Question

The Johnsons have accumulated a nest egg of $29,000 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 $1000/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 $1300. 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? (Round your answers to the nearest cent.)

least expensive $

most expensive $

Answer 1

Minimum monthly mortgage = $1,000 per month

Maximum monthly mortgage = $1,300 per month

Monthly mortgage is calculated using the below formula:

Monthly mortgage = [P * (R/n) * (1+R/n)^nT] / {[(1+R/n)^nT] - 1}

where P = Loan amount or principal

R = mortgage rate

n = number of compoundings

T = number of years

Thus for monthly mortgage = $1,000:

1,000 = [P * (0.085/12) * (1 + 0.085/12)^(12*30)] / {[(1 + 0.085/12)^(12*30)] - 1}

1,000 = [P * (0.07083) * (1.07083)^360] / [(1.07083)^360 - 1]

1,000 = (P * 0.07083 * 12.6925) / (11.6925)

11,692.50 = P * 0.07083 * 12.6925

11,692.50 = P * 0.0899

P = 11,692.50 / 0.0899

= $130,054 (rounded off)

Thus for monthly mortgage = $1,300:

1,300 = [P * (0.085/12) * (1 + 0.085/12)^(12*30)] / {[(1 + 0.085/12)^(12*30)] - 1}

1,300 = [P * (0.07083) * (1.07083)^360] / [(1.07083)^360 - 1]

1,300 = (P * 0.07083 * 12.6925) / (11.6925)

15,200.25 = P * 0.07083 * 12.6925

15,200.25 = P * 0.0899

P = 15,200.25 / 0.0899

= $169,070 (rounded off)

Answer:

Least expensive house = $130,054

Most expensive house = $169,070