Final answer:
To determine the price range of houses the Johnsons should consider, we need to find the loan amount they can afford. This can be calculated using the monthly payments they can make and the interest rate. The price range will be the range between the maximum and minimum loan amounts.
Step-by-step explanation:
The Johnsons have accumulated a nest egg of $50,000 that they intend to use as a down payment toward the purchase of a new house. To take advantage of the tax deduction, they want to invest a minimum of $2800/month, but their monthly payments should not exceed $3400 due to other financial obligations. Assuming a local mortgage rate of 5.5% compounded monthly for a conventional 30-year mortgage, we can calculate the price range of houses they should consider.
To determine the price range, we need to find the loan amount they can afford. The maximum loan amount is based on the monthly payments they can make and the interest rate. Let's say the loan amount is x. Using the formula to calculate the monthly payment of a mortgage, we can set up the following equation: x * 0.055/12 / (1 - (1 + 0.055/12)^(-30*12)) = $2800. Solving this equation will give us the maximum loan amount.
On the other hand, the monthly payment should not exceed $3400. Solving the same equation with a monthly payment of $3400 will give us the minimum loan amount.
The price range of houses they should consider will be the range between the maximum and minimum loan amounts.