The Johnsons have accumulated a nest egg of $27,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $1300/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $1600. If local mortgage rates are 9.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses they should consider? (Round your answers to the nearest cent.)

Question

The Johnsons have accumulated a nest egg of $27,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $1300/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $1600. If local mortgage rates are 9.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses they should consider? (Round your answers to the nearest cent.)

Answer 1

To determine the price range of houses the Johnsons should consider, we need to calculate the loan amount they can afford based on their monthly payment range and the mortgage rates.

Let's start by calculating the loan amount they can afford with the lower monthly payment of $1300.

Step 1: Convert the annual interest rate to a monthly interest rate.
Monthly interest rate = (1 + annual interest rate)^(1/12) - 1
Monthly interest rate = (1 + 9.5%)^(1/12) - 1 = 0.0078177 or 0.78177%

Step 2: Calculate the loan amount using the monthly payment of $1300 and the monthly interest rate.
Loan amount = Monthly payment / [(1 + monthly interest rate)^(number of months) - 1] * [1 + monthly interest rate]
Number of months = 30 years * 12 months/year = 360 months
Loan amount = $1300 / [(1 + 0.78177%)^360 - 1] * (1 + 0.78177%) ≈ $209,288.50

The Johnsons can afford a loan amount of approximately $209,288.50 if they choose the lower monthly payment of $1300.

Now, let's calculate the loan amount they can afford with the higher monthly payment of $1600.

Step 1: Calculate the loan amount using the monthly payment of $1600 and the monthly interest rate.
Loan amount = $1600 / [(1 + 0.78177%)^360 - 1] * (1 + 0.78177%) ≈ $259,445.17

The Johnsons can afford a loan amount of approximately $259,445.17 if they choose the higher monthly payment of $1600.

Therefore, the price range of houses the Johnsons should consider is approximately $209,288.50 to $259,445.17.