math
posted by amy on .
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 30yr mortgage, what is the price range of houses they should consider?

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.