculate the full purchase price of a home by taking the loan amount you can afford and dividing by 0.80 (since you will be borrowing 80% of the home's price).