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 $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 $3000. If the Johnsons decide to secure a 15-year mortgage, what is the price range of houses that they should consider when the local mortgage rate for this type of loan is 3%/year compounded monthly? (Round your answers to the nearest cent.)

least expensive	$
most expensive	$

Answer 1

Answer;

Minimum Monthly payment = $2700

No of Year = 15 Years

No of period = 15 X 12 = 180 monthly payments

Rate = 3% per annum = 3/12 = .25% per month

Minimum Loan Amount = Principle 1

Formula ; Monthly Installment =  = P × r × (1 + r)n/((1 + r)n - 1)

2700  = P1 x .25% [ (1.0025)^180/ (1.0025)^180 -1]

2700 = .0025P1 x[1.567431725/(1.567431725-1)]

2700 = .0025P1 x 2.76232656

.0025P1 = 2700/2.76232656

P1 = 2700/(2.76232656 x .0025)

P1 =$390974.77

Minimum Loan amount = $390974.77

Minimum House Price = Minimum Loan Amount + Down Payment

= $390974,77 + $ 50000(savings)

= $440974.77

Maximum Monthly payment = $3000

No of Year = 15 Years

No of period = 15 X 12 = 180 monthly payments

Rate = 3% per annum = 3/12 = .25% per month

Maximum Loan Amount = Principle 2

Formula ; Monthly Installment =  = P × r × (1 + r)n/((1 + r)n - 1)

3000  = P2 x .25% [ (1.0025)^180/ (1.0025)^180 -1]

3000 = .0025P2 x[1.567431725/(1.567431725-1)]

3000 = .0025P2 x 2.76232656

.0025P2 = 3000/2.76232656

P2 = 3000/(2.76232656 x .0025)

P2 =$434416.42

Maximum Loan amount = $434416.42

Maximum House Price = Maximum Loan Amount + Down Payment

= $434416.42 + $ 50000(savings)

= $484416.42

So, Price Range of house $440974.77-  $484416.42

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