The Johnsons have accumulated a nest egg of $40,000 that they intend to use as a
ID: 3402254 • Letter: T
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 $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? $
Explanation / Answer
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
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