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 $2500/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 $3100. 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

given The Johnsons have accumulated a nest egg of $50,000

they have decided to invest a minimum of $2500/month in monthly --- least

heir monthly payments should not exceed $3100. ---- most

intrest rate 5.5% year

30 years mortage

by this we know the formulea as

PV = PMT(1-(1+r)^-n)/r

For least expensive, house,
PMT = 2500, r = 0.055/12 = .00458, n = 12*30 = 360

keeping these values in above equations we have

2500(1-1.00458^-360)/.00458 = $440,499.09

For most expensive house,
3100(1-1.00448^-360)/.00478 = $518,797.34

We need to add the $50,000 down payment to these
least expensive: $490,499.09
most expensive: $568797.34

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