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 $2400/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 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	$

Answer 1

Value of housethey can afford		=	Downpayment+mortgage amount
Calculation of mortagage amount they can afford based on monthly payment
Mortgage amount		=	Present value of annuity of monthly payment
Present Value of annuity			=	P*PVAF(rate,time)
		where P	=	monthly payment
		t	=	time in months=30*12=360 months
		r	=	mortgage interestrate = r= 0.055/12=0.004583
	calculation of PVAF(4583%,360)
	PVAF(rate,time)		=	[1-(1+r)^-n]/r
	PVAF(0.4583%%,360)		=	[1-(1+0.004583)^-360]/0.004583
			=	[1-(1.004583)^-360]/0.004583
			=	[1-0.192798]/0.004583
			=	0.807202/0.004583
			=	176.13
Mortgage amount(monthly payment is $2400)				=	176.13*$2400
				=	$ 422,712.00
Value of house they could afford				=	$422,712+$50,000
				=	$ 472,712.00
Mortgage amount(monthly payment is $3000)				=	176.13*$3000
				=	$ 528,390.00
Value of house they could afford				=	$528,390+$50,000
				=	$ 578,390.00
	Lease expensive	=	$472,712
	Most expensive	=	$578,390
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