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