The Johnsons have accumulated a nest egg of $15,000 that they intend to use as a

Question

The Johnsons have accumulated a nest egg of $15,000 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 7.5%/year compounded monthly for a conventional 30-yr mortgage, what is the price range of houses they should consider?

Explanation / Answer

Let the price of house be P. Then, P = PV of down and future payments for 30 years. => = a*r(1-r^n)/(1-r).............(1) where, a = monthly payments = $1200 to $1500. r = DF = 1/(1+k) = 1/(1+0.085/12)= 1/1.0071, (since monthly rate, k=8.5/12% = 0.0071) n = 30*12 = 360 months. For a=1200 ($), cost of house, P1 P1 = 1200*(1/1.0071)*(1 - (1/1.0071)^360)/(1-(1/1.0071)) = 155777 For a= 1500, cost of house = P2 P2 = 1500*(1/1.0071)*(1 - (1/1.0071)^360)/(1-(1/1.0071)) = 194721 Hence, range of house price to be considered is $ 155,777 to 194,721 (ANSWER)

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