The Johnsons have accumulated a nest egg of $50,000 that they intend to use as a

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 $2100/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 $2700. 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?

Explanation / Answer

The loan that they can get will be the PV of the monthly payments discounted at 5.5% (yearly) compounded monthly.

PV if payments are $2100 per month = 2100*pvifa(5.5/12,360) = 2100*176.1225 = $369,857.25

PV for 2700 = 2700*176.1225 = $475,530.75

Apart from the loan, they have $50000 with them.

Therefore, range of houses that they can consider

Least expensive = 369857.25 + 50000 = $419,857.25

Most expensive = 475,530.75 + 50000 = $525,530.75

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