Question

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 $2900/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 $3500. If local mortgage rates are 2.5%/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 $

Answer 1

Present Value of an annuity is given by:

PV = A/i * [1 – (1+i)^-n]

Where,

PV is the present value

A is the amount of annuity

i is the current interest rate

n is the number of periods

In the given problem,

Interest Rate i = 0.025/12 = 0.002083

Scenario I: $2900/month

PV = 2900/0.002083 * [1 – (1.002083)^-360] = $733991.2

Minimum price of the house = 733991.2 + 50000 = $783991.2

Scenario II: $3500/month

PV = 3500/0.002083 * [1- (1.002083)^-360] = $ 885851.45

Maximum Price of the house = 885851.45 + 50000 = $935851.45