The Johnsons have accumulated a nest egg of 40000 that they

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 $2600/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 local mortgage rates are 3.5%/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? $

Solution

R = (P* i) / (1 - (1+i)^(-n))
... R = payment , P = loan principal, i = interest rate, n = number of periods

2600 = P (0.035/12) / (1 - (1 + 0.035/12)^(-30*12))
P = 578969.07

3200 = P (0.035/12) / (1 - (1 + 0.035/12)^(-30*12))
P = 712577.31

Least expensive $578969.07

Most expensive $712577.31