Question

Katherine and Ryan want to purchase a new house and feel that
they can afford a mortgage payment of $1000 a month for 25 years.
They are able to obtain a 6% mortgage (compounded monthly), but
must put down 10% of the mortgage value of the house now. Assuming
that they have enough savings for the down payment, how expensive
of a house can they afford?

They can afford a $ house.

Answer #1

pay 1000$ a month for 25 years and obtain a loan at 6% mortgage
therefore

90% can come from this monthly payment and 10% can come from the
down payment from their savings

Now evalualte present value of this 90%

P = EMI [ (1+r)^{n}-1 ] / r (1+r)^{n}

where P = Principal amount

r = monthly rate of interest= 0.06/12 = 0.005

n= number of months = 25*12 = 300

EMI = 1000

P = 1000 [ (1+0.005)^{300} -1 ] / [ 0.005 *
(1.005)^{300} ]

P = 155206.864

So 90% is 155206.864$

So 10% will be = 155206.864*10/90 = 17245.21

If 10% is 17245.21 then 100% will be = 172452.1

So the maximum price of the house that they can afford is =
172452.1 $

10% of this will come from down payment and

rest 90% of this will come from a monthly payment of 1000$ for 25
years

if
sally mander can afford 1100 monthly mortgage payment (30 years )
and she plans to put 20% down in the current mortgage rate is 7%
how expensive of a house is he planning to purchase
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