The Johnsons have accumulated a nest egg of 50000 that they

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 $2700/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 $3300. 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?

Solution

The formula that will be used in solving this problem is given below:

R = (amount of periodic payment)
P = (amount borrowed)
n = number of payments

i = the interest in decimal form.

Number of months in 30 years = 30 * 12 = 360 months

Interest rate = 5.5/(100*12) = 0.0045833 derrives form

Using the formula, PV = 2700* (1 - (1.000458333)^(-360))/0.000458333 = 895855.86$

House Amount = 895855.86 + 40000 = 935855.86$

In order to know the limit, you can put 3300$ in place of 2700 and add initial budget of 40000$