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 $1100/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 $1400. If local mortgage rates are 9.5%/year compounded monthly for a conventional 30-yr mortgage, what is the price range of houses they should consider? (Round your answers to the nearest cent.)

Explanation / Answer

Answer:

We know that monthly payment can be made $1100

Number of months   = 30 Years *12 = 360

Interest rate = 9.5% Yearly = 9.5% /12 = 0.007917 monthly

Down payment = $15000

Hence we can calculate the Present value of the total payaments and that shall be value of the house they should consider

Present value formula =

PV = P*[{1- (1+r)^(-n)}/r]

Here

P = monthly payment = $1100

n = Number of months   = 30 Years *12 = 360

r= Interest rate = 9.5% Yearly = 9.5% /12 = 0.007917 monthly

Hence PV = 1100*[{1- (1+0.007917)^(-360)}/ 0.007917]

= 1100*[0.9415099/ 0.007917]

= 1100*118.9226

=$130814.86

Price range of the House they should consider = 130814.86 + 15000 = $145814.86

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