# math

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The Johnsons have accumulated a nest egg of \$19,000 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 8.5%/year compounded monthly for a conventional 30-yr mortgage, what is the price range of houses they should consider?

• math -

R = the periodic payment
P = the amount borrowed
n = the number of payments and i = the periodic interest in decimal form.

The monthly payment, R, required to retire the debt of \$P over a period of n = 30(12) = 360 months at the monthly interest rate of i = 8.5/(100(12)) = .0070833 derives from

R = Pi/[1-(1+i)^(-n)]

Solve for P.

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