SOLUTION: 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

Question 1113578: 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 $2900/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 $3200. If the Johnsons decide to secure a 15-year mortgage, what is the price range of houses that they should consider when the local mortgage rate for this type of loan is 4%/year compounded monthly? (Round your answers to the nearest cent.)

Most expensive $
Least expensive $
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
their monthly mortage will be between 2900 per month and 3200 per month.
the present value of end of the month payments of 2900 at 4% compounded monthly for 15 years is equal to $392,057.23.

the present value of end of the month payments of 3200 at 4% compounded monthly for 15 years is equal to $432,614.88.

add the $50,000 down payment to that and you get:

at 2900 a month mortgage payments, they can afford a house that costs $442,057.23.

at 3200 a month mortgage payments, they can afford a house that costs $482,614.88.

to determine the present value of the mortgage, you can use the following financial value calculator.

https://arachnoid.com/finance/

my inputs and outputs for 2900 a month are shown below:

$$$

my inputs and outputs for 3200 a month are shown below:

$$$

the number of time periods was 15 * 12 = 180.

the interest rate percent per time period was 4/12 = .33333333.

monthly payments were entered as negative which made the present value come out as positive.

these are cash flow concepts.

money going out from you is negative.
money coming back to you is positive.

you get the money up front (present value is positive).
you make the monthly payments (monthly payments are negative).

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