The Johnsons have accumulated a nest egg of $40,000 that they intend to use as a

Question

The Johnsons have accumulated a nest egg of $40,000 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 2.5%/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

Explanation / Answer

Least Expensive:
This is a typical present value problem where

FV = 0, Monthly Installment = 2300, no of installments = 30 * 12 = 360, interest rate = 2.5% per year

present value in an excel sheet can be calculated as follows

PV =PV(2.5%/12,30*12,-2300,0,0) = $582,100.32

Since they already have $40,000, minimum value of the house can be 582,100.32 + 40,000 = $622,100.32

Most Expensive:
This is a typical present value problem where

FV = 0, Monthly Installment = 2900, no of installments = 30 * 12 = 360, interest rate = 2.5% per year

present value in an excel sheet can be calculated as follows

PV =PV(2.5%/12,30*12,-2900,0,0) = $733,952.57

Since they already have $40,000, minimum value of the house can be 733,952.57 + 40,000 = $773,952.57

Note: In an excel sheet cash inflows and cash outflows have to be entered with opposite signs.

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