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. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $2300/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 $2900. If local mortgage rates are 5.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider? (Round your answers to the nearest cent.)

Question

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. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $2300/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 $2900. If local mortgage rates are 5.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider? (Round your answers to the nearest cent.)

least expensive : $
most expensive : $

Answer 1

To find the price range of houses that the Johnsons should consider, we need to calculate the maximum and minimum mortgage amounts they can afford based on their monthly payments.

First, let's calculate the maximum monthly payment they can afford by considering their financial obligations. They can afford a maximum of $2900/month.

Next, let's calculate the minimum monthly payment they need to make to take advantage of the tax deduction. They plan to invest a minimum of $2300 per month.

To find the mortgage amount for these monthly payments, we can use the formula for the monthly payment on a conventional mortgage:

P = A / [ (1 - (1 + r)^(-n)) / r ]

where:
P is the monthly mortgage payment,
A is the mortgage amount,
r is the monthly interest rate (5.5% divided by 12),
and n is the total number of monthly payments (30 years multiplied by 12).

With this formula, we can calculate the mortgage amount corresponding to the minimum and maximum monthly payments.

Minimum Monthly Payment:
P = $2300
r = 5.5% / 12 = 0.00458 (monthly interest rate)
n = 30 years * 12 = 360 (total number of monthly payments)

Solving for A:

$2300 = A / [ (1 - (1 + 0.00458)^(-360)) / 0.00458 ]

A = $416,986.79 (rounded to the nearest cent)

Maximum Monthly Payment:
P = $2900

Solving for A:

$2900 = A / [ (1 - (1 + 0.00458)^(-360)) / 0.00458 ]

A = $528,040.08 (rounded to the nearest cent)

Therefore, the price range of houses that the Johnsons should consider is:
Least Expensive: $416,986.79 (rounded to the nearest cent)
Most Expensive: $528,040.08 (rounded to the nearest cent)